Analysis of plates and shells using an edge-based smoothed finite element method

Abstract

In this paper, an approach to the analysis of arbitrary thin to moderately thick plates and shells by the edge-based smoothed finite element method (ES-FEM) is presented. The formulation is based on the first order shear deformation theory, and Discrete Shear Gap (DSG) method is employed to mitigate the shear locking. Triangular meshes are used as they can be generated automatically for complicated geometries. The discretized system equations are obtained using the smoothed Galerkin weak form, and the numerical integration is applied based on the edge-based smoothing domains. The smoothing operation can provide a much needed softening effect to the FEM model to reduce the well-known "overly stiff" behavior caused by the fully compatible implementation of the displacement approach based on the Galerkin weakform, and hence improve significantly the solution accuracy. A number of benchmark problems have been studied and the results confirm that the present method can provide accurate results for both plate and shell using triangular mesh.

A combined scheme of edge-based and node-based smoothed finite element methods for Reissner–Mindlin flat shells

“…To avoid shear-locking phenomenon in thin shell elements, DSG technique [10] is used in ENS-FEM for Reissner-Mindlin shell elements. In this study, an average combination of ES-FEM and NS-FEM is proposed for all practical purpose to obtain better results for shell structural problems, compared with other methods such as DSG3 [10], MIN3 [12], MITC4 [4], ES-FEM [18,19] and NS-FEM [17,20]. Numerical results for some benchmark shell problems confirm that the present method has a good performance and is compatible to fournode quadrilateral shell elements MITC4.…”

“…We, therefore, propose immediately the average combination (α = 0.5) of ES-FEM and NS-FEM for all practical purpose. Numerical experiments show that the present method gives better solutions of shell problems than other existing techniques including stabilized discrete shear gap method using three-node triangular elements (DSG3) [10], three-node Mindlin method (MIN3) [12], edge-based smoothed discrete shear gap triangular element method [18,19], andnode-based smoothed discrete shear gap triangular element method [17,20]. It should be noted that the accuracy of solutions is often much better than FEM solutions when the average combination of ES-FEM and NS-FEM is chosen.…”

A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates

“…In the effort to overcome shortcomings of low-order elements, Liu et al have then extended the concept of smoothing domains to formulate a family of smoothed FEM (S-FEM) models with different applications such as the node-based S-FEM (NS-FEM) [42,43], edge-based S-FEM (ES-FEM) [44][45][46][47][48][49], face-based S-FEM (FS-FEM) [50,51]. Similar to the standard FEM, these S-FEM models also use a mesh of elements.…”

An enhanced cell‐based smoothed finite element method for the analysis of Reissner–Mindlin plate bending problems involving distorted mesh

“…The line integrals in Equation (22) can be calculated analytically. For example, for l D 1 and i D 1, we have Z…”