On some current procedures and difficulties in finite element analysis of elastic-plastic response

Abstract Some finite element procedures for the analysis of elastic-plastic response are presented and critically discussed: a consistent large displacement and large strain formulation is summarized, a versatile elastic-plastic model applicable to the analysis of metals and geological materials is presented, the choice of an appropriate finite element discretization is discussed, and some effective methods for the solution of the nonlinear finite element equations are briefly summarized. Finally, to illustrate the strength and shortcomings of the procedures used, the results of some sample analyses are presented and evaluated.

[1]  R. Hill The mathematical theory of plasticity , 1950 .

[2]  K. Bathe Finite Element Formulation, Modeling, and Solution of Nonlinear Dynamic Problems , 1979 .

[3]  Thomas J. R. Hughes,et al.  Stability, convergence and growth and decay of energy of the average acceleration method in nonlinear structural dynamics , 1976 .

[4]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[5]  M. P. Cleary,et al.  Fracture Discontinuities and Structural Analysis in Resource Recovery Endeavors , 1978 .

[6]  A. Pifko,et al.  Nonlinear behavior of shells of revolution under cyclic loading , 1973 .

[7]  Edward L. Wilson,et al.  Numerical methods in finite element analysis , 1976 .

[8]  K. Bathe,et al.  FINITE ELEMENT FORMULATIONS FOR LARGE DEFORMATION DYNAMIC ANALYSIS , 1975 .

[9]  Ted Belytschko,et al.  On the Unconditional Stability of an Implicit Algorithm for Nonlinear Structural Dynamics , 1975 .

[10]  D. Naylor,et al.  Stresses in nearly incompressible materials by finite elements with application to the calculation of excess pore pressures , 1974 .

[11]  Samuel W. Key,et al.  Study of the computational and theoretical differences of two finite strain elastic--plastic constitutive models , 1976 .

[12]  W. A. Marr,et al.  Incremental plasticity analysis of frictional soils , 1977 .

[13]  Klaus-Jürgen Bathe,et al.  Some practical procedures for the solution of nonlinear finite element equations , 1980 .

[14]  Klaus-Jürgen Bathe,et al.  On the application of the finite element method to metal forming processes — part I , 1979 .

[15]  L. Herrmann Elasticity Equations for Incompressible and Nearly Incompressible Materials by a Variational Theorem , 1965 .

[16]  K. Bathe,et al.  On transient analysis of fluid-structure systems , 1979 .

[17]  George Y. Baladi,et al.  Generalized Cap Model for Geological Materials , 1976 .

[18]  G. Strang,et al.  The solution of nonlinear finite element equations , 1979 .

[19]  D. C. Drucker,et al.  Soil mechanics and plastic analysis or limit design , 1952 .

[20]  F. Dimaggio,et al.  MATERIAL MODEL FOR GRANULAR SOILS , 1971 .

[21]  Carlos A. Felippa,et al.  PROCEDURES FOR COMPUTER ANALYSIS OF LARGE NONLINEAR STRUCTURAL SYSTEMS , 1977 .