Constant curvature generalized plane strain formulation for boundary element method (Q1185377)

A boundary element formulation is presented and implemented for generalized plane strain problems. Generalized plane strain is characterized by the linear dependence of the strain \(\varepsilon_{33}\) on the in-plane coordinates \(x_ 1\) and \(x_ 2\) in contrast to the classical generalized plane strain case \((\varepsilon_{33}=\text{const})\) and classical plane strain case \((\varepsilon_{33}=0)\). The main part of the paper is devoted to the derivation of the governing equations and boundary conditions for the generalized plane strain problem. The derived governing equations are nonhomogeneous partial differential equations. Determining the particular solutions, the authors transform the original boundary value problem to solution of the modified (homogeneous) partial differential equation with modified traction boundary conditions. Standard boundary element method can be applied to solution of such problem. The accuracy of this formulation has been demonstrated by a pure bending example.