An element-free computational framework for elastodynamic problems based on the IMLS-Ritz method

An element-free computational framework based on the improved moving least-squares Ritz (IMLS-Ritz) method is first explored for solving two-dimensional elastodynamic problems. Employing the IMLS approximation for the field variables, discretized governing equations of the problem are derived via the Ritz procedure. Using the IMLS approximation, an orthogonal function system with a weight function is employed to construct the two-dimensional displacement fields. The resulting algebraic equation system from the IMLS-Ritz algorithm is solved without a matrix inversion. Numerical time integration for the dynamic problems is performed using the Newmark-β method. The involved essential boundary conditions are imposed through the penalty method. To examine the numerical stability of the IMLS-Ritz method, convergence studies are carried out by considering the influences of support sizes, number of nodes and time steps involved. The applicability of the IMLS-Ritz method is demonstrated through solving a few selected examples and its accuracy is validated by comparing the present results with the available solutions.