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Inelastic section response by tangent stiffness
Civil and structural engineering Armen, H 'Assumptions, models, and computational methods for plasticity'. Comput. andStruc. Vol 10 Nos 1 & 2 (1979) pp 161-174 The objective of the papers is to familiarize the users of plastic analysis programs with the assumptions and models generally employed in describing nonlinear behaviour. Some prophetic comments are given that are concerned with the future direction of existing capabilities and problem areas that will benefit from their extensions. Durocher, L and Gasper, A 'A versatile two-dimensional mesh generator with automatic bandwidth reduction' Comput. andStruc. Vol 10 (1979) pp 561-575 A relatively straightforward mesh generation program based on isoparametric mapping concepts is presented. User-defined isoparametric superelements are subdivided, by the user, into triangular elements or isoparametric quadrilaterals. Temperatures and thicknesses (or any other characteristics) at the super-element nodes are mapped so as to provide the appropriate nodal values for the subelements. Monforton, G R 'Stiffness matrix for sandwich beams with thick anisotropic laminated faces' Comput. and Struc. Vot 10 No 3 (June 1979) pp 547-551 A finite-element capability is described for the analysis of sandwich beams with thick unbalanced laminated faces. Particular attention is focused on the effects of bending-membrane coupling in the faces. The stiffness matrix is developed using displacement functions generated from explicit solution of the governing differential equations. Hays, C!ifford O, and Santbanam, T K 'Inelastic section response by tangent stiffness' J. Struct. Dry. ASCE Vol 105 No ST7 (July 1979) pp 1 2 4 1 - 1 2 5 9 A review of inelastic analysis of a cross section is made, Given the history of deformation, the history of axial force
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and bending moment may be obtained, and vice versa. The tangent stiffness method is modified to avoid convergence difficulties due to 'large' inelastic loading. Stress-strain curves considered are nonlinear but symmetric, exhibiting hysteresis and the Bauschinger effect.
Fuchs, M B,and Brull, M A 'A new strain energy theorem and its use in the optimum design of continuous beams' Comput. and Struct. Vo110 (1979) pp 647-657 This paper discusses the design of a continuous beam for optimum support geometry. The design variables are a preselected set of simple support locations and the objective function is the strain energy of the beam. It is shown that the design for minimum strain energy is close to the design for minimum bending moment. A theorem is presented stating that the strain energy is minimized with respect to the location of simple supports if the slope of the elastic curve of the beam at the supports is zero.
Fleming, J F 'Nonlinear static analysis of cable-stayed bridge structures' Comput. andStruct. Vol 10 (1979) pp 621-635 The nonlinear static analysis of plane cablestayed bridge structures is discussed. A computer program is presented which will analyse such a structure considering the effect of initial cable tensions, member dead weights, and distributed and concentrated live loads. Glough, R W, and Wilson, E L 'Dynamic analysis of large structural systems with local nonlinearities' Comput. Methods in App. Mech. and Eng. 17/18 (1979) pp 107-129 tn many types of structures that exhibit significant nonlinearity during dynamic response, the nonlinear stiffness property is confined to a few predetermined localities. This physical characteristic may be exploited by making use of substructure concepts in the dynamic response analysis.
Both direct and indirect techniques fo~ taking advantage of localized nonlinearity are reviewed.
Zienkiewicz, O C, and Heinrich, J C, 'A unified treatment of steady-state shallow water and two-dimensional Navier-Stokes equations-finite element penalty function approach' Comput. Methods/n/tPt~. Atech. otTO Et)(], 17/18 (1979) pp 673 698 A new generalized formulation o1 shallow water equations which permits taking into account the effect of return current distribution in the depth direction is introduced. In addition, a penalty formulation in the steady state solution of the shallow water equations is introduced. The validity of various arbitrary approximations introduced in simplified shallow water equations are tested. Besseling, I F, Ernst, L J, Van Der Werff, K, De Koning, A U and Riks, E 'Geometrical and physical nonlinearities: Some developments in the Netherlands' Cornput. Methods in App. Mech. and Eng. 17/1g (1979) pp 131 157 By finite element elastic-plastic analysis it has been possible to obtain detailed information on the deformation process in the vicinity of a growing crack in sheet metal. The results obtained are compared with experimental data. An effective elastic analysis of nonlinear problems is obtained in terms of perturbation equations for the participation factors of eigenvectors.
Key, W, Krieg, R D, and Bathe, KlausJurgen 'On the application of the finite element method to metal forming processes -- Part I' Comput. Me#7ods" in App. Mech. and £ng. 17/18 (1979) pp 597 608 Metal forming processes are characterized by large amounts of plastic flow. This paper discusses the use of finite element method computational tools in making detailed examinations of these processes. Such effects as changes in tool and die shapes and changes in stress-strain behaviour due to alloying are considered.
c o m p u t e r - a i d e d design
368
and bending moment may be obtained, and vice versa. The tangent stiffness method is modified to avoid convergence difficulties due to 'large' inelastic loading. Stress-strain curves considered are nonlinear but symmetric, exhibiting hysteresis and the Bauschinger effect.
Fuchs, M B,and Brull, M A 'A new strain energy theorem and its use in the optimum design of continuous beams' Comput. and Struct. Vo110 (1979) pp 647-657 This paper discusses the design of a continuous beam for optimum support geometry. The design variables are a preselected set of simple support locations and the objective function is the strain energy of the beam. It is shown that the design for minimum strain energy is close to the design for minimum bending moment. A theorem is presented stating that the strain energy is minimized with respect to the location of simple supports if the slope of the elastic curve of the beam at the supports is zero.
Fleming, J F 'Nonlinear static analysis of cable-stayed bridge structures' Comput. andStruct. Vol 10 (1979) pp 621-635 The nonlinear static analysis of plane cablestayed bridge structures is discussed. A computer program is presented which will analyse such a structure considering the effect of initial cable tensions, member dead weights, and distributed and concentrated live loads. Glough, R W, and Wilson, E L 'Dynamic analysis of large structural systems with local nonlinearities' Comput. Methods in App. Mech. and Eng. 17/18 (1979) pp 107-129 tn many types of structures that exhibit significant nonlinearity during dynamic response, the nonlinear stiffness property is confined to a few predetermined localities. This physical characteristic may be exploited by making use of substructure concepts in the dynamic response analysis.
Both direct and indirect techniques fo~ taking advantage of localized nonlinearity are reviewed.
Zienkiewicz, O C, and Heinrich, J C, 'A unified treatment of steady-state shallow water and two-dimensional Navier-Stokes equations-finite element penalty function approach' Comput. Methods/n/tPt~. Atech. otTO Et)(], 17/18 (1979) pp 673 698 A new generalized formulation o1 shallow water equations which permits taking into account the effect of return current distribution in the depth direction is introduced. In addition, a penalty formulation in the steady state solution of the shallow water equations is introduced. The validity of various arbitrary approximations introduced in simplified shallow water equations are tested. Besseling, I F, Ernst, L J, Van Der Werff, K, De Koning, A U and Riks, E 'Geometrical and physical nonlinearities: Some developments in the Netherlands' Cornput. Methods in App. Mech. and Eng. 17/1g (1979) pp 131 157 By finite element elastic-plastic analysis it has been possible to obtain detailed information on the deformation process in the vicinity of a growing crack in sheet metal. The results obtained are compared with experimental data. An effective elastic analysis of nonlinear problems is obtained in terms of perturbation equations for the participation factors of eigenvectors.
Key, W, Krieg, R D, and Bathe, KlausJurgen 'On the application of the finite element method to metal forming processes -- Part I' Comput. Me#7ods" in App. Mech. and £ng. 17/18 (1979) pp 597 608 Metal forming processes are characterized by large amounts of plastic flow. This paper discusses the use of finite element method computational tools in making detailed examinations of these processes. Such effects as changes in tool and die shapes and changes in stress-strain behaviour due to alloying are considered.
c o m p u t e r - a i d e d design