The development of the meshless integral method and its application to two-dimensional linear elasticity is described first. The governing integral equation is obtained from the weak form of elasticity over a local subdomain, and a moving least squares approximation is employed for meshless function approximation. This formulation incorporates a subtraction method for singularity removal in the boundary integral equation, a special numerical integration for the calculation of integrals with weak singularity that further improves accuracy, a collocation method for the imposition of essential boundary conditions, and a method for incorporating natural boundary conditions in the system governing equation. Next, elastoplastic material behavior with small deformation is introduced into the meshless integral method. The constitutive law is rate-independent flow theory based on von Mises yield criterion with isotropic hardening. The method is then extended to large deformation plasticity based on Green-Naghdi's theory using updated Lagrangian description. The Green-Lagrange strain is decomposed into the elastic and plastic part, and an elastoplastic constitutive law is employed that relates the Green-Lagrange strain to the second Piola-Kirchhoff stress.
Numerical results from the meshless integral method agree well with available analytical solutions or finite element results, and the comparisons demonstrate that the meshless integral method is accurate and robust. This research lays the foundation for modeling and simulation of metal cutting/forming processes using meshless method.