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A compliant connector concept for the mobile offshore base
Marine Structures 13 (2000) 399}419
A compliant connector concept for the mobile o!shore base Mark S. Derstine*, Richard T. Brown Atlantic Research Corporation, 5945 Wellington Road, Gainesville, VA 20155-1699, USA
Abstract In order to reduce the large loads that are developed in connecting semi-submersible platforms on a 5000 ft long mobile o!shore base (MOB), a compliant connector concept was developed. This concept employs the cable compliant technology developed by NASA-Goddard and is based upon the use of 3-D Through-the-Thickness威 braid reinforced elastomeric tubes as the compliant element in the connector. By selectively placing and orienting the composite tubes, the connector can be designed to provide sti!ness in degrees of freedom critical to maintaining runway smoothness (such as relative heave or roll) while permitting larger displacements in other degrees of freedom (such as relative pitch or surge). Two di!erent connectors were designed: a four-degree-of-freedom (4 DOF) connector for the deck attachment and a 6 DOF connector for connecting at the pontoon level. The work presented includes material characterization testing, including some fatigue studies, and constitutive model development to fully understand the material behavior. The constitutive model for the material included both the material nonlinearity of the urethane elastomer matrix and geometric nonlinearities to include the "ber reorientation during loading. Tests were performed on a subscale connector design validate the analytical technique used to predict the connector performance. Six di!erent tests con"gurations were performed with di!erent loading conditions and connector con"gurations, and good correlation was found between the experimental and analytical results. The performance of full-scale connectors were determined through analysis and incorporated into a "nite element model of a scaled MOB design. The connector loads of the compliant connector are compared with the rigid or hinge-type connector for two di!erent hull con"gurations and various sea conditions and headings and is shown to reduce the loads over the conventional design. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Mobile o!shore base; Constitutive modeling; Composites; Compliant connector; Material characterization; 3D Braid
* Corresponding author. Tel.: #1-703-754-5795; fax: #1-703-754-5638. E-mail address: [email protected] (M.S. Derstine). 0951-8339/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 1 - 8 3 3 9 ( 0 0 ) 0 0 0 1 7 - 4
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1. Introduction A mobile o!shore base (MOB) is a multi-purpose, #oating logistics facility that can be used for conducting #ight, maintenance, supply and other military support operations [1,2]. The MOB is an assembly of semi-submersible modules with a total length of about 5000 ft to permit landing of aircraft in various sizes up to the C-17 Globemaster cargo aircraft. The design of the devices for connecting the adjacent modules is critical to the operation of the MOB. It has been shown that for a rigid connection between the semi-submersible units, the axial tensile loads generated in the connector are approximately 280 million pounds for Sea State 8 storms [3]. In order to reduce the magnitude of the connection loads, a #exible connector can be used to permit some relative motion between adjacent modules while maintaining the required continuity of the MOB deck. The basic objective of this work was to develop a concept for a #exible connector system for the MOB that uses an elastomeric, braided composite as the basis for the #exible design. This concept was then to be evaluated analytically to determine its feasibility. The connector concept is not speci"c to a particular MOB con"guration but was developed as a generic design that can be easily tailored to be incorporated into any given MOB design. Using cable compliant connector technology developed by NASA-Goddard [4], a concept using elastomeric composite tubes was developed that can be tailored to the MOB connection loads. Analysis techniques were developed for determining the nonlinear `spring constantsa for these compliant connectors. A large-scale test article was fabricated and tested to verify the analysis methodology. Finally, a full-scale concept for the connector system was designed and analyzed to determine the MOB response to sea conditions.
2. Material characterization Test specimens were fabricated in tubular form since the connector system will employ elastomeric tubes. The materials selected for the material characterization are carbon "ber for the reinforcement and urethane for the matrix. AS4-12K威 carbon "ber was selected for its sti!ness and strength, and Adiprene L-100威 urethane was selected as the matrix for its molding characteristics and for its durability in the marine environment. The carbon "bers are braided using Atlantic Research Corporation's (ARC) 3-D Through-the-Thickness威 braiding process. With this process, the "bers are continuously intertwined to form a fully integrated preform through the entire thickness of the material. This "ber construction eliminates delamination as a failure mode. This is important because the elastomeric composite is expected to undergo large deformations in bending that could create high `interlaminara shear strains. Since the reinforcement is continuous through the thickness, these strains are reacted by the reinforcement rather than by the matrix alone. The test plan includes testing of individual composite tubes of two di!erent braided architectures to quantify these highly nonlinear responses in support of the design
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Table 1 Material de"nition Property
Triaxial
Biaxial
Fiber type Matrix type Inside diameter Thickness Braid angle Fiber volume Axial content
AS4 12 K Adiprene威 L-100 2.50 in 0.252 in $403 40% 37%
AS4 12 K Adiprene威 L-100 2.50 in 0.160 in $403 40% 0%
process. The two architectures were chosen to represent both a soft material response and a sti! response. A description of the two di!erent architectures is given in Table 1. The tension and compression specimens were 12 in long, and the bending specimens were 24 in long. The "xtures used for gripping the specimens were 3 in long, leaving a 6 in gage length for tension and compression and 18 in long for bending. The tests performed on the material included tension, compression, bending and torsion. Combined tension-bending and compression-bending tests were done to investigate the interaction. Tension and compression tests were also performed on specimens with the inside "lled with a urethane rubber `pluga. This was used to investigate the e!ect of internal constraint on the tensile and compressive response.
3. Constitutive model The development of an analytical model for determining the mechanical properties of the proposed material system for the MOB compliant connectors presented many challenges in accurately representing the material response. These include a nonlinear, nearly compressive urethane matrix, inhomogeneity of high-sti!ness (assumed linear elastic) "ber and low-sti!ness matrix, and high-failure strains that allow signi"cant reorientation of braided "bers. The analysis method selected for this program is based on the fabric geometry model (FGM) developed by Pastore [5]. With FGM, an idealized unit cell of the 3-D braid is de"ned to describe the in-plane and out of plane "ber angles as well as the relative volume of each orientation within the unit cell. The nonlinear, orthotropic material properties of the unit cell can then be determined. The basic assumption for describing the elastomeric composite material with the FGM is that the material could be treated as a homogeneous, nonlinear material. A volume averaging technique is used to determine the equivalent composite properties from the constituent properties, "ber orientations and relative volume fractions of the constituents. An idealized unit cell for the material is derived from geometric quantities based on the braid processing parameters, such as yarn size, number of yarns and braid angle.
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Each orientation is assigned a relative volume based on the length of the yarn in that direction relative to the total length of yarn in the unit cell. The transversely isotropic sti!ness tensor of an impregnated yarn is calculated from a micromechanics model using the global "ber volume fraction of the composite. For this model, the micromechanics model of Vanyin [6,7] was selected. The properties of the yarn are then transformed to each orientation in the unit cell. These individual sti!ness tensors are multiplied by the corresponding relative volume fractions then summed to form the sti!ness average of the homogenized global composite response. To account for the material nonlinearity of the urethane matrix and the geometric nonlinearity of the composite, the sti!ness of the unit cell was determined for each increment of strain. For a given value of strain in either uniaxial or plane strain tension or compression, the orientations of the "bers as well as percentage of axial "bers, were recalculated and the sti!ness of the matrix was determined from an experimentally derived stress}strain curve. The sti!ness tensor for the unit cell was then determined for the new geometry and matrix material properties. The nonlinear material properties of the two material architectures were used as a basis for a "nite element structural analysis of the test specimen con"gurations. This analysis provided a more detailed representation of the response of the tubes that accounted for the structural deformations that occurred and their e!ect on the perceived material response. The tension, compression and bending tests were analyzed. The torsion and "lled tests were not considered. The analysis was carried out using ABAQUS 5.6. Comparisons between the experimental results and the FE/FGM predictions were made to assess the accuracy of the analytical methodology. The model seems to predict low strain response in both tension and compression well. The model predicts
Fig. 1. Comparison of experimental and FE/FGM results * triaxial.
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Fig. 2. Comparison of experimental and FE/FGM results * biaxial.
reasonable stresses at higher tensile strains, but signi"cantly overpredicts stress at high compressive strains. The comparative results for the triaxial architecture in both tension and compression is shown in Fig. 1. The correlation in tension is quite good. However, in compression, the experiment exhibits local surface buckling at relatively low strains. The model formulation permits buckling, but the model appears too sti! to predict signi"cant buckling. The results for the biaxial tube are shown in Fig. 2. In both tension and compression, the model overpredicts the sti!ness. Fig. 3 shows a comparison between experimental and FE/FGM predicted bending response for a biaxial tube. The applied load and displacement are shown on the "gure. Although the response is rather linear, it should be noted that the FE/FGM predictions of the axial stress in the tube during this deformation process are markedly nonlinear as would be expected for the biaxial material.
4. Connector design In previous analytical and experimental studies performed on the Brown & Root MOB [3,8], it was assumed that the connectors were not compliant but perfectly rigid in all conditions. This assumption resulted in very high connector loads in severe sea conditions. Flexible connections can reduce the connector loads by allowing displacements to occur. Because the deck of the MOB is used as a runway, the relative
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Fig. 3. Comparison of experimental and FE/FGM bending results * biaxial.
Fig. 4. MOB joint degrees of freedom.
displacements of the decks of the adjacent modules must be closely controlled during runway operations in order to prevent damage to aircraft and possible injury or loss of life. Subscale tests were performed on a 1/60th scale model of the Brown & Root MOB to determine the rigid connector loads under Sea States 4, 5, 7, and 8 [3]. The nomenclature for the six joint degrees of freedom is de"ned in Fig. 4. Because no speci"c performance requirements pertaining to a compliant connector existed at the time the connector concept was in work, a qualitative set of requirements was outlined for the compliant connector and some design targets were de"ned.
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Table 2 MOB joint requirements MOB Joint DOF
Requirement
Relative Relative Relative Relative Relative Relative
Soft Sti! Sti! Soft Sti! Sti!
surge heave sway pitch yaw roll
The qualitative requirements are represented by de"nitions of relative sti!nesses of the six degrees of freedom (DOF) at each intermodule connection (not for the individual connectors). These are given in Table 2. The requirements shown as `Softa refer to those DOF that can be allowed to have some #exibility; the DOF shown as `Sti!a are required to minimize de#ections to maintain operational capability of the MOB. Other requirements and assumptions for the connectors are: E Assume that there will be a bridge across the module joint to allow the adjacent modules to be separated by some distance to allow relative motion between the modules without contact. E The joint must keep the MOB from bowing (relative yaw) to maintain a straight runway and to keep the vessel straight for maneuvering. Prior to the conceptual design of the MOB connector, it was decided to employ the cable compliant mechanism technology to the design of the connector. With this technology, the tailoring of the relative sti!ness of each degree of freedom was possible as well as a means for providing active control of the connector sti!ness. Steel cables, or wire ropes, are traditionally used as tensile members. They were "rst used in a curved con"guration in bending in 1957 for shock, vibration and noise isolation for electronics in launch vehicles [4]. These isolation devices are widely used today for many applications. Work on using straight cables rather than curved as a means of providing control of motion began in the early 1970 s. Through this work, the technology was developed and matured, and a six DOF system was patented. A typical six DOF system is shown in Fig. 5. The six DOF system permits motion in all six DOF. The mechanical response of a compliant device is nonlinear in that it gets sti!er as the de#ection increases; the sti!ness increases as the loading in the cable transitions from a bending-dominated state to a tension-dominated state. 4.1. Deck connector design Using the requirements stated above, several concepts for the connectors were conceived and evaluated. No restriction was placed on making the upper and lower connectors identical. In fact, it was felt that it would be advantageous to use di!erent
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Fig. 5. Six-degree-of-freedom coupling.
Fig. 6. Schematic representation of deck connector.
design concepts for the two connectors. At the time, it was felt that both upper (deck) and lower (keel) connectors would be required to meet the loading requirements. It will be shown later that the impact on the keel connector was negligible and could be eliminated from the design. The basic concept for the deck connector was a row (or rows) of #exible members across the width of the MOB along the deck. By using many small (relative to MOB dimensions) tubes distributed across the width, the large loads anticipated could be more evenly spread over the structure rather than concentrating large loads over a small area of the hull. Five concepts were evaluated relating to the requirements of Table 2. The concept selected is shown schematically in Fig. 6. This "gure is a side view of two adjacent MOB modules with a row of vertical tubes joining the two. 4.2. Keel connector design Because of the general arrangement of the MOB modules with two separate pontoons, `pointa connectors were selected for the con"guration of the lower connectors. NASA's six-degree-of freedom joint seemed to provide the desired compliant
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properties for these connectors. With compliance in all six degrees of freedom, it will allow the global behavior of the joint to be governed by the characteristics of the upper connection. By including the capability for varying the compliance in the lower connection, it will act to further restrict the motions of the upper connections while allowing greater compliance during engagement and sea states greater than 6. The possibility of using only the deck connection and eliminating the pontoon connectors will also be investigated.
5. Connector analysis The connector concepts developed as part of this project are complex in both the geometry and in the materials used. Predicting the behavior of these connectors under multi-axial loading requires an analytical technique with su$cient detail to capture the individual tubes in the connector while being simple enough to include in a MOB hydrodynamic analysis. Therefore, the objective of this task was to develop an analytical scheme for predicting the connector behavior using nonlinear "nite element analysis (FEA). In order to validate this analytical approach, some comparison with experimental results is required. Therefore, test "xture was designed, built and tested to obtain these results. 5.1. Verixcation testing The objective of the tests were to generate load/de#ection responses for a subscale MOB connector system using both keel and deck connectors in the con"guration developed described previously. Since this testing was to occur in parallel with the material development and characterization, steel cables were used as the #exible elements. The "xture was designed to represent the ends of two MOB modules with the compliant connectors between them. The two sections representing the MOB modules were mounted on the #oor as if long axis of the MOB were set on end. The "xture is shown in Fig. 7. The width across the deck was 10 ft with 76 in long `legsa. The four DOF deck connector was a single row of 1 in diameter steel cables distributed across the full-width of the "xture; a total of 55 cables were used for the deck connector. The 55 cables were broken up into "ve separate `modulesa for ease of assembly and installation. Each one of the modules was attached to the lower part of the "xture with four load cells. The load cells allowed the load distributions between the modules in the deck connection to be determined. To allow for variation of the sti!ness of the deck connector, it was designed to permit using two di!erent lengths of cable, 1 and 3 in. The six DOF keel connector was designed with a double row of three cables on each of the four sides. Each cable was in diameter with a length to diameter ratio, l/d, of 6. Like the deck connector modules, each keel connector was mounted on four load cells.
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Fig. 7. Veri"cation test "xture.
Table 3 Veri"cation test matrix Deck cable length (in)
Active actuator
3 3 3 1 1 1
Deck Keel Deck & Keel Deck Keel Deck & Keel
Two hydraulic actuators were mounted on the "xture to provide loads in two di!erent degrees-of-freedom: surge and relative pitch (vertical bending). In addition, two di!erent bending moments were possible with the two actuators. Each actuator was equipped with a displacement transducer, and rotation transducers were mounted to each side of the "xture. The test matrix for the veri"cation tests is given in Table 3. The two actuators were located at the midpoint between the two legs of the "xture with one actuator nearer to the deck and one closer to the keel. Hence, one actuator was referred to as the `decka actuator and one as the `keela actuator. The test plan was repeated for each of the two keel connector con"gurations. 5.2. Verixcation analysis Analysis of the veri"cation test con"guration was performed using two di!erent "nite element models. The "rst model fully represented the geometry of the "xture and connector components except that, because the "xture and applied loads were
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Fig. 8. Full model.
symmetric, only half of the "xture was modeled. This model is referred to as the `fulla model. The second model was simpli"ed in that the structure of the "xture was represented by beam elements and the connectors were represented by spring elements. This model is referred to as the `beama model. The connectors were analyzed separately to determine the spring constants for use in the beam model. The purpose for using the beam model was to simulate the type of model used in the global MOB analysis. The mesh for the full model is shown in Fig. 8. The "xture and connector structure was modeled using shell elements. The steel cables were modeled using beam elements. The load cells were included in the analysis; they are represented by beam elements. Only the top half of the "xture is included in the model since the lower half was only used as an attachment platform. In order to represent the initial conditions of the model when using gravity more accurately (to account for the weight of the "xture), node-to-ground gap elements were used to represent the blocks placed under the "xture at the start of the test to prevent the weight of the structure from resting on the connectors. The e!ective modulus and diameter for the beam elements representing the steel cables was calculated based on experimental bending and extensional sti!nesses of in diameter cables and scaled to and 1 in diameters. 5.3. Beam model The mesh for the beam model is shown in Fig. 9. At each keel connector and at each of the "ve deck connector module, node-to-ground spring elements were used to represent the connectors. At each connector position, two spring elements were used: one spring element for the three rotational sti!nesses and one for the three translational sti!nesses. The sti!nesses for the spring elements were determined using individual models of the keel connector and the deck connector module. The keel connector model is
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Fig. 9. Beam model.
Fig. 10. Keel connector subelement model.
shown in Fig. 10 and the deck connector module is shown Fig. 11. These two models were analyzed in each of the six-degrees-of-freedom to determine the respective spring constants. Since nonlinear spring elements were not available in the FEA codes used, the analysis on the beam model was performed using linear analysis. Since the overall displacements in the "xture in the tests were relatively small compared to the overall
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Fig. 11. Deck connector subelement model.
Fig. 12. Analysis comparison, surge loading * 3 in deck cable length.
dimensions (about 1 in over 80 in), it was felt that for the purposes of comparison, the linear analysis would su$ce. 5.4. Analysis results Comparisons between the results of the two "nite element models and the test results for the 3 in deck cable con"guration with both deck and keel actuators active (surge condition) is shown in Fig. 12. The correlation between the test and analysis is
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quite good. The full model generally predicts a softer response that was seen in the test, and the beam analysis, which is a linear analysis, was very close to the test results.
6. MOB global analysis The "nal step in determining the response of the compliant connector is to analyze the connectors on a MOB subjected to wave loading. The University of Maine performed this analysis using their "nite element models of the Brown & Root MOB wave tank test article [3]. Hydrodynamic tests were performed on scale models of both the Brown & Root MOB concept. Both models were th scale and were designed for hydrodynamic testing only; no e!ort was made to scale the structural response of a full-scale MOB design. In the model, four `rigida connectors connected the six individual modules. The connectors were actually load cells for measuring the induced loads at each of the "ve joints. Under separate Navy funding, the University of Maine analyzed the MOB con"guration using the "nite element analysis package, ABAQUS2+. The results of the analysis were then compared with the experimental results. The approach used for this connector design was to determine the `spring constantsa for the individual connectors and use these spring constants in the MOB "nite element analysis to determine their behavior under wave loading. The goal, of course, was to reduce the connector loads from the baseline con"gurations. Since the FE model of the MOB is th scale, the sti!nesses of the connectors also have to be scaled down. The results are then scaled back up to full-scale. A #owchart of the analysis process is shown in Fig. 13. 6.1. Full-scale connector point design Until this point the in connector development, the connector existed only as a concept and had not been speci"cally sized to meet the anticipated MOB loading. In
Fig. 13. Global analysis overview.
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Table 4 Load and de#ection requirements * Brown & Root MOB
Vertical bending Vertical shear Transverse bending Transverse shear
Joint load * SS 7
Maximum de#ection
6,138,643 ft lton 14,164 lton 14,250,215 ft lton 32,786 lton
23 13
order to move ahead in the analysis, an approach for determining a connector con"guration for both the deck and keel connectors that have speci"c de"nition of the tube size(s) and tube arrangement was required. To this end, a simple mechanics of material approach was used where the maximum allowable de#ections in each direction were de"ned and the reacted loads from each tube were summed. The tube length and cross section and the tube spacing and number was varied until the maximum loads generated for the Brown & Root MOB tests for Sea State 7 were generated and the individual tube stresses were below the material strength. For the tubes, material properties for the biaxial tubes generated in the characterization testing were used. Since the properties are generally nonlinear, the secant moduli at the maximum stress were used. The maximum loads for a module-to-module joint under Sea State 7 conditions for the Brown & Root MOB are shown in Table 4 with the maximum allowable de#ections. Sea State 7 was selected as a basis since, at the time the work was done, the prevailing opinion in the MOB community was that the modules would be disconnected in sea states greater than Sea State 7. Since the loads were expected to come down from what was seen in the rigid connector design, this was used as a starting point of de"ning the design. It was assumed that the deck connector would act as a hinge such that the center of rotation for the relative pitch (vertical bending) would be the midspan of the deck connector tubes, and the center of rotation for the relative yaw (transverse bending) was the MOB centerline. 6.1.1. Deck connector The general con"guration for the deck connector is shown in Fig. 14. The "gure indicates the parameters that were adjusted to achieve the loads required. For simplicity, the deck connector was broken up into three separate regions. Each region can have a separate de"nition for the number of rows and columns (row and col ), G G tube diameter, length and thickness (dia , ¸ , and t ), and tube spacing in the fore-aft ' ' G direction (d ). The inboard/outboard spacing of the tubes is the same in all regions (s). G In theory, it is possible that there are more than three separate regions, but for the purposes of this exercise, three was su$cient. For the requirements listed in Table 4, the deck connector con"guration parameters are as given in Table 5. For this design, there are a total of 7949 tubes. Also, in the center region, there is only a single row of 29 tubes. Since it is a very small
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Fig. 14. Full-scale design parameters * deck connector.
Table 5 Design parameters * baseline Parameter
Center (i"1)
Mid (i"2)
Outbd (i"3)
col G row G dia G t G ¸ G d G s
29 1 7.5 in 0.75 in 24 in N/A 8 in
80 12 7.5 in 1.75 in 30 in 8 in 8 in
125 24 7.5 in 2.25 in 48 in 8 in 8 in
percentage of the total number of tubes, these tubes could probably be neglected. They were left in for the initial analysis performed. 6.1.2. Keel connector The general arrangement for the six DOF keel connector is shown in Fig. 15. The parameters that can be varied are indicated in the "gure. The connector consists of an array of tubes on each of its four sides. The tube spacing between both rows and columns is constant throughout the connector (d). The number of rows and columns (row, column) is also held constant on each side as are the tube diameter, thickness and length (dia, t, ¸). The values for the keel connector parameters that were determined for the baseline analysis are given in Table 6. With this design, there are a total of 80 tubes in each keel connector. 6.2. Connector xnite element analysis The individual connectors were modeled in ABAQUS according to the point design concept described above. Each connector was modeled using the full 3-D geometry (i.e. no symmetry assumptions) using shell elements for the connector structure and beam elements for the urethane composite tubes similar to the veri"cation test models.
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Fig. 15. Keel connector.
Table 6 Baseline keel connector design parameters Parameter
Value
row col d dia t ¸
5 4 18 in 8 in 1.25 in 42 in
The analysis approach used to determine the spring constants was to apply a force(s) in a single-degree-of-freedom with constraints/restraints applied to prevent motion in all other degrees-of-freedom. The reaction loads at the constraints/restraints were then used to determine the coupling between the degrees-of-freedom. In ABAQUS, the coupling terms in the spring elements are limited to coupling rotational forces with only rotational displacement and translational forces with only translational displacements. This loss in coupling terms will tend to decrease the overall sti!ness of a coupling. In addition, the remaining coupling terms were all found to be relatively small compared to the diagonal terms. Therefore, these o!diagonal terms were also neglected leaving only a diagonal matrix. The intent for this analysis was to use the same material model that was developed using the constitutive model. However, since this material model was not available for the element type that was to be used in the connector models, the material model had to be reformulated. To accomplish this stress}strain data for the biaxial tubes were
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Fig. 16. Full-scale keel connector FE mesh.
taken from the characterization tests and used input for the hypoelastic material model. 6.2.1. Full-scale keel connector analysis The mesh for the full-scale keel connector is shown in Fig. 16. The mesh consists of beam elements representing the composite tubes, shell elements for the connector structure, and rigid elements were used at the ends of each tube to account for the material thickness of the metal connector structure. There were a total of 1230 elements in the model. 6.2.2. Full-scale deck connector analysis A portion of the deck connector mesh is shown in Fig. 17. Like the keel connector mesh, the deck connector is represented by beam elements for the composite tubes and shell elements for the connector structure. There are a total of 45,791 elements in the mesh. 6.3. MOB analysis 6.3.1. Scaling The connector sti!nesses were determined using analysis of full-scale connectors. The MOB-FE models are of the th scale wave tank models. Therefore, the sti!nesses of the connectors must be scaled to be used in the MOB model. For structural dynamic scaling consistent with Froude scaling, the forces are scaled according to: S "S $ *
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Fig. 17. Deck connector mesh.
Fig. 18. MOB analysis results.
and the moments are scaled according to: S "S , + * where S is the length scale factor ( in this case). * 6.3.2. Results The Brown & Root MOB model was analyzed for two sea conditions: Sea State 5 at a 453 heading, and Sea State 7 at a 453 heading. Both con"gurations were analyzed
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M.S. Derstine, R.T. Brown / Marine Structures 13 (2000) 399}419 Table 7 Baseline natural periods B & R Baseline Mode C
Period (S)
Shape
1 2 3 4 5 6 7 8 9 10
2.63 0.75 0.56 0.52 0.47 0.46 0.45 0.43 0.40 0.39
Torsion Transverse Vertical N/A N/A N/A N/A N/A N/A N/A
Table 8 Compliant connector natural periods B & R w/ARC Connector Mode C
Period (S)
Shape
1 2 3 4 5 6 7 8 9 10
70.1 44.7 26.9 26.2 17.8 15.4 13.5 10.6 10.2 9.0
Vertical Transverse Vertical Torsion Transverse Vertical Torsion Vertical Transverse Torsion
at operational draft. The RMS vertical bending moments (relative pitch) reacted by the compliant connector system for the Sea State 5, 453 heading condition are shown in Fig. 18 and are compared with the loads in the model tests on the rigid connector concept. These results are scaled to full-scale values. By using the compliant connector, the vertical bending loads have been reduced by over an order of magnitude. The results for Sea State 7, 453 heading show a maximum vertical bending moment of 50,000 ft lton which is a 85% reduction from the Sea State 5 loads. The natural periods for the baseline Brown & Root MOB model and for the Brown & Root model with the compliant connectors are given in Tables 7 and 8, respectively. The natural periods are shown for the full-scale MOB. These tables show that the periods for the MOB con"guration with the compliant connectors have been signi"cantly increased, producing much lower natural frequencies. While some of the higher-order natural periods may coincide with those of the waves (approximately 9 s
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for Sea State 5), the RMS loads over the Sea State 5 frequency spectrum are have been reduced.
7. Conclusions A concept for a compliant connector for a mobile o!shore base (MOB) has been developed to permit reduction of the loads associated with joining semi-submersible units into a 5000 ft vessel. This concept is tailorable to meet the speci"c requirements of the MOB. A methodology for analytically determining the behavior of these compliant connectors from the material level through the structural level was demonstrated. This permits the design optimization of this connector concept to meet the needs of the mobile o!shore base.
Acknowledgements This work was funded by the Defense Advanced Research Projects Administration administered by the Mobile O!shore Base Project O$ce at the O$ce of Naval Research. The contract was managed by Dr. Jo Wen Lin, Code 5040, Naval Surface Weapons Center, Carderock Division.
References [1] Mills TRJ, Chen L. Mobile o!shore base * nonlinear compliant connectors. US}Japan Marine Facilities Panel 22nd Meeting, Arlington, VA, October 1998. [2] Remmers G, Zueck R, Paolo P, Taylor R. Mobile o!shore base. International O!shore and Polar Engineering Conference, International O!shore and Polar Engineering (ISOPE), Montreal, Canada, May 24}29, 1998. [3] Lewis RR. Measured and predicted structural responses and connector loads of a mobile o!shore base (MOB). CARDEROCKDIV-U-SSM-65-95/10, December 1994. [4] Kerley J, Eklund W, Burkhardt R, Rossoni P. Cable compliance. NASA Technical Paper 3216, June 1992. [5] Pastore CM. A processing science of three dimensional braiding. Ph.D. Thesis, Drexel University, Philadelphia, PA, March 1988. [6] Vanin GA. Micromechanics of composite materials. Kiev: Durya, 1985 (in Russian). [7] Van Fo Fy. Elastic constants and state of stress of glass-reinforced strip. Polym Mech 1966;2(4):593}602. [8] Mobile o!shore bases (MOBs). Vol. II. Technical and Operational Issues, Brown & Root Report No. HE94-002, November 1994.
A compliant connector concept for the mobile o!shore base Mark S. Derstine*, Richard T. Brown Atlantic Research Corporation, 5945 Wellington Road, Gainesville, VA 20155-1699, USA
Abstract In order to reduce the large loads that are developed in connecting semi-submersible platforms on a 5000 ft long mobile o!shore base (MOB), a compliant connector concept was developed. This concept employs the cable compliant technology developed by NASA-Goddard and is based upon the use of 3-D Through-the-Thickness威 braid reinforced elastomeric tubes as the compliant element in the connector. By selectively placing and orienting the composite tubes, the connector can be designed to provide sti!ness in degrees of freedom critical to maintaining runway smoothness (such as relative heave or roll) while permitting larger displacements in other degrees of freedom (such as relative pitch or surge). Two di!erent connectors were designed: a four-degree-of-freedom (4 DOF) connector for the deck attachment and a 6 DOF connector for connecting at the pontoon level. The work presented includes material characterization testing, including some fatigue studies, and constitutive model development to fully understand the material behavior. The constitutive model for the material included both the material nonlinearity of the urethane elastomer matrix and geometric nonlinearities to include the "ber reorientation during loading. Tests were performed on a subscale connector design validate the analytical technique used to predict the connector performance. Six di!erent tests con"gurations were performed with di!erent loading conditions and connector con"gurations, and good correlation was found between the experimental and analytical results. The performance of full-scale connectors were determined through analysis and incorporated into a "nite element model of a scaled MOB design. The connector loads of the compliant connector are compared with the rigid or hinge-type connector for two di!erent hull con"gurations and various sea conditions and headings and is shown to reduce the loads over the conventional design. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Mobile o!shore base; Constitutive modeling; Composites; Compliant connector; Material characterization; 3D Braid
* Corresponding author. Tel.: #1-703-754-5795; fax: #1-703-754-5638. E-mail address: [email protected] (M.S. Derstine). 0951-8339/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 1 - 8 3 3 9 ( 0 0 ) 0 0 0 1 7 - 4
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1. Introduction A mobile o!shore base (MOB) is a multi-purpose, #oating logistics facility that can be used for conducting #ight, maintenance, supply and other military support operations [1,2]. The MOB is an assembly of semi-submersible modules with a total length of about 5000 ft to permit landing of aircraft in various sizes up to the C-17 Globemaster cargo aircraft. The design of the devices for connecting the adjacent modules is critical to the operation of the MOB. It has been shown that for a rigid connection between the semi-submersible units, the axial tensile loads generated in the connector are approximately 280 million pounds for Sea State 8 storms [3]. In order to reduce the magnitude of the connection loads, a #exible connector can be used to permit some relative motion between adjacent modules while maintaining the required continuity of the MOB deck. The basic objective of this work was to develop a concept for a #exible connector system for the MOB that uses an elastomeric, braided composite as the basis for the #exible design. This concept was then to be evaluated analytically to determine its feasibility. The connector concept is not speci"c to a particular MOB con"guration but was developed as a generic design that can be easily tailored to be incorporated into any given MOB design. Using cable compliant connector technology developed by NASA-Goddard [4], a concept using elastomeric composite tubes was developed that can be tailored to the MOB connection loads. Analysis techniques were developed for determining the nonlinear `spring constantsa for these compliant connectors. A large-scale test article was fabricated and tested to verify the analysis methodology. Finally, a full-scale concept for the connector system was designed and analyzed to determine the MOB response to sea conditions.
2. Material characterization Test specimens were fabricated in tubular form since the connector system will employ elastomeric tubes. The materials selected for the material characterization are carbon "ber for the reinforcement and urethane for the matrix. AS4-12K威 carbon "ber was selected for its sti!ness and strength, and Adiprene L-100威 urethane was selected as the matrix for its molding characteristics and for its durability in the marine environment. The carbon "bers are braided using Atlantic Research Corporation's (ARC) 3-D Through-the-Thickness威 braiding process. With this process, the "bers are continuously intertwined to form a fully integrated preform through the entire thickness of the material. This "ber construction eliminates delamination as a failure mode. This is important because the elastomeric composite is expected to undergo large deformations in bending that could create high `interlaminara shear strains. Since the reinforcement is continuous through the thickness, these strains are reacted by the reinforcement rather than by the matrix alone. The test plan includes testing of individual composite tubes of two di!erent braided architectures to quantify these highly nonlinear responses in support of the design
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Table 1 Material de"nition Property
Triaxial
Biaxial
Fiber type Matrix type Inside diameter Thickness Braid angle Fiber volume Axial content
AS4 12 K Adiprene威 L-100 2.50 in 0.252 in $403 40% 37%
AS4 12 K Adiprene威 L-100 2.50 in 0.160 in $403 40% 0%
process. The two architectures were chosen to represent both a soft material response and a sti! response. A description of the two di!erent architectures is given in Table 1. The tension and compression specimens were 12 in long, and the bending specimens were 24 in long. The "xtures used for gripping the specimens were 3 in long, leaving a 6 in gage length for tension and compression and 18 in long for bending. The tests performed on the material included tension, compression, bending and torsion. Combined tension-bending and compression-bending tests were done to investigate the interaction. Tension and compression tests were also performed on specimens with the inside "lled with a urethane rubber `pluga. This was used to investigate the e!ect of internal constraint on the tensile and compressive response.
3. Constitutive model The development of an analytical model for determining the mechanical properties of the proposed material system for the MOB compliant connectors presented many challenges in accurately representing the material response. These include a nonlinear, nearly compressive urethane matrix, inhomogeneity of high-sti!ness (assumed linear elastic) "ber and low-sti!ness matrix, and high-failure strains that allow signi"cant reorientation of braided "bers. The analysis method selected for this program is based on the fabric geometry model (FGM) developed by Pastore [5]. With FGM, an idealized unit cell of the 3-D braid is de"ned to describe the in-plane and out of plane "ber angles as well as the relative volume of each orientation within the unit cell. The nonlinear, orthotropic material properties of the unit cell can then be determined. The basic assumption for describing the elastomeric composite material with the FGM is that the material could be treated as a homogeneous, nonlinear material. A volume averaging technique is used to determine the equivalent composite properties from the constituent properties, "ber orientations and relative volume fractions of the constituents. An idealized unit cell for the material is derived from geometric quantities based on the braid processing parameters, such as yarn size, number of yarns and braid angle.
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Each orientation is assigned a relative volume based on the length of the yarn in that direction relative to the total length of yarn in the unit cell. The transversely isotropic sti!ness tensor of an impregnated yarn is calculated from a micromechanics model using the global "ber volume fraction of the composite. For this model, the micromechanics model of Vanyin [6,7] was selected. The properties of the yarn are then transformed to each orientation in the unit cell. These individual sti!ness tensors are multiplied by the corresponding relative volume fractions then summed to form the sti!ness average of the homogenized global composite response. To account for the material nonlinearity of the urethane matrix and the geometric nonlinearity of the composite, the sti!ness of the unit cell was determined for each increment of strain. For a given value of strain in either uniaxial or plane strain tension or compression, the orientations of the "bers as well as percentage of axial "bers, were recalculated and the sti!ness of the matrix was determined from an experimentally derived stress}strain curve. The sti!ness tensor for the unit cell was then determined for the new geometry and matrix material properties. The nonlinear material properties of the two material architectures were used as a basis for a "nite element structural analysis of the test specimen con"gurations. This analysis provided a more detailed representation of the response of the tubes that accounted for the structural deformations that occurred and their e!ect on the perceived material response. The tension, compression and bending tests were analyzed. The torsion and "lled tests were not considered. The analysis was carried out using ABAQUS 5.6. Comparisons between the experimental results and the FE/FGM predictions were made to assess the accuracy of the analytical methodology. The model seems to predict low strain response in both tension and compression well. The model predicts
Fig. 1. Comparison of experimental and FE/FGM results * triaxial.
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Fig. 2. Comparison of experimental and FE/FGM results * biaxial.
reasonable stresses at higher tensile strains, but signi"cantly overpredicts stress at high compressive strains. The comparative results for the triaxial architecture in both tension and compression is shown in Fig. 1. The correlation in tension is quite good. However, in compression, the experiment exhibits local surface buckling at relatively low strains. The model formulation permits buckling, but the model appears too sti! to predict signi"cant buckling. The results for the biaxial tube are shown in Fig. 2. In both tension and compression, the model overpredicts the sti!ness. Fig. 3 shows a comparison between experimental and FE/FGM predicted bending response for a biaxial tube. The applied load and displacement are shown on the "gure. Although the response is rather linear, it should be noted that the FE/FGM predictions of the axial stress in the tube during this deformation process are markedly nonlinear as would be expected for the biaxial material.
4. Connector design In previous analytical and experimental studies performed on the Brown & Root MOB [3,8], it was assumed that the connectors were not compliant but perfectly rigid in all conditions. This assumption resulted in very high connector loads in severe sea conditions. Flexible connections can reduce the connector loads by allowing displacements to occur. Because the deck of the MOB is used as a runway, the relative
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Fig. 3. Comparison of experimental and FE/FGM bending results * biaxial.
Fig. 4. MOB joint degrees of freedom.
displacements of the decks of the adjacent modules must be closely controlled during runway operations in order to prevent damage to aircraft and possible injury or loss of life. Subscale tests were performed on a 1/60th scale model of the Brown & Root MOB to determine the rigid connector loads under Sea States 4, 5, 7, and 8 [3]. The nomenclature for the six joint degrees of freedom is de"ned in Fig. 4. Because no speci"c performance requirements pertaining to a compliant connector existed at the time the connector concept was in work, a qualitative set of requirements was outlined for the compliant connector and some design targets were de"ned.
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Table 2 MOB joint requirements MOB Joint DOF
Requirement
Relative Relative Relative Relative Relative Relative
Soft Sti! Sti! Soft Sti! Sti!
surge heave sway pitch yaw roll
The qualitative requirements are represented by de"nitions of relative sti!nesses of the six degrees of freedom (DOF) at each intermodule connection (not for the individual connectors). These are given in Table 2. The requirements shown as `Softa refer to those DOF that can be allowed to have some #exibility; the DOF shown as `Sti!a are required to minimize de#ections to maintain operational capability of the MOB. Other requirements and assumptions for the connectors are: E Assume that there will be a bridge across the module joint to allow the adjacent modules to be separated by some distance to allow relative motion between the modules without contact. E The joint must keep the MOB from bowing (relative yaw) to maintain a straight runway and to keep the vessel straight for maneuvering. Prior to the conceptual design of the MOB connector, it was decided to employ the cable compliant mechanism technology to the design of the connector. With this technology, the tailoring of the relative sti!ness of each degree of freedom was possible as well as a means for providing active control of the connector sti!ness. Steel cables, or wire ropes, are traditionally used as tensile members. They were "rst used in a curved con"guration in bending in 1957 for shock, vibration and noise isolation for electronics in launch vehicles [4]. These isolation devices are widely used today for many applications. Work on using straight cables rather than curved as a means of providing control of motion began in the early 1970 s. Through this work, the technology was developed and matured, and a six DOF system was patented. A typical six DOF system is shown in Fig. 5. The six DOF system permits motion in all six DOF. The mechanical response of a compliant device is nonlinear in that it gets sti!er as the de#ection increases; the sti!ness increases as the loading in the cable transitions from a bending-dominated state to a tension-dominated state. 4.1. Deck connector design Using the requirements stated above, several concepts for the connectors were conceived and evaluated. No restriction was placed on making the upper and lower connectors identical. In fact, it was felt that it would be advantageous to use di!erent
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Fig. 5. Six-degree-of-freedom coupling.
Fig. 6. Schematic representation of deck connector.
design concepts for the two connectors. At the time, it was felt that both upper (deck) and lower (keel) connectors would be required to meet the loading requirements. It will be shown later that the impact on the keel connector was negligible and could be eliminated from the design. The basic concept for the deck connector was a row (or rows) of #exible members across the width of the MOB along the deck. By using many small (relative to MOB dimensions) tubes distributed across the width, the large loads anticipated could be more evenly spread over the structure rather than concentrating large loads over a small area of the hull. Five concepts were evaluated relating to the requirements of Table 2. The concept selected is shown schematically in Fig. 6. This "gure is a side view of two adjacent MOB modules with a row of vertical tubes joining the two. 4.2. Keel connector design Because of the general arrangement of the MOB modules with two separate pontoons, `pointa connectors were selected for the con"guration of the lower connectors. NASA's six-degree-of freedom joint seemed to provide the desired compliant
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properties for these connectors. With compliance in all six degrees of freedom, it will allow the global behavior of the joint to be governed by the characteristics of the upper connection. By including the capability for varying the compliance in the lower connection, it will act to further restrict the motions of the upper connections while allowing greater compliance during engagement and sea states greater than 6. The possibility of using only the deck connection and eliminating the pontoon connectors will also be investigated.
5. Connector analysis The connector concepts developed as part of this project are complex in both the geometry and in the materials used. Predicting the behavior of these connectors under multi-axial loading requires an analytical technique with su$cient detail to capture the individual tubes in the connector while being simple enough to include in a MOB hydrodynamic analysis. Therefore, the objective of this task was to develop an analytical scheme for predicting the connector behavior using nonlinear "nite element analysis (FEA). In order to validate this analytical approach, some comparison with experimental results is required. Therefore, test "xture was designed, built and tested to obtain these results. 5.1. Verixcation testing The objective of the tests were to generate load/de#ection responses for a subscale MOB connector system using both keel and deck connectors in the con"guration developed described previously. Since this testing was to occur in parallel with the material development and characterization, steel cables were used as the #exible elements. The "xture was designed to represent the ends of two MOB modules with the compliant connectors between them. The two sections representing the MOB modules were mounted on the #oor as if long axis of the MOB were set on end. The "xture is shown in Fig. 7. The width across the deck was 10 ft with 76 in long `legsa. The four DOF deck connector was a single row of 1 in diameter steel cables distributed across the full-width of the "xture; a total of 55 cables were used for the deck connector. The 55 cables were broken up into "ve separate `modulesa for ease of assembly and installation. Each one of the modules was attached to the lower part of the "xture with four load cells. The load cells allowed the load distributions between the modules in the deck connection to be determined. To allow for variation of the sti!ness of the deck connector, it was designed to permit using two di!erent lengths of cable, 1 and 3 in. The six DOF keel connector was designed with a double row of three cables on each of the four sides. Each cable was in diameter with a length to diameter ratio, l/d, of 6. Like the deck connector modules, each keel connector was mounted on four load cells.
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Fig. 7. Veri"cation test "xture.
Table 3 Veri"cation test matrix Deck cable length (in)
Active actuator
3 3 3 1 1 1
Deck Keel Deck & Keel Deck Keel Deck & Keel
Two hydraulic actuators were mounted on the "xture to provide loads in two di!erent degrees-of-freedom: surge and relative pitch (vertical bending). In addition, two di!erent bending moments were possible with the two actuators. Each actuator was equipped with a displacement transducer, and rotation transducers were mounted to each side of the "xture. The test matrix for the veri"cation tests is given in Table 3. The two actuators were located at the midpoint between the two legs of the "xture with one actuator nearer to the deck and one closer to the keel. Hence, one actuator was referred to as the `decka actuator and one as the `keela actuator. The test plan was repeated for each of the two keel connector con"gurations. 5.2. Verixcation analysis Analysis of the veri"cation test con"guration was performed using two di!erent "nite element models. The "rst model fully represented the geometry of the "xture and connector components except that, because the "xture and applied loads were
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Fig. 8. Full model.
symmetric, only half of the "xture was modeled. This model is referred to as the `fulla model. The second model was simpli"ed in that the structure of the "xture was represented by beam elements and the connectors were represented by spring elements. This model is referred to as the `beama model. The connectors were analyzed separately to determine the spring constants for use in the beam model. The purpose for using the beam model was to simulate the type of model used in the global MOB analysis. The mesh for the full model is shown in Fig. 8. The "xture and connector structure was modeled using shell elements. The steel cables were modeled using beam elements. The load cells were included in the analysis; they are represented by beam elements. Only the top half of the "xture is included in the model since the lower half was only used as an attachment platform. In order to represent the initial conditions of the model when using gravity more accurately (to account for the weight of the "xture), node-to-ground gap elements were used to represent the blocks placed under the "xture at the start of the test to prevent the weight of the structure from resting on the connectors. The e!ective modulus and diameter for the beam elements representing the steel cables was calculated based on experimental bending and extensional sti!nesses of in diameter cables and scaled to and 1 in diameters. 5.3. Beam model The mesh for the beam model is shown in Fig. 9. At each keel connector and at each of the "ve deck connector module, node-to-ground spring elements were used to represent the connectors. At each connector position, two spring elements were used: one spring element for the three rotational sti!nesses and one for the three translational sti!nesses. The sti!nesses for the spring elements were determined using individual models of the keel connector and the deck connector module. The keel connector model is
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Fig. 9. Beam model.
Fig. 10. Keel connector subelement model.
shown in Fig. 10 and the deck connector module is shown Fig. 11. These two models were analyzed in each of the six-degrees-of-freedom to determine the respective spring constants. Since nonlinear spring elements were not available in the FEA codes used, the analysis on the beam model was performed using linear analysis. Since the overall displacements in the "xture in the tests were relatively small compared to the overall
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Fig. 11. Deck connector subelement model.
Fig. 12. Analysis comparison, surge loading * 3 in deck cable length.
dimensions (about 1 in over 80 in), it was felt that for the purposes of comparison, the linear analysis would su$ce. 5.4. Analysis results Comparisons between the results of the two "nite element models and the test results for the 3 in deck cable con"guration with both deck and keel actuators active (surge condition) is shown in Fig. 12. The correlation between the test and analysis is
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quite good. The full model generally predicts a softer response that was seen in the test, and the beam analysis, which is a linear analysis, was very close to the test results.
6. MOB global analysis The "nal step in determining the response of the compliant connector is to analyze the connectors on a MOB subjected to wave loading. The University of Maine performed this analysis using their "nite element models of the Brown & Root MOB wave tank test article [3]. Hydrodynamic tests were performed on scale models of both the Brown & Root MOB concept. Both models were th scale and were designed for hydrodynamic testing only; no e!ort was made to scale the structural response of a full-scale MOB design. In the model, four `rigida connectors connected the six individual modules. The connectors were actually load cells for measuring the induced loads at each of the "ve joints. Under separate Navy funding, the University of Maine analyzed the MOB con"guration using the "nite element analysis package, ABAQUS2+. The results of the analysis were then compared with the experimental results. The approach used for this connector design was to determine the `spring constantsa for the individual connectors and use these spring constants in the MOB "nite element analysis to determine their behavior under wave loading. The goal, of course, was to reduce the connector loads from the baseline con"gurations. Since the FE model of the MOB is th scale, the sti!nesses of the connectors also have to be scaled down. The results are then scaled back up to full-scale. A #owchart of the analysis process is shown in Fig. 13. 6.1. Full-scale connector point design Until this point the in connector development, the connector existed only as a concept and had not been speci"cally sized to meet the anticipated MOB loading. In
Fig. 13. Global analysis overview.
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Table 4 Load and de#ection requirements * Brown & Root MOB
Vertical bending Vertical shear Transverse bending Transverse shear
Joint load * SS 7
Maximum de#ection
6,138,643 ft lton 14,164 lton 14,250,215 ft lton 32,786 lton
23 13
order to move ahead in the analysis, an approach for determining a connector con"guration for both the deck and keel connectors that have speci"c de"nition of the tube size(s) and tube arrangement was required. To this end, a simple mechanics of material approach was used where the maximum allowable de#ections in each direction were de"ned and the reacted loads from each tube were summed. The tube length and cross section and the tube spacing and number was varied until the maximum loads generated for the Brown & Root MOB tests for Sea State 7 were generated and the individual tube stresses were below the material strength. For the tubes, material properties for the biaxial tubes generated in the characterization testing were used. Since the properties are generally nonlinear, the secant moduli at the maximum stress were used. The maximum loads for a module-to-module joint under Sea State 7 conditions for the Brown & Root MOB are shown in Table 4 with the maximum allowable de#ections. Sea State 7 was selected as a basis since, at the time the work was done, the prevailing opinion in the MOB community was that the modules would be disconnected in sea states greater than Sea State 7. Since the loads were expected to come down from what was seen in the rigid connector design, this was used as a starting point of de"ning the design. It was assumed that the deck connector would act as a hinge such that the center of rotation for the relative pitch (vertical bending) would be the midspan of the deck connector tubes, and the center of rotation for the relative yaw (transverse bending) was the MOB centerline. 6.1.1. Deck connector The general con"guration for the deck connector is shown in Fig. 14. The "gure indicates the parameters that were adjusted to achieve the loads required. For simplicity, the deck connector was broken up into three separate regions. Each region can have a separate de"nition for the number of rows and columns (row and col ), G G tube diameter, length and thickness (dia , ¸ , and t ), and tube spacing in the fore-aft ' ' G direction (d ). The inboard/outboard spacing of the tubes is the same in all regions (s). G In theory, it is possible that there are more than three separate regions, but for the purposes of this exercise, three was su$cient. For the requirements listed in Table 4, the deck connector con"guration parameters are as given in Table 5. For this design, there are a total of 7949 tubes. Also, in the center region, there is only a single row of 29 tubes. Since it is a very small
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Fig. 14. Full-scale design parameters * deck connector.
Table 5 Design parameters * baseline Parameter
Center (i"1)
Mid (i"2)
Outbd (i"3)
col G row G dia G t G ¸ G d G s
29 1 7.5 in 0.75 in 24 in N/A 8 in
80 12 7.5 in 1.75 in 30 in 8 in 8 in
125 24 7.5 in 2.25 in 48 in 8 in 8 in
percentage of the total number of tubes, these tubes could probably be neglected. They were left in for the initial analysis performed. 6.1.2. Keel connector The general arrangement for the six DOF keel connector is shown in Fig. 15. The parameters that can be varied are indicated in the "gure. The connector consists of an array of tubes on each of its four sides. The tube spacing between both rows and columns is constant throughout the connector (d). The number of rows and columns (row, column) is also held constant on each side as are the tube diameter, thickness and length (dia, t, ¸). The values for the keel connector parameters that were determined for the baseline analysis are given in Table 6. With this design, there are a total of 80 tubes in each keel connector. 6.2. Connector xnite element analysis The individual connectors were modeled in ABAQUS according to the point design concept described above. Each connector was modeled using the full 3-D geometry (i.e. no symmetry assumptions) using shell elements for the connector structure and beam elements for the urethane composite tubes similar to the veri"cation test models.
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Fig. 15. Keel connector.
Table 6 Baseline keel connector design parameters Parameter
Value
row col d dia t ¸
5 4 18 in 8 in 1.25 in 42 in
The analysis approach used to determine the spring constants was to apply a force(s) in a single-degree-of-freedom with constraints/restraints applied to prevent motion in all other degrees-of-freedom. The reaction loads at the constraints/restraints were then used to determine the coupling between the degrees-of-freedom. In ABAQUS, the coupling terms in the spring elements are limited to coupling rotational forces with only rotational displacement and translational forces with only translational displacements. This loss in coupling terms will tend to decrease the overall sti!ness of a coupling. In addition, the remaining coupling terms were all found to be relatively small compared to the diagonal terms. Therefore, these o!diagonal terms were also neglected leaving only a diagonal matrix. The intent for this analysis was to use the same material model that was developed using the constitutive model. However, since this material model was not available for the element type that was to be used in the connector models, the material model had to be reformulated. To accomplish this stress}strain data for the biaxial tubes were
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Fig. 16. Full-scale keel connector FE mesh.
taken from the characterization tests and used input for the hypoelastic material model. 6.2.1. Full-scale keel connector analysis The mesh for the full-scale keel connector is shown in Fig. 16. The mesh consists of beam elements representing the composite tubes, shell elements for the connector structure, and rigid elements were used at the ends of each tube to account for the material thickness of the metal connector structure. There were a total of 1230 elements in the model. 6.2.2. Full-scale deck connector analysis A portion of the deck connector mesh is shown in Fig. 17. Like the keel connector mesh, the deck connector is represented by beam elements for the composite tubes and shell elements for the connector structure. There are a total of 45,791 elements in the mesh. 6.3. MOB analysis 6.3.1. Scaling The connector sti!nesses were determined using analysis of full-scale connectors. The MOB-FE models are of the th scale wave tank models. Therefore, the sti!nesses of the connectors must be scaled to be used in the MOB model. For structural dynamic scaling consistent with Froude scaling, the forces are scaled according to: S "S $ *
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Fig. 17. Deck connector mesh.
Fig. 18. MOB analysis results.
and the moments are scaled according to: S "S , + * where S is the length scale factor ( in this case). * 6.3.2. Results The Brown & Root MOB model was analyzed for two sea conditions: Sea State 5 at a 453 heading, and Sea State 7 at a 453 heading. Both con"gurations were analyzed
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Period (S)
Shape
1 2 3 4 5 6 7 8 9 10
2.63 0.75 0.56 0.52 0.47 0.46 0.45 0.43 0.40 0.39
Torsion Transverse Vertical N/A N/A N/A N/A N/A N/A N/A
Table 8 Compliant connector natural periods B & R w/ARC Connector Mode C
Period (S)
Shape
1 2 3 4 5 6 7 8 9 10
70.1 44.7 26.9 26.2 17.8 15.4 13.5 10.6 10.2 9.0
Vertical Transverse Vertical Torsion Transverse Vertical Torsion Vertical Transverse Torsion
at operational draft. The RMS vertical bending moments (relative pitch) reacted by the compliant connector system for the Sea State 5, 453 heading condition are shown in Fig. 18 and are compared with the loads in the model tests on the rigid connector concept. These results are scaled to full-scale values. By using the compliant connector, the vertical bending loads have been reduced by over an order of magnitude. The results for Sea State 7, 453 heading show a maximum vertical bending moment of 50,000 ft lton which is a 85% reduction from the Sea State 5 loads. The natural periods for the baseline Brown & Root MOB model and for the Brown & Root model with the compliant connectors are given in Tables 7 and 8, respectively. The natural periods are shown for the full-scale MOB. These tables show that the periods for the MOB con"guration with the compliant connectors have been signi"cantly increased, producing much lower natural frequencies. While some of the higher-order natural periods may coincide with those of the waves (approximately 9 s
M.S. Derstine, R.T. Brown / Marine Structures 13 (2000) 399}419
419
for Sea State 5), the RMS loads over the Sea State 5 frequency spectrum are have been reduced.
7. Conclusions A concept for a compliant connector for a mobile o!shore base (MOB) has been developed to permit reduction of the loads associated with joining semi-submersible units into a 5000 ft vessel. This concept is tailorable to meet the speci"c requirements of the MOB. A methodology for analytically determining the behavior of these compliant connectors from the material level through the structural level was demonstrated. This permits the design optimization of this connector concept to meet the needs of the mobile o!shore base.
Acknowledgements This work was funded by the Defense Advanced Research Projects Administration administered by the Mobile O!shore Base Project O$ce at the O$ce of Naval Research. The contract was managed by Dr. Jo Wen Lin, Code 5040, Naval Surface Weapons Center, Carderock Division.
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