Free and forced vibration analysis using the smoothed finite element method (SFEM)

Smoothed finite element method (SFEM) was recently proposed by the authors to improve the accuracy and convergence rate of the existing standard four-node isoparametric finite element method (FEM) by 2×2 quadrature in the static analysis. In this work, it is further extended to the free and forced analysis of two-dimensional (2D) dynamic problems. It is found that SFEM achieves more accurate results and higher convergence rates as compared with the corresponding finite elements in solving dynamic problems without increasing the computational cost. As only shape function itself is involved in computing the field gradients and no coordinate transformation is required, the method is very easy to implement. Nonlinear elastic forced vibration problem is also examined by using smoothed deformation gradients on each cell.