Elasto‐plastic stress analysis. A generalization for various contitutive relations including strain softening

SEVERAL SIMILAR PROCESSES FOR SOLVING ELASTO-PLASTIC PROBLEMS ARE DISCUSSED IN THE CONTEXT OF A GENERAL FORMULATION WHICH INCLUDES ASSOCIATED AND NON- ASSOCIATED PLASTICITY RELATIONS AND STRAIN HARDENING AS WELL AS STRAIN SOFTENING BEHAVIOR. ADVANTAGES OF THE "INITIAL STRESS" PROCESS ARE EMPHASIZED FOR A WIDE CATEGORY OF PROBLEMS; THE ISOPARAMETRIC FORMULATION IS USED THROUGHOUT. THIS PROCESS, RENAMED THE "RESIDUAL FORCE METHOD", FORMS THE BASIS OF THIS PAPER; IT IS DEMONSTRATED THAT FURTHER IMPROVEMENTS CAN BE OBTAINED BY SUITABLE MODIFICATIONS. /DOT/

[1]  R. Southwell,et al.  Relaxation methods applied to engineering problems XIV. Plastic straining in two-dimensional stress-systems , 1950, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[2]  O. C. Zienkiewicz,et al.  Curved, isoparametric, “quadrilateral” elements for finite element analysis , 1968 .

[3]  O. Zienkiewicz,et al.  Stress Analysis of Rock as a ‘No Tension’ Material , 1968 .

[4]  D. R. Bland,et al.  The associated flow rule of plasticity , 1957 .

[5]  Ian P. King,et al.  Elastic-plastic analysis of two-dimensional stress systems by the finite element method , 1967 .

[6]  S. S. Gill,et al.  An experimental investigation into the plastic behaviour of oblique flush nozzles in spherical pressure vessels , 1965 .

[7]  O. Zienkiewicz.  The Finite Element Method In Engineering Science , 1971 .

[8]  O. C. Zienkiewicz,et al.  Elasto‐plastic solutions of engineering problems ‘initial stress’, finite element approach , 1969 .

[9]  Hans-Werner Ziegler.  A Modification of Prager's Hardening Rule , 1959 .

[10]  Y. Yamada,et al.  Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method , 1968 .

[11]  O. C. Zienkiewicz,et al.  Note on the ‘Alpha’‐constant stiffness method for the analysis of non‐linear problems , 1972 .

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

[13]  J. Argyris,et al.  Elasto-plastic Matrix Displacement Analysis of Three-dimensional Continua , 1965, The Journal of the Royal Aeronautical Society.

[14]  P. M. Naghdi,et al.  STRESS-STRAIN RELATIONS IN PLASTICITY AND THERMOPLASTICITY* , 1960 .

[15]  P. B. Mellor,et al.  Plasticity for mechanical engineers , 1962 .

[16]  O. C. Zienkiewicz,et al.  Reduced integration technique in general analysis of plates and shells , 1971 .

[17]  B. Irons,et al.  Engineering applications of numerical integration in stiffness methods. , 1966 .

[18]  W. T. Koiter.  Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface , 1953 .

[19]  Discrete element methods for the plastic analysis of structures subjected to cyclic loading , 1970 .

[20]  William Prager,et al.  The Theory of Plasticity: A Survey of Recent Achievements , 1955 .

[21]  Pedro Marcal.  A comparative study of numerical methods of elastic-plastic analysis. , 1967 .