Application of new error estimators based on gradient recovery and external domain approaches to 2D elastostatics problems

Jorge, Ariosto Bretanha; Ribeiro, Gabriel O; Fisher, Timothy S.

doi:10.1016/j.enganabound.2005.03.004

Cited by 2 publications

(7 citation statements)

References 9 publications

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“…This section is based on new error estimation and adaptivity approaches for BEM, presented in , for 2D potential-BEM, and in (Jorge et al, 2005), for 2-D elastostastics BEM. These approaches were originally presented in the PhD Dissertation (Jorge, 2002) at Vanderbilt University.…”

Section: Error Estimators In Boundary Element Methods (Bem)mentioning

confidence: 99%

“…New Error Estimators based on Gradient Recovery and External Domain Approaches were extended to 2D Elastostatics Problems in (Jorge et al, 2005). These error estimator approaches were derived for 2D potential problems in , and the extension of these error estimators for a problem with a different integral formulation highlights their generality of use.…”

Section: Proposed Error Estimators Formentioning

confidence: 99%

“…To eliminate any influence of the choice of the global directions on the values of the stress error estimates, the stresses at the exterior point are first combined into stress invariants, the mean stress and the octahedral stress, before any error information is evaluated. In (Jorge et al, 2005), the two error estimators were computed for two 2D elastostatics problems, one of which contains a singularity. A comparison was made between global and local error estimates, and the error consistency with mesh refinement is also compared.…”

Section: Proposed Error Estimators Formentioning

confidence: 99%

See 2 more Smart Citations

On Error Estimators and Bayesian Approaches in Computational Model Validation

Jorge¹,

Carneiro²,

Goulart³

et al. 2022

Uncertainty Modeling: Fundamental Concepts and Models

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Section: Error Estimators In Boundary Element Methods (Bem)mentioning

confidence: 99%

Section: Proposed Error Estimators Formentioning

confidence: 99%

Section: Proposed Error Estimators Formentioning

confidence: 99%

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On Error Estimators and Bayesian Approaches in Computational Model Validation

Jorge¹,

Carneiro²,

Goulart³

et al. 2022

Uncertainty Modeling: Fundamental Concepts and Models

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“…The external domain error estimator was derived in Jorge et al [19] for potential theory and extended to elastostatics in reference [20].…”

Section: Non-symmetric System Of Equations From Minimization Of Energmentioning

confidence: 99%

“…4. The numerical results for the local element errors were obtained using error estimators recently derived by the authors for potential theory [19] and extended to elastostatics problems [20].…”

Section: Introductionmentioning

confidence: 99%

A new variational self-regular traction-BEM formulation for inter-element continuity of displacement derivatives

Jorge

Cruse

Fisher

et al. 2003

Computational Mechanics

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In this work, a non-symmetric variational approach is derived to enforce C 1;a continuity at interelement nodes for the self-regular traction-BIE. This variational approach uses only Lagrangian C 0 elements. Two separate algorithms are derived. The first one enforces C 1;a continuity at smooth inter-element nodes, and the second enforces continuity of displacement derivatives in global coordinates at corner nodes, where C 1;a continuity cannot be enforced. The variational formulation for the traction-BIE is implemented in this work for two elastostatics problems with various discretizations and polynomial interpolants. Local and global measures of the discretization error are obtained by means of an error estimator recently derived by the authors. Comparisons are also made with the displacement-BIE, which does not require C 1;a continuity for the displacement. The lack of smoothness of the displacement derivatives at the inter-element nodes is shown to be an important source of both local and global error for the traction-BIE formulation, especially for quadratic elements. The accuracy of the boundary solution obtained from the traction-BIE improves significantly when C 1;a continuity is enforced where possible, i.e., at the smooth interelement nodes only. IntroductionRegularization of the traction-BIE eliminates the need for special numerical integration procedures for singular and hyper-singular integrals, but stricter continuity requirements must be satisfied by the density for the boundary solution to exist. The self-regular formulation, developed by Cruse and co-workers [1, 2, 3], based on conforming C 0 elements, uses a relaxed continuity approach and does not satisfy these continuity requirements, even though reasonably accurate numerical results are obtained. In this work, a variational formulation is presented for the selfregular traction-BIE, enforcing the necessary inter-element continuity conditions as subsidiary constraining equations.Somigliana's Stress Identity can be regularized by adding and subtracting appropriate terms [1]. This process is equivalent to imposing on the problem a simple linear solution for the displacement, or, equivalently, imposing a constant stress state [4]. The regularized SSI can be written with regularization based on a collocation boundary point [5]. When the limit is taken as the collocation point tends to a smooth point of the boundary and the resulting stress-BIE is multiplied with the surface normal at P, a self-regular traction-BIE is obtained [2].For problems in which the stress tensor is unique, the traction BIE gives a unique value for tractions at all smooth boundary points. A condition for the existence of a limit to the boundary of the traction BIE requires that the primary density (the displacement) must be Hölder continuous of the type C 1;a at the collocation points [6,7].The discretization of the self-regular traction-BIE into C 0 elements violates the C 1;a continuity requirement for the displacement at the interface between elements. Three approaches can...

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Application of new error estimators based on gradient recovery and external domain approaches to 2D elastostatics problems

Cited by 2 publications

References 9 publications

On Error Estimators and Bayesian Approaches in Computational Model Validation

On Error Estimators and Bayesian Approaches in Computational Model Validation

A new variational self-regular traction-BEM formulation for inter-element continuity of displacement derivatives

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