An accurate and efficient scheme for linear and nonlinear analyses based on a gradient-weighted technique

An accurate and efficient gradient weighted finite element method (GW-FEM) is developed for linear elastic, free vibration and material nonlinear analyses. The new approach is based on the triangular and tetrahedral elements that can be generated automatically for any complicated geometries in 2D and 3D spaces. Shepard interpolation technique (SIT) is used to formulate the weighted gradient field considering the effect of the element itself and its adjacent elements sharing common edges (2D) or faces (3D). Due to the simple formulations, the SIT is easily implemented and coded in constructing the weighted gradient field. Both of the linear elastic and work-hardening-based elastic-plastic material models are incorporated in the GW-FEM for the linear and nonlinear analyses. The GW-FEM is then coupled with the total strain theory and projection method to solve the nonlinear elastic-plastic problem. Our numerical examples, including both of benchmark and practical engineering cases, reveal that GW-FEM provides superior performance in accuracy and efficiency, compared to the standard finite element method.