Adaptive mesh refinements for analyses of 2D linear elasticity problems using the Kriging-based finite element method (original) (raw)
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International Journal for Numerical Methods in Engineering, 1990
A modified global approach to choosing stress terms for hybrid finite elements in plane stress problems is based on the known requirement of minimum number of stress parameters. Let nS be the number of independent B-stress parameters, n, the number of nodal displacements and nR the number of rigid body degrees of freedom, then the satisfaction of the criterion na 2 n, -nR of the assembled structure instead of the individual element enables the reduction of np. New rectangular hybrid transition elements applied in adaptive mesh refinement and a new eight node rectangular invariant element including only 12 / I parameters, based on the modified criterion, are presented here.
An Adaptive Strategy for Elastic-Plastic Two-Dimensional Finite Element Analysis
tecgraf.puc-rio.br
In recent years several strategies for self-adaptive linear-elastic finite element analysis have been developed. These methodologies will be available in a near future for the end user in commercial finite element codes. However, adaptive analysis for non-linear plasticity problems is still an on going research effort. This work presents a methodology for self-adaptive analysis of two-dimensional elastic-plastic structures. The self-adaptive process is based on an h-type refinement, with 'a posteriori' error estimation. Two types of error estimators are available. The first is based on effective stress 1 and the second is based on a ratio of plastic work 2 . Automatic mesh generation is based on spatial decomposition techniques: binary recursive partition for the refinement of boundary and crack-line curves, and quadtree partition for mesh generation in the model interior. The 'a priori' refinement of the curves has the advantage of generating good transition meshes at boundary regions 3 . The system integrates different tools: a geometric modeler to create the model geometry, a preprocessor for mesh generation and attribute assignment, a numerical analysis module to evaluate the finite element response, and a module to manage the self-adaptive procedures. This latter module also incorporates post-processor features for model and response visualization 4 . In the non-linear adaptive process for incremental plasticity analysis, a technique for interpolating analysis variables across distinct meshes 5 is used. The von Mises yielding criterion, with isotropic hardening, is adopted. Some examples are presented to evaluate the performance of the adaptive process.
Controlled cost of adaptive mesh refinement in practical 3D finite element analysis
Advances in Engineering Software, 2007
In this paper, attention is restricted to mesh adaptivity. Traditionally, the most common mesh adaptive strategies for linear problems are used to reach a prescribed accuracy. This goal is best met with an h-adaptive scheme in combination with an error estimator. In an industrial context, the aim of the mechanical simulations in engineering design is not only to obtain greatest quality but more often a compromise between the desired quality and the computation cost (CPU time, storage, software, competence, human cost, computer used). In this paper we propose the use of alternative mesh refinement with an h-adaptive procedure for 3D elastic problems. The alternative mesh refinement criteria allow to obtain the maximum of accuracy for a prescribed cost. These adaptive strategies are based on a technique of error in constitutive relation (the process could be used with other error estimators) and an efficient adaptive technique which automatically takes into account the steep gradient areas. This work proposes a 3D method of adaptivity with the latest version of the INRIA automatic mesh generator GAMHIC3D.
Adaptive Mesh Refinement in Finite Element Analysis
Indian Journal of Engineering and Materials Sciences, 1999
Among the acce pt ab le numerical methods. Finite Element Analysis stands as the most acceptable one for problems characterised by partial differential equations. However. in accuracy in Finite Element An alysis is• unavoidable since a co ntinuum with infinite degrees of freedo m is modelled into finite degrees of freed o m. In addition to the mesh generation tas k being tedious and e rror prone. the accuracy and cost of the analysis de pe nd directly o n size. shape and number of d e ments in the mes h. The procedure of refining the mesh automatic ally based on the error estimate and distribution of the e rror is known as "adap ti ve" mesh refineme nt. A si mplified method called " Divide and Conquer" rule based on "Fuzzy Logic" is used to refi ne th e mes h by using Ir, p and Irp versions. Aut o matic mes h generato r develo ped in thi s paper based on Fuzzy log ic is able to develop well shaped elements. The program for automati c mes h gene ration and subsequent mesh re linement is developed in "C' language and the analys is is carried o ut usi ng " ANSYS " I package. Automatic mesh ge ne ratio n i~ app li cd to problems suc h as dam, square pl ate with a ho le. thi ck sphe rical press ure vessel and a co rbel and e rror less than 5 % is ac hi eved in most of th e cases.
Computers & Structures, 1992
Mesh refinement has become a standard tool in practical engineering stress analysis problems. In this paper, an algorithm is presented which combines the process of mesh refinement and redistribution in order to position the new nodes at asymptotically optimal locations. The algorithm is described in the context of a two-dimensional boundary element treatment of the equations of linear elasticity. Two examples are presented which verify the algorithm in the case of problems with and without singularities.
Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method
Applied Sciences, 2021
The adaptive mesh techniques applied to the Finite Element Method have continuously been an active research line. However, these techniques are usually applied to tetrahedra. Here, we use the triangular prismatic element as the discretization shape for a Finite Element Method code with adaptivity. The adaptive process consists of three steps: error estimation, marking, and refinement. We adapt techniques already applied for other shapes to the triangular prisms, showing the differences here in detail. We use five different marking strategies, comparing the results obtained with different parameters. We adapt these strategies to a conformation process necessary to avoid hanging nodes in the resulting mesh. We have also applied two special rules to ensure the quality of the refined mesh. We show the effect of these rules with the Method of Manufactured Solutions and numerical results to validate the implementation introduced.
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
Adaptive Poly-FEM for the analysis of plane elasticity problems
International Journal for Computational Methods in Engineering Science and Mechanics, 2017
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.
IEEE Transactions on Magnetics, 1990
In this paper a comparative evaluation of performance of adaptive meshing algorithms with different error estimators is presented. The performance of a selected set of algorithms, based on an element-by-element h-refinement technique, are assessed in some test cases in comparison with analytical results, in a uniform environment. Finally, the features of various possible refinement indicators, adaption convergence criteria and error estimation parameters a r e presented and discussed.
Configurational-force-based finite element mesh refinement for elastic-plastic problems
Periodica Polytechnica Mechanical Engineering, 2012
In this paper the computation of configurational forces in case of elastic-ideally plastic material will be examined. Numerical computation of the error in configurational forces will also be introduced in elastic and plastic domain. It will be shown that the so-called r-adaptive mesh refinement procedure [1] is also applicable for elastic-plastic problems as well as the configurational force driven h-adaptive scheme. In some special examples configurational forces are computable in analytic way. This is useful to compare the solution with numerical results, therefore validating the finite element procedure. Two plane problems will be considered where analytical solutions are known. The first one is the thick walled tube model loaded by internal pressure. Second one is an artificial problem where the displacement field assumed to be known in every point of the domain considered. According to the papers Krieg [5] and Szabó [8] analytical solution is obtainable for stress and strain distributions, if the time derivative of the strain is constant. R− and h−adaptive procedures will demonstrated on these two examples.