Mesh Refinement Criteria Research Articles

Nonlinear Finite-Element Analysis by Progressive Mesh Refinement (2nd Report, Application to Large-Displacement Analysis).

In the previous report, the authors proposed a simple adaptive mesh refinement technique for the elastoplastic finite-element analysis, where an element is refined when the absorbed energy density reaches a prescribed value during the loading procedure. Though the method gave accurate solutions when the prescribed value for mesh refinement was not very large, the solutions were not accurate when the prescribed value was so large that the material yielded. In the present report, several algorithms are added to the original one to overcome this problem. The additional algorithms are summarized as follows, (1) If interpolated stresses of the elements newly created by refinement exceed the yield surface, the stress components are reduced to the yield surface. (2) When the material yields, the method proposed by Owen and Hinton is employed in order to prevent the stresses drifting away from the initial yield surface. (3) The effective stress at a node is employed as a criterion for mesh refinement in addition to the absorbed energy density. Through numerical examples, it is shown that the modified algorithm gives accurate solutions. Secondly, the algorithm is applied to large-deformation problems. Consequently, it is shown that a more precise solution is obtained effectively by the present method compared with the solution obtained by the initial mesh subdivision.

Application of complementary formulations and adaptive mesh refinements to non-linear magnetostatic problems

Solving a magnetostatic problem by two complementary formulations, one H-oriented and the other B-oriented, allows all Maxwell's equations in magnetostatics to be satisfied The error due to the finite element discretisation appears only in the constitutive law and can serve as a mesh refinement criteria. In the present work, this refinement strategy is applied to non-linear magnetostatic problems. Special attention is given to the choice of a suitable error estimate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A second order finite difference error indicator for adaptive transonic flow computations

An adaptive finite element method for the calculation of transonic potential flows was developed. An error indicator based on first order finite differences of gradients is introduced as a local error estimator. It measures second order distributional derivatives. Estimates involving this error estimator, a residual and the error are given. The error estimator can be used as a criterion for mesh refinement. We also give some computational results.

A methodology for adaptive mesh refinement in optimum shape design problems

This work presents a methodology based on the use of adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element Method (FEM). A suitable and very general technique for the parametrization of the optimization problem using B-splines to define the boundary is first presented. Then, mesh generation using the advancing front method, the error estimation and the mesh refinement criteria are dealt with in the context of a shape optimization problems. In particular, the sensitivities of the different ingredients ruling the problem (B-splines, finite element mesh, design behaviour, and error estimator) are studied in detail. The sensitivities of the finite element mesh coordinates and the error estimator allow their projection from one design to the next, giving an “ a priori knowledge” of the error distribution on the new design. This allows to build up a finite element mesh for the new design with a specified and controlled level of error. The robustness and reliability of the proposed methodology is checked out with some 2D examples.

A general methodology for structural shape optimization problems using automatic adaptive remeshing

AbstractThe proposed methodology is based on the use of the adaptive mesh refinement (AMR ) techniques in the context of 2D shape optimization problems analysed by the finite element method. A suitable and very general technique for the parametrization of the optimization problem, using B‐splines to define the boundary, is first presented. Then mesh generation, using the advancing frontal method, the error estimator and the mesh refinement criterion are studied in the context of shape optimization problems In particular, the analytical sensitivity analysis of the different items ruling the problem (B‐splines. finite element mesh, structural behaviour and error estimator) is studied in detail. The sensitivities of the finite element mesh and error estimator permit their projection from one design to the next one leading to an a priori knowledge of the finite element error distribution on the new design without the necessity of any additional structural analysis. With this information the mesh refinement criterion permits one to build up a finite element mesh on the new design with a specified and controlled level of error. The robustness and reliability of the proposed methodology is checked by means of several examples.

An error analysis and mesh adaptation method for shape design of structural components

A finite element error analysis and mesh adaptation method that can be used for improving analysis accuracy in carrying out shape design of structural components is presented in this paper. The simple error estimator developed by Zienkiewicz is adopted in this study for finite element error analysis, using only post-processing finite element data. The mesh adaptation algorithm implemented in ANSYS is investigated and the difficulties found are discussed. An improved algorithm that utilizes ANSYS POST1 capabilities is proposed and found to be more efficient than the ANSYS algorithm. An example is given to show the efficiency. An interactive mesh adaptation method that utilizes PATRAN meshing and result-displaying capabilities is proposed. This proposed method displays error distribution and stress contour of analysis results using color plots, to help the designer in identifying the critical regions for mesh refinement. Also, it provides guidance for mesh refinement by computing and displaying the desired element size information, based on error estimate and a mesh refinement criterion defined by the designer. This method is more efficient and effective than the semi-automatic algorithm implemented in ANSYS, and is suitable for structural shape design. This method can be applied not only to set-up a finite element mesh of the structure at initial design but to ensure analysis accuracy in the design process. Examples are given to demonstrate feasibility of the proposed method.

Adaptive refinement in 2‐D finite element applications

AbstractAn adaptive mesh refinement scheme in the finite element method is presented in this paper. The new criterion Bdiff for adaptive refinement is tested for its validity. A technique for approximating curved boundaries employing the concept of triangle subdivision in conjunction with Delauney triangulation is also considered, so that the mesh produced is optimal. The implementation of the adaptive mesh refinement criterion in conjunction with the proposed technique of including the curved boundaries in the finite element model is described in detail and several examples of its application are given by way of illustration.