On elastoplastic analysis of some plane stress problems with meshless methods and successive approximations method

A numerical method based on the method of fundamental solutions (MFS) and the method of particular solutions (MPS) together with the successive-approximation iteration process is presented. The nonlinear behaviour of the material that hardens with plastic deformation is characterized by the Chakrabarty model. The considerations are based on the incremental theory of plasticity. Furthermore, the incremental strain equations relate the plastic strain increments to the total strains only (the stresses do not appear there). The method is used for solving three example boundary value problems that describe the stress state in some plates subjected to external loads. The accuracy of the results is examined on the basis of the boundary conditions fulfilment and the comparison with the finite element method (FEM). Finally, the regions of elastic/plastic deformation are identified. Then, the distribution of the equivalent stress is shown.