On the application of the method of fundamental solutions for the study of the stress state of a plate subjected to elastic-plastic deformation

The plane elastoplastic problem for the stress state of a plate with a narrowing subjected to uniaxial extension is considered. The behaviour of the material that hardens with plastic deformation is characterised by the Ramberg-Osgood stress-strain relation. Since this relation provides a smooth continuous curve over the whole elastic and plastic deformation range, the same governing equation can be used for both deformation regions. The paper provides a method for solving the resulting nonlinear boundary-value problem. The algorithm is based on meshless methods, i.e. the method of fundamental solutions and the method of particular solutions, together with a Picard iteration process. The approximate solution, i.e. the stress function, obtained in each iteration step is a linear combination of fundamental and particular solutions. It can thus be further used to compute the values of stresses and some effective material parameters (i.e. the Young modulus and the Poisson ratio) at any point of the domain.