Linear smoothed finite element method for quasi-incompressible hyperelastic media

Abstract

This work presents a linear smoothing scheme over high-order triangular elements within the framework of the cell-based strain smoothed finite element method for two-dimensional nonlinear problems. The main idea behind the proposed linear smoothing scheme is that it unlike the classical SFEM, it does not require the subdivision of the finite element cells into smoothing sub-cell. The other features of the classical SFEM are retained, such as: it does not require an explicit form of the derivatives of the basis functions, all the computations are done in the physical space, and the results are less sensitive to mesh distortion. A series of benchmark tests are done to demonstrate the validity and the stability of the proposed scheme. The validity and accuracy are confirmed by comparing the obtained numerical results with the standard FEM using quadratic triangular element and the exact solutions.