Exact imposition of inhomogeneous Dirichlet boundary conditions based on weighted finite cell method and level-set function

Abstract

The imposition of inhomogeneous Dirichlet boundary conditions (IDBCs) is essential in numerical analysis of a structure. It is especially difficult and no longer straightforward whenever non-conformal mesh is used to discretize a structure. The original contribution of this paper is to develop a weighted finite cell method (FCM) with high computing accuracy. The commonly used transfinite interpolation in the computer-aided design (CAD) community is now extended to define boundary value function so that the IDBCs are imposed exactly. Unlike existing weak imposition forms and weighted interpolation methods, it is shown that the weighting function and boundary value function involved in the weighted FCM can directly be applied to the physical field independently of the mesh discretization. Besides, level-set function (LSF) is used to represent the geometry of the considered physical domain. To verify the effectiveness, convergence performance and the generality of the proposed method, numerical examples ranging from purely elastic to thermoelastic problems are illustrated. Computing results are compared with analytical and FEA solutions.