A high-order edge-based smoothed finite element (ES-FEM) method with four-node triangular element for solid mechanics problems

In this paper, a high-order edge-based smoothed finite element method (ES-FEM) is proposed using special triangular elements with four nodes (T4). The T4 elements are created by simply adding in an extra internal node at the center. In the proposed high-order ES-FEM, smoothing strain is reconstructed based on the so-called pick-out theory. The strain field in each smoothing domain is expressed by polynomials of complete order. We proved that for T4 elements, the strain field can be expressed in the form of first-order and second-order shape functions. Smoothing strain field with both constant and linear are developed for this T4 element and implemented in our ES-FEM, which leads to two types of ES-FEM models: constant-strain ES-FEM-T4 and linear-strain ES-FEM-T4. It is found that: 1) The constant-strain ES-FEM-T4 has high calculation accuracy, higher than the widely-used ES-FEM with three-node triangular (T3) elements. 2) Volumetric locking is removed in the constant-strain ES-FEM-T4, it works well for incompressible or nearly incompressible solids. 3) For the linear-strain ES-FEM-T4, the solution accuracy is a little lower than that of ES-FEM-T3, however, it has special feature of producing upper-bound solutions, which is important for certified solutions for solid mechanics problems.