Node moving adaptive refinement strategy for planar elasticity problems using discrete least squares meshless method (original) (raw)
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Journal of Applied Sciences and Environmental Management, 2017
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Engineering Analysis with Boundary Elements, 2012
In this paper, an adaptive refinement procedure is proposed to be used with Discrete Least Squares Meshless (DLSM) method to obtain accurate solution of planar elasticity problems. DLSM method is a newly introduced meshless method based on the least squares concept. The method leads the solution to a given problem that minimizes a least squares functional defined as the weighted summation of the squared residual of the governing differential equation and its boundary conditions. A moving least square is also used to construct the shape function making the approach a fully least squares based approach. An error estimate and adaptive refinement strategy is proposed in this paper to further increase the efficiency of DLSM method. For this, a residual based error estimator is introduced and used to discover the region of higher errors. The proposed error estimator has the advantages of being available at the end of each analysis adaptive configuration contributing to the efficiency of the proposed process. An enrichment method is then used by adding more nodes in the vicinity of nodes with higher errors. A Voronoi diagram is used to locate the position of the nodes to be added to the current nodal configuration. Efficiency and effectiveness of the proposed procedure is examined by adaptively solving two benchmark problems. The results show the ability of the proposed strategy for accurate simulation of elasticity problems.
Finite Element Method: An Overview
DOAJ: Directory of Open Access Journals - DOAJ, 2013
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Adaptive Poly-FEM for the analysis of plane elasticity problems
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In this work we present polygonal finite element method (Poly-FEM) for the analysis of two dimensional plane elasticity problems. The generation of meshes consisting of n− sided polygonal finite elements is based on the generation of a centroidal Voronoi tessellation (CVT). An unstructured tessellation of a scattered point set, that minimally covers the proximal space around each point in the point set is generated whereby the method also includes tessellation of nonconvex domains.In this work, a patch recovery type of stress smoothing technique that utilizes polygonal element patches for obtaining smooth stresses is proposed for obtaining the smoothed finite element stresses. A recovery type a − posteriori error estimator that estimates the energy norm of the error from the recovered solution is then adopted for the polygonal finite element method. The refinement of the polygonal elements is then made on an region by region basis through a refinement index. For the numerical integration of the Galerkin weak form over polygonal finite element domains we resort to classical Gaussian quadrature applied to triangular sub domains of each polygonal element.
Computational Mechanics, 1995
This paper presents a novel method for error estimation and h-version adaptive mesh refinement for potential problems which are solved by the boundary element method (BEM). Special sensitivities, denoted as mesh sensitivities, are used to evaluate a posteriori error indicators for each element, and a global error estimator. A mesh sensitivity is the sensitivity of a physical quantity at a boundary node with respect to perturbation of the mesh. The element error indicators for all the elements can be evaluated from these mesh sensitivities. Mesh refinement can then be performed by using these element error indicators as guides. The method presented here is suitable for both potential and elastostatics problems, and can be applied for adaptive mesh refinement with either linear or quadratic boundary elements. For potential problems, the physical quantities are potential and/or flux; for elastostatics problems, the physical quantities are tractions/displacements (or tangential derivatives of displacements). In this paper, the focus is on potential problems with linear elements, and the proposed method is validated with two illustrative examples. However, it is easy to extend these ideas to elastostatics problems and to quadratic elements. 1 Introduction This paper proposes the use of mesh sensitivities as error indicators, and the use of these indicators to carry out an h-version adaptive mesh refinement procedure. The analysis method of interest here is the boundary element method (BEM). The focus here is on potential problems, which is related to