A Performance Study on Configurational Force and Spring-Analogy Based Mesh Optimization Schemes
01 Aug 2006-International Journal for Computational Methods in Engineering Science and Mechanics (Taylor & Francis Group)-Vol. 7, Iss: 4, pp 241-262
TL;DR: Assessment of r-adaption algorithms based on configurational force method and spring analogy approach and results confirm that the proposed combined r − h adaption is more efficient and more flexible than a purely h-adaptive approach with better convergence characteristics.
Abstract: Assessment of r-adaption algorithms based on configurational force method and spring analogy approach is made. Assessment is made based on qualitative and quantitative aspects of error estimates, convergence rates and mesh quality. Appropriate modifications to node relocation procedures are proposed for enhanced performance. A simple linear projection technique is used to improve convergence characteristics of the material force node relocation algorithm. Performing mesh adaption on initial mesh results in a considerable reduction in gradients of strain energy. Assessment based on suitability of mesh adaption algorithms for structured and unstructured initial meshes has been performed. It has been observed that the configurational force method is more robust. Comparitive study indicates the superiority of the configurational force method. The proposed enhancement to the mesh adaption is based on configuration force method for r-adaption together with weighted Laplacian smoothing and mesh enrichment throug...
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TL;DR: In this paper, it was shown that a finite element mesh optimized with respect to discrete configurational forces also renders superior results in terms of classical error measures. But this was not the case in the case of finite element meshes.
Abstract: Over the recent years configurational mechanics has developed into a very active and successful topic both in continuum mechanics as well as in computational mechanics. On the continuum mechanics side the basic idea is to consider energy variations that go along with changes of the material configuration. Configurational forces are then energetically dual to these configurational changes. Configurational forces take the interpretation as being the driving forces in the kinetics of defects; like e.g., cracks, inclusions, phase boundaries, dislocations and the like. On the computational side it turns out that a discretisation scheme brings in artificial, discrete configurational forces that indicate in a certain sense the quality, e.g., of a finite-element mesh. This information can then be used to optimize the nodal material positions. Surprisingly, even driven by energetical arguments, it turns out that a finite element mesh optimized with respect to discrete configurational forces also renders superior results in terms of classical error measures. The manuscript will span the field from the underlying theoretical foundations over the algorithmic challenges to various computational applications.
24 citations
TL;DR: In this paper, an r-h adaptive scheme has been proposed and formulated for analysis of bimaterial interface problems using adaptive finite element method, which involves a combination of the configurational force based r-adaption with weighted laplacian smoothing and mesh enrichment by h-refinement.
Abstract: An r-h adaptive scheme has been proposed and formulated for analysis of bimaterial interface problems using adaptive finite element method. It involves a combination of the configurational force based r-adaption with weighted laplacian smoothing and mesh enrichment by h-refinement. The Configurational driving force is evaluated by considering the weak form of the material force balance for bimaterial inerface problems. These forces assembled at nodes act as an indicator for r-adaption. A weighted laplacian smoothing is performed for smoothing the mesh. The h-adaptive strategy is based on a modifed weighted energy norm of error evaluated using supercovergent estimators. The proposed method applies specific non sliding interface strain compatibility requirements across inter material boundaries consistent with physical principles to obtain modified error estimators. The best sequence of combining r- and h-adaption has been evolved from numerical study. The study confirms that the proposed combined r-h adaption is more efficient than a purely h-adaptive approach and more flexible than a purely r-adaptive approach with better convergence characteristics and helps in obtaining optimal finite element meshes for a specified accuracy.
21 citations
TL;DR: A stable numerical solution strategy in which two approaches of nonlinear programming are combined is developed, in which the mesh optimization problem is transformed into a sequence of problems without inequality constraints.
16 citations
TL;DR: This paper deals with energy based r-adaptivity in finite hyperelastostatics with a focus on the development of a numerical solution strategy for the constrained problem and uses a classical barrier method as a solution strategy.
Abstract: This paper deals with energy based r-adaptivity in finite hyperelastostatics. The focus lies on the development of a numerical solution strategy. Although the concept of improving the accuracy of a finite element solution by minimizing the discrete potential energy with respect to the material node point positions is well-known, the numerical implementation of the underlying minimization problem is difficult. In this paper, energy based r-adaptivity is defined as a minimization problem with inequality constraints. The constraints are introduced to restrict the maximum distortion of the finite element mesh. As a solution strategy for the constrained problem, we use a classical barrier method. Beside the theoretical aspects and the implementation, a numerical experiment is presented. We illustrate the performance of the proposed r-adaptivity in the case of a cracked specimen.
14 citations
TL;DR: In this article, an adaptive isogeometric analysis is proposed for plane elasticity problems, where the control net is considered to be a network of springs with the individual spring stiffness values being proportional to the error estimated at the control points.
Abstract: In the present work, an r-h adaptive isogeometric analysis is proposed for plane elasticity problems. For performing the r-adaption, the control net is considered to be a network of springs with the individual spring stiffness values being proportional to the error estimated at the control points. While preserving the boundary control points, relocation of only the interior control points is made by adopting a successive relaxation approach to achieve the equilibrium of spring system. To suit the noninterpolatory nature of the isogeometric approximation, a new point-wise error estimate for the h-refinement is proposed. To evaluate the point-wise error, hierarchical B-spline functions in Sobolev spaces are considered. The proposed adaptive h-refinement strategy is based on using De-Casteljau’s algorithm for obtaining the new control points. The subsequent control meshes are thus obtained by using a recursive subdivision of reference control mesh. Such a strategy ensures that the control points lie ...
3 citations
References
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Book•
01 Jan 2000TL;DR: In this paper, a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics is presented, focusing on methods for linear elliptic boundary value problems.
Abstract: This monograph presents a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics. The study primarily focuses on methods for linear elliptic boundary value problems. However, error estimation for unsymmetrical systems, nonlinear problems, including the Navier-Stokes equations, and indefinite problems, such as represented by the Stokes problem are included. The main thrust is to obtain error estimators for the error measured in the energy norm, but techniques for other norms are also discussed.
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TL;DR: A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes.
Abstract: A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes.
The estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors. It can thus be combined with a full adaptive process of refinement or, more simply, provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials.
When combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable.
Estimates other than the energy norm have successfully been applied giving, for instance, a predetermined accuracy of stresses.
2,449 citations
"A Performance Study on Configuratio..." refers background in this paper
...There has been a considerable focus on theoretical and computational aspects of adaptive finite element analysis since the earliest works by [2, 23]....
[...]
TL;DR: In this article, a-posteriori error estimates for finite element solutions are derived in an asymptotic form for h 0 where h measures the size of the elements.
Abstract: Computable a-posteriori error estimates for finite element solutions are derived in an asymptotic form for h 0 where h measures the size of the elements. The approach has similarity to the residual method but differs from it in the use of norms of negative Sobolev spaces corresponding to the given bilinear (energy) form. For clarity the presentation is restricted to one-dimensional model problems. More specifically, the source, eigenvalue, and parabolic problems are considered involving a linear, self-adjoint operator of the second order. Generalizations to more general one-dimensional problems are straightforward, and the results also extend to higher space dimensions; but this involves some additional considerations. The estimates can be used for a practical a-posteriori assessment of the accuracy of a computed finite element solution, and they provide a basis for the design of adaptive finite element solvers.
1,211 citations
"A Performance Study on Configuratio..." refers background in this paper
...There has been a considerable focus on theoretical and computational aspects of adaptive finite element analysis since the earliest works by [ 2 , 23 ]....
[...]
21 Aug 2000
1,031 citations
29 Dec 1998
TL;DR: Current Practice Block-Structured Grids Unstructuring Grids Cartesian Grids Overset Grids Hybrid Grids Adaptive and Moving Grids System Implementation Block Structured GrIDS Unstructured Grid System Implementation User Interfaces Grid Automation CAD Interfaces grid Visualization MDO Coupling Grid Generation Systems Algebraic Generation Elliptic Generation Hyperbolic Generation Delaunay Tetrahedral Generation Advancing-Front unstructured Generation Hexahedral Generation.
Abstract: Current Practice Block-Structured Grids Unstructured Grids Cartesian Grids Overset Grids Hybrid Grids Adaptive and Moving Grids System Implementation Block Structured Grids Unstructured Grids Cartesian Grids Overset Grids Hybrid Grids User Interfaces Grid Automation CAD Interfaces Grid Visualization MDO Coupling Grid Generation Systems Algebraic Generation Elliptic Generation Hyperbolic Generation Delaunay Tetrahedral Generation Advancing-Front Unstructured Generation Hexahedral Generation Structured Surface Grids Unstructured Surface Grids Supporting Technology Available Codes
909 citations
"A Performance Study on Configuratio..." refers methods in this paper
...In literature simple relaxation-type iterative procedures have been used [14, 21]....
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