An error estimator for adaptive mesh refinement analysis based on strain energy equalisation

Mahomed, Nawaz; Kekana, M. C.

doi:10.1007/s004660050367

Cited by 5 publications

(2 citation statements)

References 6 publications

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“…The size of problem ("#DoF") increases when a finer mesh h or a higher-order polynomial p is used. As the FE mesh is refined in h, the norm of the strain energy computed from the FE solution converges to the exact norm of strain energy [31]. Therefore, we use the discrete elastic strain energy h to compute relative error in the FE simulations with respect to smaller size problems.…”

Section: Achieving Reduced L 2 Strain Energy Error Via H-and P-refinement In Tube Meshes Subjected To Bendingmentioning

confidence: 99%

Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Elasticity on Unstructured Meshes

Mehraban¹,

Tufo²,

Sture³

et al. 2021

Computer Modeling in Engineering &Amp; Sciences

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Higher-order displacement-based finite element methods are useful for simulating bending problems and potentially addressing mesh-locking associated with nearly-incompressible elasticity, yet are computationally expensive. To address the computational expense, the paper presents a matrix-free, displacement-based, higher-order, hexahedral finite element implementation of compressible and nearly-compressible (ν → 0.5) linear isotropic elasticity at small strain with p-multigrid preconditioning. The cost, solve time, and scalability of the implementation with respect to strain energy error are investigated for polynomial order p = 1, 2, 3, 4 for compressible elasticity, and p = 2, 3, 4 for nearly-incompressible elasticity, on different number of CPU cores for a tube bending problem. In the context of this matrix-free implementation, higher-order polynomials (p = 3, 4) generally are faster in achieving better accuracy in the solution than lower-order polynomials (p = 1, 2). However, for a beam bending simulation with stress concentration (singularity), it is demonstrated that higher-order finite elements do not improve the spatial order of convergence, even though accuracy is improved.

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Section: Achieving Reduced L 2 Strain Energy Error Via H-and P-refinement In Tube Meshes Subjected To Bendingmentioning

confidence: 99%

Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Elasticity on Unstructured Meshes

Mehraban¹,

Tufo²,

Sture³

et al. 2021

Computer Modeling in Engineering &Amp; Sciences

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show abstract

“…Rannacher and Suttmeier (1997) have suggested a feedback approach for error control in the FEM. Mahomed and Kekana (1998) have presented an adaptive procedure based on strain energy equalisation. Moreover, a summary of recent advances in adaptive computational mechanics can be found in the book edited by Ladeve Áze and Oden (1998).…”

Section: Motivation and Related Workmentioning

confidence: 99%

A methodology for adaptive finite element analysis: Towards an integrated computational environment

Paulino

Menezes

Neto

et al. 1999

Computational Mechanics

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This work introduces a methodology for selfadaptive numerical procedures, which relies on the various components of an integrated, object-oriented, computational environment involving pre-, analysis, and post-processing modules. A basic platform for numerical experiments and further development is provided, which allows implementation of new elements/error estimators and sensitivity analysis. A general implementation of the Superconvergent Patch Recovery (SPR) and the recently proposed Recovery by Equilibrium in Patches (REP) is presented. Both SPR and REP are compared and used for error estimation and for guiding the adaptive remeshing process. Moreover, the SPR is extended for calculating sensitivity quantities of ®rst and higher orders. The mesh (re-)generation process is accomplished by means of modern methods combining quadtree and Delaunay triangulation techniques. Surface mesh generation in arbitrary domains is performed automatically (i.e. with no user intervention) during the self-adaptive analysis using either quadrilateral or triangular elements. These ideas are implemented in the Finite Element System Technology in Adaptivity (FESTA) software. The effectiveness and versatility of FESTA are demonstrated by representative numerical examples illustrating the interconnections among ®nite element analysis, recovery procedures, error estimation/adaptivity and automatic mesh generation.Key words ®nite element analysis, error estimation, adaptivity, h-re®nement, sensitivity, superconvergent patch recovery (SPR), recovery by equilibrium in patches (REP), object oriented programming (OOP), interactive computer graphics. IntroductionThis work presents an integrated (object-oriented) computational environment for self-adaptive analyses of generic two-dimensional (2D) problems. This environment includes analysis procedures to insure a given level of accuracy according to certain criteria, and also the procedures to generate and modify the ®nite element discretization. This computational system, called FESTA (Finite Element System Technology in Adaptivity), involves ®ve main components (see shaded boxes in Figure 1):A graphical preprocessor, for de®ning the geometry of the problem, the initial ®nite element mesh (together with boundary conditions), and the main parameters used in a self-adaptive analysis. Here the geometrical model is dissociated from the ®nite element model. A ®nite element module for solving the current boundary value problem. The code has been developed so that it is highly modular, expandable, and user-friendly. Thus, it can be properly maintained and continued. Moreover, other users/developers should be able to modify the basic programming system to ®t their speci®c applications. An error estimation and sensitivity module. Discretization errors are estimated according to available recovery procedures, e.g. Zienkiewicz and Zhu (ZZ), superconvergent patch recovery (SPR) and recovery by equilibrium in patches (REP). Sensitivities of various orders (1st., 2nd. or higher) are calculated by means of...

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Adaptive nearest-nodes finite element method guided by gradient of linear strain energy density

Luo

2009

Finite Elements in Analysis and Design

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An error estimator for adaptive mesh refinement analysis based on strain energy equalisation

Cited by 5 publications

References 6 publications

Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Elasticity on Unstructured Meshes

Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Elasticity on Unstructured Meshes

A methodology for adaptive finite element analysis: Towards an integrated computational environment

Adaptive nearest-nodes finite element method guided by gradient of linear strain energy density

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