Complex variable boundary element-free method for two-dimensional elastodynamic problems

We proposed a new direct meshless boundary integral equation technique – the complex variable boundary element-free method (CVBEFM) based on the complex variable moving least-squares (CVMLS) approximation and the boundary element-free method (BEFM), to study the two-dimensional elastodynamic problems. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-squares (MLS) approximation. Therefore it requires fewer nodes in the meshless method which formed from the CVMLS approximation than that formed from the MLS approximation with no lose of precision. The Laplace transform is used to formulate the boundary integral equations of the two-dimensional elastodynamics and then the formulae of the CVBEFM for two-dimensional elastodynamic problems are derived. The CVBEFM is a direct numerical method in which the basic unknown quantities are the real solutions of the nodal variables. Moreover in the CVBEFM, the boundary conditions can be applied directly and easily that leads to a greater computational precision. In this paper, we selected a few numerical examples to illustrate the applicability of the CVBEFM.