An accurate improved complex variable element-free method for numerical solutions of elastodynamic problems

In this paper, an improved complex variable element-free method (ICVEFM) is proposed and implemented for elastodynamic problems. The modeling process involves element-free approximation based on an improved complex variable moving least-squares (ICVMLS) and employs the Galerkin procedure to derive the discretized equation system. Since the best mean-square approximation for both real and imaginary parts is simultaneously achieved, the ICVEFM facilitates a higher computing efficiency. The Newmark-β method for time integration and penalty method for essential boundary conditions are introduced to derive the corresponding formulae. Several numerical examples including free vibration and forced vibration with time history analyses are presented to demonstrate the accuracy of the proposed method, vis-à-vis the analytical and numerical solutions.