A dual interpolation boundary face method for elasticity problems

Abstract

A dual interpolation boundary face method (DiBFM) is proposed to unify the conforming and nonconforming elements in boundary element method (BEM) implementation. In the DiBFM, the nodes of a conventional conforming element are sorted into two groups: the nodes on the boundary (called virtual nodes) and the internal nodes (called source nodes). Without virtual nodes, the conforming element turns to be a conventional nonconforming element of a lower order. Physical variables are interpolated using the conforming elements, the same way as conforming BEM. Boundary integral equations are collocated at source nodes, the same way as nonconforming BEM. To make the final system of linear equations solvable, additional constraint equations are required to condense the degrees of freedom for all the virtual nodes. These constraints are constructed using the moving least-squares (MLS). Besides, both boundary integration and MLS are performed in the parametric spaces of curves, namely, the geometric data, such as coordinates, out normals and Jacobians, are calculated directly from curves rather than from elements. Thus, no geometric errors are introduced no matter how coarse the discretization is. The method has been implemented successfully for solving two-dimensional elasticity problems. A number of numerical examples with real engineering background have demonstrated the accuracy and efficiency of the new method.