The Theory And Application Of HT FEM On Linear Fracture Problems

Based on the Trefftz method, J.Jirousek developed an HT (Hybrid-Trefftz) FEM model. The model uses two different shape functions in the non-conforming intra-element field and the auxiliary conforming frame field, then makes these two fields conformed, at last obtained the relationship between force and displacement. In the stiffness equation of the model, the nodal displacements are still the unknown variables. The intra -element shape function and the element frame shape function feature the HT FEM model, and just because of these two shape functions this model has high efficiency in solving some special local effects problem.Based on the modified complementary principles, the variational functions of linear eleastic plane and anti-plane fracture problems are founded, then the element stiffness equations are derived, and the special HT element is constructed. Then formulations of the stress intensity factors( are derived. So we can obtained of the inclined crack,V-notched crack by HT FEM. Finally ,results of several examples from HT FEM program are presented to access the performance of the proposed element model with those obtained by other approaches. The size of special element and the number of trial functions have definite effects on the precision ,convergence of the ruslts. The HT FEM is demonstrated to be ideally suited for the analysis of the fracture problem.The concept of special elements presented in this paper forms the foundation of solving plastic fracture problems.