Engineering Transactions, 32, 3, pp. 315-327, 1984

A Note on the Perturbation Approach to Nonlinear Static Analysis of Elastic Plane Trusses

M. Saran
Technical University of Warsaw
Institute of Fundamental Technological Research, Warszawa

M. Kleiber
Technical University of Warsaw
Institute of Fundamental Technological Research, Warszawa

A perturbation proceduro for the incremental finite element analysis of large deformation problems is presented. The proposed approach takes into account the nonlinearity of kinematics at the incremental step. Explicit forms of the finite element "higher-order" matrices for truss element and numerical examples are given. Comparison of the results obtained by the perturbation approach, tangential stiffness method and closed-form solution are carried out. The appropriate computational cost analyses are presented implying conditions for the economical use of the method.

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J. M. T. THOMPSON, A. C. WALKER, The nonlinear perturbation analysis of structural systems, J. J. Solids and Struct., 4, 757-768, 1968.

Y. HANGAY, S. KAWAMATA, Perturbation melted in the analysis of geometrically nonlinear and stability problems, in: Advances Computing Methods in Structural Mechanics and Design UAH Press, Univ. of Alabama, Huntsville, 473-492, 1971.

J. J. CONNOR, N. MORIN, Perturbation techniques in the analysis of geometrically nonlinear shells, High speed computing of elastic structures, Univ. of Liege, 683-706, 1971.

R. H. GALLAGHER, S. T. MAU, A finite element procedure for nonlinear prebuckling and initial postbuckling analysis, NASA CR - 1936, Jan. 1972.

A. ECER, Finite element analysis of the postbuckling behavior of structures, AIAA J., 11, 1532- 1538, 1973.

Y. YAKOO, T. NAKAMURA, K. VETANI, The incremental perturbation method for large dis­placement analysis of elastic structures, Int. J. Num. Meths. Eng., 10, 503-525, 1976.

P. DESTUYNDER, Asymptotic analysis of a finite element method for Naghdi-Reissner's plate model application to the biharmonic problem, Comptes Rendus des Seances de l'Academie des Sciences, 291, 1, 65-68, 1980.

A. N. RUDEV, Asymptotic theory of elastic plate bucking under lateral compression, PWM J. Appl. Math. Mech., 44, 5, 622-628, 1981.

V. A. IVOVICH, Nonlinear vibrations of a circular shround net, Soviet Applied Mechanics, 16, II, 1010-1014, 1981.

CZ. WOZNIAK, M. KLEIBER, Nieliniowa mechanika konstrukcji, PWN, Warszawa-Poznań 1982.

M. KLEIBER, J. A. KONIG, A. SAWCZUK, Studies on plastic structures: stability, anisotropic hardening, cyclic loads, Comp. Mech. Eng., 33, 487-556, 1982.