The complex variable meshless local Petrov-Galerkin method for elastodynamic problems

The complex variable meshless local Petrov-Galerkin (CVMLPG) method is further developed for structural dynamic analyses of two-dimensional (2D) solids. The complex variable moving least-square (CVMLS) approximation is used to construct the shape function and the Heaviside step function is chosen for representing the test function. In the construction of the well-performed shape function, the trial function of 2D problem is formed with a one-dimensional (1D) basis function, thus improving computational efficiency. The governing elastodynamic equations are transformed into a standard local weak formulation, and then it is discretized into a meshfree system of time-dependent equations, which are solved by the standard implicit Newmark time integration scheme. Numerical results obtained from the proposed CVMLPG method are compared with the exact solutions and those of the conventional MLPG method and excellent agreement is achieved.