MIXED PROJECTION-MESH SCHEME OF THE FINITE-ELEMENT METHOD FOR THE SOLUTION OF THE BOUNDARY-VALUE PROBLEMS OF THE THEORY OF SMALL ELASTIC-PLASTIC STRAINS

摘要

A mixed projection-mesh scheme for the solution of nonlinear boundary-value problems of the theory of small elastic-plastic strains has been formulated. Correctness and convergence of the mixed approximations for stresses, strains, and displacements have been analyzed. The properties of projection operators are studied in detail, and on the basis of the results obtained, a condition has been formulated, which ensures the existence, uniqueness, and stability of the solution to a discrete problem. Application of the numerical integration has been analyzed and the obtained results are presented. The correctness and convergence estimates are based on the theory of generalized functions and the functional analysis method.