Finite Displacements in Reciprocity Based Multi-Domain BE/FE Formulations

Abstract

In this chapter, Trefftz (T-) functions are used for the development of Multi-Domain (MD) BEM/FEM based on the reciprocity relations. This reciprocity principles are well known from the Boundary Element formulations, however, using the Trefftz functions (polynomials, fundamental solutions with the source point defined outside the sub-domain, or other type of non-singular T-function) in the reciprocity relations instead of the fundamental solutions yields the non-singular integral equations for the evaluation of corresponding sub-domain relations. A weak form satisfaction of the equilibrium is used for the inter-domain connectivity relations. For linear problems, the element stiffness matrices are defined in the boundary integral equation form. In non-linear problems the total Lagrangian formulation leads to the evaluation of the boundary integrals over the original (related) sub-domain evaluated only once during the solution and to the domain integrals containing the non-linear terms. Considering the examples of simple tension, pure bending and tension of fully clamped rectangular 2D domain (2D stress/strain problems) for large strain-large rotation problems, the use of the initial stiffness, the Newton-Raphson procedure, and the incremental Newton- Raphson procedure is considered.