Application of the mixed approximation to the solution of two-dimensional problems of the theory of small elastoplastic strains using the finite element method

A triangular finite element that provides the stability and convergence of the mixed approximation is used for the solution of two-dimensional boundary-value problems of the theory of small elastoplastic strains. A system of resolving matrix equations of a mixed type is presented for the solution of which a three-layer iteration algorithm with a preconditioning matrix is used. Numerical results for the solution of model problems obtained by the classical and combined finite element methods are compared. __________ Translated from Problemy Prochnosti, No. 2, pp. 124–136, March–April, 2006.