Elastoplastic meshless integral method

In this paper, the meshless integral method based on regularized boundary integral equation [A. Bodin, J. Ma, X.J. Xin, P. Krishnaswami, A meshless integral method based on regularized boundary integral equation, Comput. Methods Appl. Mech. Engrg. 195 (2006) 6258–6286] has been extended to elastoplastic materials. In the formulation, the domain of interest is populated with a set of nodes using an automatic node generation algorithm. The sub-domain and support domain associated with each node are also generated automatically using algorithms that have been developed for this purpose. The governing integral equation is obtained from the weak form of elastoplasticity over a local sub-domain, and the moving least-squares approximation is used for meshless function approximation. The constitutive law is the small deformation, rate-independent flow theory based on von Mises yielding criterion with isotropic hardening. The generalized collocation method is employed to enforce the essential boundary conditions exactly, which is simple and computationally efficient. Natural boundary conditions are incorporated in the system governing equation and require no special handling. The solution algorithm for elastoplastic analysis is discussed in detail. The proposed method can handle any prescribed loading profile, including unloading and reversed loading. Numerical examples show that the elastoplastic integral meshless method is accurate and robust.