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Buckling analysis of thin cylindrical CFRP panel with oval cutout
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 21 (2020) 1270–1277
www.materialstoday.com/proceedings
ICRACM-2019
Buckling analysis of thin cylindrical CFRP panel with oval cutout Mohammed A. K.a* , M. Naushad Alamb, Raisuddin Ansarib a
Ph.D. scholar, Dept. of Mech. Engg. ZHCET. Aligarh Muslim Univercity, Aligarh, UP, 202002, India b Professor , Dept. of Mech. Engg. ZHCET. Aligarh Muslim Univercity, Aligarh, UP, 202002, India
Abstract The use of laminated composite is growing rapidly in many fields due to their high stiffness to weight and strength to weight ratios, low modulus of expansion, thermal conductivity etc. According to their applications, composite materials undergo different loading conditions. One of the common failures is buckling, when the laminate is subjected to axial compressive load. Hence buckling analysis of composite structure is very important from design point of view. Different cutout shapes of thin cylindrical shells have been studied for buckling, but oval shaped cutouts with different orientations seems scanty and requires more investigation. In the present study, buckling analysis of thin cylindrical carbon fiber reinforced polymer (CFRP) composite shell with oval cutout has been investigated. The effects of three types of variables viz. layup orientation, element type and cutout orientation are analyzed numerically. The results show that the buckling load and mode shape depend on all three variables. The four ply stack orientations panel show significantly higher buckling load than two ply stack, and large decrease in buckling load with respect to cutout orientation. The buckling modes are highly affected by the cutout orientation. The minimum value of buckling load with respect to cutout orientation depends upon layup configuration. The lowest value of buckling load has been obtained for configuration 2 at 90º cutout orientation. © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of SIXTH INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN COMPOSITE MATERIALS, ICRACM-2019. Keywords: Buckling; Carbon fibres; Composite shells; Oval cutout.
* Corresponding author. Tel.: +9647825425574. E-mail address: [email protected]
1. Introduction Most fabricated composite structures are subjected to post curing processing to gain their final functionality. The post processing may include: trimming excess edges, drilling, making cutouts, painting, fining surfaces, etc. The 2214-7853 © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of SIXTH INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN COMPOSITE MATERIALS, ICRACM-2019.
A.K. Mohammed et al. / Materials Today: Proceedings 21 (2020) 1270–1277
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fabrication of cutouts is common post curing process which is performed to maintain the designed shape and purpose. These cutouts are affecting the performance of the structures in many ways like: decreasing buckling load, minimizing the structure stiffness, changing the buckling mode shape, tendency to delamination, etc. Tafreshi [1] implemented finite element package ABAQUS to analyze the buckling and post buckling response of composite shells containing cutouts and subjected to internal pressure combined with axial compression. Different layup configurations and cutout size have been studied. Allahbakhsh and Dadrasi [2] performed numerical analysis to analyze cylindrical laminated composite panel with elliptic cutout under axial loading with changing composite ply angle, cutout size and location. Simple equations for buckling load reduction factor were concluded, to simplify the designing procedure of composite cylindrical panel. Shi et al [3] investigated numerically the initial and post buckling response of advanced grid stiffened cylindrical composite shell under axial loading, with rectangular or circular cutouts. Various configurations were used to reinforce the shells near the cutout areas with grid reinforcement and skin reinforcement. Arbelo et al [4] investigated the combination of initial geometric imperfection with buckling load characteristics for thin walled composite curved panel structures. The radius to the thickness ratio and cutout size effect on buckling load behavior has been studied utilizing simulation software Abaqus. Kepple et al [5] proposed an improved procedure for axially compressed cylinders using stochastic modeling of material and thickness imperfections of imperfection sensitive structures (composite cylindrical shells). The described stochastic methods were being able to capture the scatters introduced from imperfections. Suhara et al [6] studied the nonlinear buckling of laminated thin composite cylinder with circular cutout under axial loading. The composite was considered to be made of eight layers of graphite fiber-epoxy. The cutouts shaped as a circular and square where both are of the same area. The effect of cutout location on buckling loads was studied. Çelebi et al [7] investigated the characteristics of progressive failure of carbon fiber reinforced polymer cylindrical shells subjected to pure bending. The geometric imperfection calculated from linear buckling analysis then used for nonlinear analysis of failure. Specific failure modes of three types are identified and correlated to cutout size and location. Chaudhuri et al [8,9] investigated numerically the composite stiffened hypar shells with cutout under bending for different load intensity and boundary conditions. Displacements, force and moment resultants computed for different boundary conditions around the cutouts edges. Wang et al [10,11] performed parametric numerical investigation on the buckling and torsional buckling behavior of cylindrical shells with elliptic cutouts made of graphene platelets reinforced composite. The shape of graphene platelets fillers and weight fraction, number of layers, shell geometry, the orientation and position of the cutout are investigated. They found that under buckling condition the cutout orientation significantly affects the buckling load when the orientation -90º ≤ θ ≤ -45º and 45º ≤ θ ≤ 90º. Numerical parametric study presented by Hu and Chen [12] for laminated truncated conical shells with and without circular cutouts subjected to external hydrostatic compression. They demonstrated the optimal buckling loads associated with the optimal fiber orientations and buckling modes. Mohammed et al [13] presented experimental and numerical quasi static crush analysis of linearly variable thickness thin frusta. Different linear buckling modes are used as a geometric imperfection to induce the proper collapsing modes. Mohammed et al [14] investigated nonlinear quasi static crush analysis aluminum frusta tubes with oval, square and circular cutouts. In this work, numerical analysis of a cylindrical thin composite shell with oval cutout has been investigated under static buckling load. The effect of layup configuration has been investigated through three layup configurations with 16 layers of unidirectional graphite fiber-epoxy composite. The cutout is oval shaped which has been schematized in Fig. 1(b). The orientation of the cutout has been taken as a variable with values of 0º, 10º, 20º, .... 90º. The numerical model utilized shell elements for analyzing the structure, where three different element types have been used to show the element type effect. 2. Characteristics of the CFRP panel The panel investigated in this work is thin cylindrical CFRP composite shell with oval shaped cutout. The main details of considered panel are:
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2.1. Panel Geometry The structure analyzed is a cylindrical panel of 2.27mm (0.0896 in) thickness, 355.6mm (14 in) square platform and radius of curvature 381mm (15 in), so the panel covers a 55.6º arc of the cylinder. The cutout is located centrally in the panel. These configurations are chosen as in ref. [2]. Cylindrical coordinate system is used to model the panel. The axis of the cylinder is considered to be coinciding with the vertical z-axis, as shown in Fig. 1(a). Z
a
y
b R
55.6º
T
25.4
θ
θ x
381 12.7
355.6
355.6 Fig. 1. (a) cylindrical coordinate system and cylindrical shell geometry; (b) cutout geometry, (all dimensions in mm).
2.2. Cutout geometry The shape of the cutout is oval. The oval shape is drawn on a flat plane then projected normally on the cylindrical shell at the center. The dimensions of the cutout are: circular ends of diameter 25.4mm, with 25.4mm distance between centers and overall cutout length of 50.8mm. The main axis of the cutout is making angle θº with the horizontal plane. The orientation of the cutout (θº) is chosen as a variable from 0º to 90º with 10º increment each step. The cutout geometry is shown in Fig. 1(b). 2.3. Material properties of the panel The investigated panel is cylindrical shell of 16 layers; all layers are unidirectional graphite fibers in an epoxy resin and arranged in symmetric stacking sequence. The panel material is considered as orthotropic elastic material with properties given in Table 1. The laminate 1-direction is along the fibers, 2-direction is the transverse to the fibers and the 3-direction is the normal to the panel refer Fig. 2(a). Three layup configurations have been considered, all are with 16 layers of symmetric stacking sequence, see Table 2.
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Table 1. Material properties: [2]. Property
Symbol
Value
Units
Elastic modulus
E11 E22 ν12 G12= G13 G23
135 13 0.38 6.4 4.3
GPa. GPa. ---GPa. GPa.
Poisson’s ratio Shear modulus
3. Numerical analysis Simulations in this work are carried out using static linear eigenvalue buckling technique. Lanczos eigensolver is used to calculate the buckling load (eigenvalues) of the cylindrical CFRP panel. The buckling mode shapes (eigenvector) are also determined. All simulations in this study are performed using Abaqus 6.14 implicit solver. The main aspects of the simulation are as follows: 3.1. Layup configuration Three layup configurations are studied; all are of symmetric stacking sequence. The thickness of each lamina is 0.142mm (0.0056 in). Each configuration is given code number as shown in Table 2. Configuration 3 with layup sequence, ply thickness and orientation and coordinate system is shown in Fig. 2(a). Table 2. Layup configurations and their codes. Layup configuration. code 1 2 3
a
Layup sequence [(90,0)4]s [(±45)4]s [(±45,90,0)s]s
b
Fig. 2. (a) ply stack plot for configuration 3. (b) sample mesh for 50º cutout orientation.
3.2. Boundary conditions and meshing The bottom edge of the panel is fully clamped. All degrees of freedom are clamped except the axial motion along z-axis for the top edge which is left free. Simply supported boundary conditions are applied on the vertical edges. The meshing of the panel is done by using quad shell elements. The approximate element size is 4×4mm quad elements. This mesh size has been chosen so that it gives acceptable results within reasonable elapsed time. Sample meshing of 8×8mm for 50º cutout orientation demonstrated in Fig. 2(b).
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3.3. Element type Shell elements are used to model structures in which one dimension (the thickness is significantly smaller than the other dimensions). The transverse shear deformation becomes very small as the shell thickness is small compared to the other dimensions. When the thickness is more than about 1/15 of a characteristic length on the shell surface, the transverse shear deformation can be neglected, still good accuracy is maintained. Continuum shell has been used with the following types of elements [15]. 1. S4 elements: Elements type S4 is fully integrated, general-purpose, finite-membrane-strain shell elements. They are 4-node, quadrilateral, stress/displacement shell elements 2. S4R5 elements: These elements impose the Kirchhoff constraint numerically; they are 4-node shell elements. These elements should not be used for applications in which transverse shear deformation is important. They provide only large rotation but small strain 3. S8R5 elements: These elements impose the Kirchhoff constraint numerically; they are three-dimensional 8-node shell elements. They are available only as “thin” shells (they cannot be used as “thick” shells nor be used for finite-strain applications). They model large rotations with small strains accurately. 4. Results and discussion 4.1. Validation of model The layup configuration 3 with circular hole has been simulated for the purpose of validation of the model. The validation is performed by changing only the cutout shape from oval shape into circular shape (for configuration 3) and holding all the other parameters same. The obtained results are quite close to the ref. [2], refer Fig. 5 for the circular cutout convergence curve. 4.2. Mesh size convergence Three different panel configurations illustrated in Table 3. These panels have been analyzed to show the meshing size convergence for the 1st buckling mode. The panel with circular cutout is chosen for comparison [2]. Cutout orientations of 30º and 90º with S4 and S4R5 element type are chosen arbitrarily to study the mesh size effect on solution convergence. Fig. 5 shows the buckling load convergence vs. mesh size in (mm), it’s clear from this figure that the mesh size less than 4mm very close to the convergence value. The mesh size of 4×4 mm is adopted to avoid unnecessary computational cost. Table 3. Mesh convergence configurations. Cutout orientation 1 2 3
30º 90º Circular cutout
Element type
Layup configuration
S4
3
S4R5
3
S4
3
S4 R5
3
S4
3
S4 R5
3
4.3. Prediction of buckling load Linear eigenvalue analysis has been used to predict the buckling load of the cylindrical composite shell with cutout, subjected to axial compression. The first eigenvalue is taken as buckling load because the structure will collapse catastrophically before reaching the second eigenvalue. The buckling mode shape (eigenvector) represents the collapsing mode when the structure collapses under compression.
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1. Element type effect: The three element types used in in simulations are shown different responses. The S8R5 elements show the minimum buckling loads where the difference is around 1% less than the other elements, see Fig. 4 and Fig. 3(b). The elements S4 and S4R5 are showing close results. 2. Layup configurations: The configurations 1 and 2 (with two ply stack orientations see Table 2) show small difference for small values of orientation angle θ, but the difference increases with the increase of θ refer Fig. 3(a). When the ply stack orientations are four (configuration 3) the buckling limits show significantly higher values, see Fig. 3(a). The configurations 1, 2 and 3 show the peak buckling loads at θ = 40º, 15º and 25º respectively. The configuration 1 shows minimum buckling load at θ = 0º while the configurations 2 and 3 at θ = 90º. The configuration 1 shows the minimum change of buckling load (2.2%) decrease of its maximum value with respect to θ while the configuration 3 shows the maximum decrease (10.6%). 3. Buckling mode: The buckling modes are highly affected by the cutout orientation. Different buckles shapes are obtained where the buckles are changing their shape and position around the vicinity of the cutout as the cutout orientation is changes. The configuration 2 shows the same mode shape for all θ values while the configurations 1 and 3 undergo mode shape change with respect to the change in θ values, refer Figs. 5-8.
a
b
Fig. 3. (a) buckling load vs. cutout orientation angle and layup configurations for S4 elements; (b) buckling load vs. cutout orientation angle and element type for configuration 1.
a
b
Fig. 4. buckling load vs. cutout orientation angle and element type for: (a) configuration 2; (b) configuration 3.
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a
b
Fig. 5. (a) mesh size effect on linear buckling load convergence; (b) 1st buckling mode for circular cutout configuration 3.
a
b
c
Fig. 6. 1st buckling mode for configuration 1. (a) θ = 0º; (b) θ = 50º; (c) θ = 90º.
a
b
c
Fig. 7. 1st buckling mode for configuration 2. (a) θ = 0º; (b) θ = 50º; (c) θ = 90º.
A.K. Mohammed et al. / Materials Today: Proceedings 21 (2020) 1270–1277
a
b
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c
Fig. 8. 1st buckling mode for configuration 3. (a) θ = 0º; (b) θ = 50º; (c) θ = 90º
5. Conclusions The nature of buckling response of the cylindrical CFRP panel with different layup configurations and oval cutouts reveals the following conclusions. Buckling load is changed significantly with the change of layup configuration and cutout orientation. Panel with four ply stack orientations show significantly higher buckling stiffness than the two ply stack orientations. The buckling stiffness of panels with two ply stack orientations exhibited significantly less sensitive to cutout orientation than four ply stack orientations. Buckling modes are changed according to the change of cutout orientation for configurations 1 and 3, but remains unchanged for configuration 2. In spite of the relatively large decrease in buckling load with cutout orientation for the four ply stack orientations panel than two ply stack orientations, it is still having significantly higher values. Acknowledgements The support of DST-Purse scheme of Gov. of India and TEQIP project is highly acknowledged. References [1] A. Tafreshi, International journal of Pressure Vessels and Piping 79 (Elsevier), vol. 79, 2002, pp. 351-359. [2] Hamidreza Allahbakhsh, Ali Dadrasi, Modelling and Simulation in Engineering, vol. 2012, 2012. [3] Shanshan Shi, Zhi Sun, Mingfa Ren, Haoran Chen, Xiaozhi Hu, Composites: Part B, vol. 44, 2013, pp. 26-33. [4] Mariano A. Arbelo, Annemarie Herrmann, Saullo G. P. Castro, Regina Khakimova, Rolf Zimmermann, Richard Degenhardt, Appl Compos Mater, 2014. [5] Jendi Kepple, Manudha Herath, Garth Pearce, Gangadhara Prusty, Rodney Thomson, Richard Degenhardt, Engineering Structures, vol. 100, 2015, pp. 385-398. [6] Suhara C. A., Soni Syed, Smitha K. K., International Research Journal of Engineering and Technology, vol. 03, no. 09, 2016, pp. 205-209. [7] Mansur Çelebi, Zafer Gürdal, Brian F. Tatting, Agnes Blom-Schieber, Mostafa Rassaian, Steven Wanthal, in AIAA SciTech Forum, Grapevine, Texas, 9 - 13 January 2017. [8] Puja Basu Chaudhuri, Anirban Mitra, Sarmila Sahoo, Materials Today: Proceedings, vol. 4, 2017, pp. 9718-9722. [9] Puja Basu Chaudhuri, Anirban Mitra, Sarmila Sahoo, Materials Today: Proceedings, vol. 4, 2017, pp. 575-583. [10] Yu Wang, Chuang Feng, Zhan Zhao, Jie Yang, International Journal of Structural Stability and Dynamics, vol. 18, no. 3, 2018 . [11] Yu Wang, Chuang Feng, Zhan Zhao, Fangzhou Lu, Jie Yang, Composite Structures, vol. 197, 2018, pp. 72-79. [12] Hsuan-Teh Hu, Hsien-Chih Chen, Composites Part B, vol. 135, 2018, pp. 95-109. [13] Mohammed A. K., M. Naushad Alam, Raisuddin Ansari, International Journal of Crashworthiness, doi: 10.1080/13588265.2019.1613762, (2019) pp. 1-12. [14] Mohammed A. K., M. Naushad Alam, Raisuddin Ansari, in ICRAMMES (International Conference on Recent Advances in Materials Manufacturing & Energy Systems, 2019, accepted. [15] 3DS Simulia, Abaqus 6.14 Analysis User's Guide Volume IV: Elements. United States: 3DS Dassault Systèmes., 2014.
ScienceDirect Materials Today: Proceedings 21 (2020) 1270–1277
www.materialstoday.com/proceedings
ICRACM-2019
Buckling analysis of thin cylindrical CFRP panel with oval cutout Mohammed A. K.a* , M. Naushad Alamb, Raisuddin Ansarib a
Ph.D. scholar, Dept. of Mech. Engg. ZHCET. Aligarh Muslim Univercity, Aligarh, UP, 202002, India b Professor , Dept. of Mech. Engg. ZHCET. Aligarh Muslim Univercity, Aligarh, UP, 202002, India
Abstract The use of laminated composite is growing rapidly in many fields due to their high stiffness to weight and strength to weight ratios, low modulus of expansion, thermal conductivity etc. According to their applications, composite materials undergo different loading conditions. One of the common failures is buckling, when the laminate is subjected to axial compressive load. Hence buckling analysis of composite structure is very important from design point of view. Different cutout shapes of thin cylindrical shells have been studied for buckling, but oval shaped cutouts with different orientations seems scanty and requires more investigation. In the present study, buckling analysis of thin cylindrical carbon fiber reinforced polymer (CFRP) composite shell with oval cutout has been investigated. The effects of three types of variables viz. layup orientation, element type and cutout orientation are analyzed numerically. The results show that the buckling load and mode shape depend on all three variables. The four ply stack orientations panel show significantly higher buckling load than two ply stack, and large decrease in buckling load with respect to cutout orientation. The buckling modes are highly affected by the cutout orientation. The minimum value of buckling load with respect to cutout orientation depends upon layup configuration. The lowest value of buckling load has been obtained for configuration 2 at 90º cutout orientation. © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of SIXTH INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN COMPOSITE MATERIALS, ICRACM-2019. Keywords: Buckling; Carbon fibres; Composite shells; Oval cutout.
* Corresponding author. Tel.: +9647825425574. E-mail address: [email protected]
1. Introduction Most fabricated composite structures are subjected to post curing processing to gain their final functionality. The post processing may include: trimming excess edges, drilling, making cutouts, painting, fining surfaces, etc. The 2214-7853 © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of SIXTH INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN COMPOSITE MATERIALS, ICRACM-2019.
A.K. Mohammed et al. / Materials Today: Proceedings 21 (2020) 1270–1277
1271
fabrication of cutouts is common post curing process which is performed to maintain the designed shape and purpose. These cutouts are affecting the performance of the structures in many ways like: decreasing buckling load, minimizing the structure stiffness, changing the buckling mode shape, tendency to delamination, etc. Tafreshi [1] implemented finite element package ABAQUS to analyze the buckling and post buckling response of composite shells containing cutouts and subjected to internal pressure combined with axial compression. Different layup configurations and cutout size have been studied. Allahbakhsh and Dadrasi [2] performed numerical analysis to analyze cylindrical laminated composite panel with elliptic cutout under axial loading with changing composite ply angle, cutout size and location. Simple equations for buckling load reduction factor were concluded, to simplify the designing procedure of composite cylindrical panel. Shi et al [3] investigated numerically the initial and post buckling response of advanced grid stiffened cylindrical composite shell under axial loading, with rectangular or circular cutouts. Various configurations were used to reinforce the shells near the cutout areas with grid reinforcement and skin reinforcement. Arbelo et al [4] investigated the combination of initial geometric imperfection with buckling load characteristics for thin walled composite curved panel structures. The radius to the thickness ratio and cutout size effect on buckling load behavior has been studied utilizing simulation software Abaqus. Kepple et al [5] proposed an improved procedure for axially compressed cylinders using stochastic modeling of material and thickness imperfections of imperfection sensitive structures (composite cylindrical shells). The described stochastic methods were being able to capture the scatters introduced from imperfections. Suhara et al [6] studied the nonlinear buckling of laminated thin composite cylinder with circular cutout under axial loading. The composite was considered to be made of eight layers of graphite fiber-epoxy. The cutouts shaped as a circular and square where both are of the same area. The effect of cutout location on buckling loads was studied. Çelebi et al [7] investigated the characteristics of progressive failure of carbon fiber reinforced polymer cylindrical shells subjected to pure bending. The geometric imperfection calculated from linear buckling analysis then used for nonlinear analysis of failure. Specific failure modes of three types are identified and correlated to cutout size and location. Chaudhuri et al [8,9] investigated numerically the composite stiffened hypar shells with cutout under bending for different load intensity and boundary conditions. Displacements, force and moment resultants computed for different boundary conditions around the cutouts edges. Wang et al [10,11] performed parametric numerical investigation on the buckling and torsional buckling behavior of cylindrical shells with elliptic cutouts made of graphene platelets reinforced composite. The shape of graphene platelets fillers and weight fraction, number of layers, shell geometry, the orientation and position of the cutout are investigated. They found that under buckling condition the cutout orientation significantly affects the buckling load when the orientation -90º ≤ θ ≤ -45º and 45º ≤ θ ≤ 90º. Numerical parametric study presented by Hu and Chen [12] for laminated truncated conical shells with and without circular cutouts subjected to external hydrostatic compression. They demonstrated the optimal buckling loads associated with the optimal fiber orientations and buckling modes. Mohammed et al [13] presented experimental and numerical quasi static crush analysis of linearly variable thickness thin frusta. Different linear buckling modes are used as a geometric imperfection to induce the proper collapsing modes. Mohammed et al [14] investigated nonlinear quasi static crush analysis aluminum frusta tubes with oval, square and circular cutouts. In this work, numerical analysis of a cylindrical thin composite shell with oval cutout has been investigated under static buckling load. The effect of layup configuration has been investigated through three layup configurations with 16 layers of unidirectional graphite fiber-epoxy composite. The cutout is oval shaped which has been schematized in Fig. 1(b). The orientation of the cutout has been taken as a variable with values of 0º, 10º, 20º, .... 90º. The numerical model utilized shell elements for analyzing the structure, where three different element types have been used to show the element type effect. 2. Characteristics of the CFRP panel The panel investigated in this work is thin cylindrical CFRP composite shell with oval shaped cutout. The main details of considered panel are:
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2.1. Panel Geometry The structure analyzed is a cylindrical panel of 2.27mm (0.0896 in) thickness, 355.6mm (14 in) square platform and radius of curvature 381mm (15 in), so the panel covers a 55.6º arc of the cylinder. The cutout is located centrally in the panel. These configurations are chosen as in ref. [2]. Cylindrical coordinate system is used to model the panel. The axis of the cylinder is considered to be coinciding with the vertical z-axis, as shown in Fig. 1(a). Z
a
y
b R
55.6º
T
25.4
θ
θ x
381 12.7
355.6
355.6 Fig. 1. (a) cylindrical coordinate system and cylindrical shell geometry; (b) cutout geometry, (all dimensions in mm).
2.2. Cutout geometry The shape of the cutout is oval. The oval shape is drawn on a flat plane then projected normally on the cylindrical shell at the center. The dimensions of the cutout are: circular ends of diameter 25.4mm, with 25.4mm distance between centers and overall cutout length of 50.8mm. The main axis of the cutout is making angle θº with the horizontal plane. The orientation of the cutout (θº) is chosen as a variable from 0º to 90º with 10º increment each step. The cutout geometry is shown in Fig. 1(b). 2.3. Material properties of the panel The investigated panel is cylindrical shell of 16 layers; all layers are unidirectional graphite fibers in an epoxy resin and arranged in symmetric stacking sequence. The panel material is considered as orthotropic elastic material with properties given in Table 1. The laminate 1-direction is along the fibers, 2-direction is the transverse to the fibers and the 3-direction is the normal to the panel refer Fig. 2(a). Three layup configurations have been considered, all are with 16 layers of symmetric stacking sequence, see Table 2.
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Table 1. Material properties: [2]. Property
Symbol
Value
Units
Elastic modulus
E11 E22 ν12 G12= G13 G23
135 13 0.38 6.4 4.3
GPa. GPa. ---GPa. GPa.
Poisson’s ratio Shear modulus
3. Numerical analysis Simulations in this work are carried out using static linear eigenvalue buckling technique. Lanczos eigensolver is used to calculate the buckling load (eigenvalues) of the cylindrical CFRP panel. The buckling mode shapes (eigenvector) are also determined. All simulations in this study are performed using Abaqus 6.14 implicit solver. The main aspects of the simulation are as follows: 3.1. Layup configuration Three layup configurations are studied; all are of symmetric stacking sequence. The thickness of each lamina is 0.142mm (0.0056 in). Each configuration is given code number as shown in Table 2. Configuration 3 with layup sequence, ply thickness and orientation and coordinate system is shown in Fig. 2(a). Table 2. Layup configurations and their codes. Layup configuration. code 1 2 3
a
Layup sequence [(90,0)4]s [(±45)4]s [(±45,90,0)s]s
b
Fig. 2. (a) ply stack plot for configuration 3. (b) sample mesh for 50º cutout orientation.
3.2. Boundary conditions and meshing The bottom edge of the panel is fully clamped. All degrees of freedom are clamped except the axial motion along z-axis for the top edge which is left free. Simply supported boundary conditions are applied on the vertical edges. The meshing of the panel is done by using quad shell elements. The approximate element size is 4×4mm quad elements. This mesh size has been chosen so that it gives acceptable results within reasonable elapsed time. Sample meshing of 8×8mm for 50º cutout orientation demonstrated in Fig. 2(b).
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3.3. Element type Shell elements are used to model structures in which one dimension (the thickness is significantly smaller than the other dimensions). The transverse shear deformation becomes very small as the shell thickness is small compared to the other dimensions. When the thickness is more than about 1/15 of a characteristic length on the shell surface, the transverse shear deformation can be neglected, still good accuracy is maintained. Continuum shell has been used with the following types of elements [15]. 1. S4 elements: Elements type S4 is fully integrated, general-purpose, finite-membrane-strain shell elements. They are 4-node, quadrilateral, stress/displacement shell elements 2. S4R5 elements: These elements impose the Kirchhoff constraint numerically; they are 4-node shell elements. These elements should not be used for applications in which transverse shear deformation is important. They provide only large rotation but small strain 3. S8R5 elements: These elements impose the Kirchhoff constraint numerically; they are three-dimensional 8-node shell elements. They are available only as “thin” shells (they cannot be used as “thick” shells nor be used for finite-strain applications). They model large rotations with small strains accurately. 4. Results and discussion 4.1. Validation of model The layup configuration 3 with circular hole has been simulated for the purpose of validation of the model. The validation is performed by changing only the cutout shape from oval shape into circular shape (for configuration 3) and holding all the other parameters same. The obtained results are quite close to the ref. [2], refer Fig. 5 for the circular cutout convergence curve. 4.2. Mesh size convergence Three different panel configurations illustrated in Table 3. These panels have been analyzed to show the meshing size convergence for the 1st buckling mode. The panel with circular cutout is chosen for comparison [2]. Cutout orientations of 30º and 90º with S4 and S4R5 element type are chosen arbitrarily to study the mesh size effect on solution convergence. Fig. 5 shows the buckling load convergence vs. mesh size in (mm), it’s clear from this figure that the mesh size less than 4mm very close to the convergence value. The mesh size of 4×4 mm is adopted to avoid unnecessary computational cost. Table 3. Mesh convergence configurations. Cutout orientation 1 2 3
30º 90º Circular cutout
Element type
Layup configuration
S4
3
S4R5
3
S4
3
S4 R5
3
S4
3
S4 R5
3
4.3. Prediction of buckling load Linear eigenvalue analysis has been used to predict the buckling load of the cylindrical composite shell with cutout, subjected to axial compression. The first eigenvalue is taken as buckling load because the structure will collapse catastrophically before reaching the second eigenvalue. The buckling mode shape (eigenvector) represents the collapsing mode when the structure collapses under compression.
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1. Element type effect: The three element types used in in simulations are shown different responses. The S8R5 elements show the minimum buckling loads where the difference is around 1% less than the other elements, see Fig. 4 and Fig. 3(b). The elements S4 and S4R5 are showing close results. 2. Layup configurations: The configurations 1 and 2 (with two ply stack orientations see Table 2) show small difference for small values of orientation angle θ, but the difference increases with the increase of θ refer Fig. 3(a). When the ply stack orientations are four (configuration 3) the buckling limits show significantly higher values, see Fig. 3(a). The configurations 1, 2 and 3 show the peak buckling loads at θ = 40º, 15º and 25º respectively. The configuration 1 shows minimum buckling load at θ = 0º while the configurations 2 and 3 at θ = 90º. The configuration 1 shows the minimum change of buckling load (2.2%) decrease of its maximum value with respect to θ while the configuration 3 shows the maximum decrease (10.6%). 3. Buckling mode: The buckling modes are highly affected by the cutout orientation. Different buckles shapes are obtained where the buckles are changing their shape and position around the vicinity of the cutout as the cutout orientation is changes. The configuration 2 shows the same mode shape for all θ values while the configurations 1 and 3 undergo mode shape change with respect to the change in θ values, refer Figs. 5-8.
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Fig. 3. (a) buckling load vs. cutout orientation angle and layup configurations for S4 elements; (b) buckling load vs. cutout orientation angle and element type for configuration 1.
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Fig. 4. buckling load vs. cutout orientation angle and element type for: (a) configuration 2; (b) configuration 3.
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Fig. 5. (a) mesh size effect on linear buckling load convergence; (b) 1st buckling mode for circular cutout configuration 3.
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Fig. 6. 1st buckling mode for configuration 1. (a) θ = 0º; (b) θ = 50º; (c) θ = 90º.
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Fig. 7. 1st buckling mode for configuration 2. (a) θ = 0º; (b) θ = 50º; (c) θ = 90º.
A.K. Mohammed et al. / Materials Today: Proceedings 21 (2020) 1270–1277
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Fig. 8. 1st buckling mode for configuration 3. (a) θ = 0º; (b) θ = 50º; (c) θ = 90º
5. Conclusions The nature of buckling response of the cylindrical CFRP panel with different layup configurations and oval cutouts reveals the following conclusions. Buckling load is changed significantly with the change of layup configuration and cutout orientation. Panel with four ply stack orientations show significantly higher buckling stiffness than the two ply stack orientations. The buckling stiffness of panels with two ply stack orientations exhibited significantly less sensitive to cutout orientation than four ply stack orientations. Buckling modes are changed according to the change of cutout orientation for configurations 1 and 3, but remains unchanged for configuration 2. In spite of the relatively large decrease in buckling load with cutout orientation for the four ply stack orientations panel than two ply stack orientations, it is still having significantly higher values. Acknowledgements The support of DST-Purse scheme of Gov. of India and TEQIP project is highly acknowledged. References [1] A. Tafreshi, International journal of Pressure Vessels and Piping 79 (Elsevier), vol. 79, 2002, pp. 351-359. [2] Hamidreza Allahbakhsh, Ali Dadrasi, Modelling and Simulation in Engineering, vol. 2012, 2012. [3] Shanshan Shi, Zhi Sun, Mingfa Ren, Haoran Chen, Xiaozhi Hu, Composites: Part B, vol. 44, 2013, pp. 26-33. [4] Mariano A. Arbelo, Annemarie Herrmann, Saullo G. P. Castro, Regina Khakimova, Rolf Zimmermann, Richard Degenhardt, Appl Compos Mater, 2014. [5] Jendi Kepple, Manudha Herath, Garth Pearce, Gangadhara Prusty, Rodney Thomson, Richard Degenhardt, Engineering Structures, vol. 100, 2015, pp. 385-398. [6] Suhara C. A., Soni Syed, Smitha K. K., International Research Journal of Engineering and Technology, vol. 03, no. 09, 2016, pp. 205-209. [7] Mansur Çelebi, Zafer Gürdal, Brian F. Tatting, Agnes Blom-Schieber, Mostafa Rassaian, Steven Wanthal, in AIAA SciTech Forum, Grapevine, Texas, 9 - 13 January 2017. [8] Puja Basu Chaudhuri, Anirban Mitra, Sarmila Sahoo, Materials Today: Proceedings, vol. 4, 2017, pp. 9718-9722. [9] Puja Basu Chaudhuri, Anirban Mitra, Sarmila Sahoo, Materials Today: Proceedings, vol. 4, 2017, pp. 575-583. [10] Yu Wang, Chuang Feng, Zhan Zhao, Jie Yang, International Journal of Structural Stability and Dynamics, vol. 18, no. 3, 2018 . [11] Yu Wang, Chuang Feng, Zhan Zhao, Fangzhou Lu, Jie Yang, Composite Structures, vol. 197, 2018, pp. 72-79. [12] Hsuan-Teh Hu, Hsien-Chih Chen, Composites Part B, vol. 135, 2018, pp. 95-109. [13] Mohammed A. K., M. Naushad Alam, Raisuddin Ansari, International Journal of Crashworthiness, doi: 10.1080/13588265.2019.1613762, (2019) pp. 1-12. [14] Mohammed A. K., M. Naushad Alam, Raisuddin Ansari, in ICRAMMES (International Conference on Recent Advances in Materials Manufacturing & Energy Systems, 2019, accepted. [15] 3DS Simulia, Abaqus 6.14 Analysis User's Guide Volume IV: Elements. United States: 3DS Dassault Systèmes., 2014.