A BOUNDARY-PERTURBATION FINITE-ELEMENT METHOD FOR PLANE ELASTICITY PROBLEMS

A boundary perturbation (BP) technique is combined with a finite element (FE) scheme to facilitate the solution of two-dimensional boundary value problems associated with imperfect boundaries. In this method the actual imperfect boundary is first replaced by a simpler and smoother curve, referred to as the 'ideal boundary'. This leads to the replacement of the original problem by a sequence of problems which are associated with the ideal boundary. Finally, the simplified problems are solved sequentially by using the finite element method. A general BP formulation is presented in the context of plane elasticity for an arbitrary smooth ideal boundary with an arbitrary smooth distortion, up to and including second order terms. Various computational aspects of the method are discussed. Numerical results for problems in two-dimensional elasticity are given, which demonstrate the applicability of the proposed technique.