Abstract
In this paper, we present an automatic procedure that enhances the solution accuracy of edge-based smoothed 2D solid finite elements (three-node triangular and four-node quadrilateral elements). To obtain an enhanced solution, an adaptive enrichment scheme that uses enriched 2D solid finite elements and can effectively improve solution accuracy by applying cover functions adaptively without mesh-refinement is adopted in this procedure. First, the error of the edge-based finite element solution is estimated using a devised error estimation method, and appropriate cover functions are assigned for each node. While the edge-based smoothed finite elements provide piecewise constant strain fields, the proposed enrichment scheme uses the enriched finite elements to obtain a higher order strain field within the finite elements. Through various numerical examples, we demonstrate the accuracy improvement and efficiency achieved.
Highlights
In S-finite element method (FEM), the strain smoothing technique originally developed for the Galerkin mesh-free method is applied to the FEM, and constant strain fields are constructed in newly defined smoothing domains [12,13]
We propose an automatic procedure to effectively improve the solution accuracy of edge-based 2D solid finite elements (4-node quadrilateral and 3-node triangular) without mesh-refinement or introducing additional nodes
It is not necessary to explicitly define the shape function to calculate the stiffness matrix of edge-based smoothed finite elements [6], but we present the formulation of edgebased smoothed finite elements (ES-FE) and enriched finite elements (EN-FE) with linear and piecewise linear shape functions [33]
Summary
The finite element method (FEM) is one of the most successful numerical methods and has been widely used to solve mechanics problems in various engineering fields [1,2,3,4,5]. The enrichment scheme was developed as another method of improving finite element solution accuracy [5,9,11]. A procedure for automatically improving the analysis accuracy of the standard finite elements using enriched finite elements has been proposed [34,35]. We propose an automatic procedure to effectively improve the solution accuracy of edge-based 2D solid finite elements (4-node quadrilateral and 3-node triangular) without mesh-refinement or introducing additional nodes. The adaptive enrichment scheme can enhance the solution of edge-based finite elements and capture high gradients efficiently. We suggest an automatic procedure that provides solution improvement through adaptive enrichment including the error indicator and cover function selection scheme. The feasibility of improving the accuracy of edge-based 2D finite element solutions is demonstrated
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