An H-adaptive refinement BEM procedure using modified sample point error analysis in two-dimensional elastic problems

Chao, Ru-Min; Lee, S. Y.

doi:10.1016/s0965-9978(98)00085-4

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…This problem has been used extensively as a benchmark problem for adaptive meshing implementations. Several authors have presented it, including Guiggiani [32], Charaÿ, Neves and Wrobel [12], and Chao and Lee [33], among others.…”

Section: Example 1: Inÿnite Plate With a Circular Hole Under Uni-axiamentioning

confidence: 99%

Use of the tangent derivative boundary integral equations for the efficient computation of stresses and error indicators

Muci-Küchler

Miranda-Valenzuela

Soriano-Soriano³

2001

Numerical Meth Engineering

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SUMMARYIn this work, a new global reanalysis technique for the e cient computation of stresses and error indicators in two-dimensional elastostatic problems is presented. In the context of the boundary element method, the global reanalysis technique can be viewed as a post-processing activity that is carried out once an analysis using Lagrangian elements has been performed. To do the reanalysis, the functional representation for the displacements is changed from Lagrangian to Hermite, introducing the nodal values of the tangential derivatives of those quantities as additional degrees of freedom. Next, assuming that the nodal values of the displacements and the tractions remain practically unchanged from the ones obtained in the analysis using Lagrangian elements, the tangent derivative boundary integral equations are collocated at each functional node in order to determine the additional degrees of freedom that were introduced. Under this scheme, a second system of equations is generated and, once it is solved, the nodal values of the tangential derivatives of the displacements are obtained. This approach gives more accurate results for the stresses at the nodes since it avoids the need to di erentiate the shape functions in order to obtain the normal strain in the tangential direction. When compared with the use of Hermite elements, the global reanalysis technique has the attraction that the user does not have to give as input data the additional information required by this type of elements. Another important feature of the proposed approach is that an e cient error indicator for the values of the stresses can also be obtained comparing the values for the stresses obtained through the use of Lagrangian elements and the global reanalysis technique.

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Section: Example 1: Inÿnite Plate With a Circular Hole Under Uni-axiamentioning

confidence: 99%

Use of the tangent derivative boundary integral equations for the efficient computation of stresses and error indicators

Muci-Küchler

Miranda-Valenzuela

Soriano-Soriano³

2001

Numerical Meth Engineering

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“…Liapis [22] presented a residual error estimator. Error estimators based on di erences between the BEM solution and the element approximation or interpolation can be found in Chao and Lee [23] and in Zhao [24]. Ammons and Vable [25] employed a L 1 norm as a measure of error.…”

Section: Introductionmentioning

confidence: 99%

New approaches for error estimation and adaptivity for 2D potential boundary element methods

Jorge

Ribeiro

Fisher

2002

Numerical Meth Engineering

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SUMMARYThis work presents two new error estimation approaches for the BEM applied to 2D potential problems. The ÿrst approach involves a local error estimator based on a gradient recovery procedure in which the error function is generated from di erences between smoothed and non-smoothed rates of change of boundary variables in the local tangential direction. The second approach involves the external problem formulation and gives both local and global measures of error, depending on a choice of the external evaluation point. These approaches are post-processing procedures. Both estimators show consistency with mesh reÿnement and give similar qualitative results. The error estimator using the gradient recovery approach is more general, as this formulation does not rely on an 'optimal' choice of an external parameter. This work presents also the use of a local error estimator in an adaptive mesh reÿnement procedure. This r-reÿnement approach is based on the minimization of the standard deviation of the local error estimate. A non-linear programming procedure using a feasible-point method is employed using Lagrange multipliers and a set of active constraints. The optimization procedure produces ÿner meshes close to a singularity and results that are consistent with the problem physics.

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An H-adaptive refinement BEM procedure using modified sample point error analysis in two-dimensional elastic problems

Cited by 2 publications

References 16 publications

Use of the tangent derivative boundary integral equations for the efficient computation of stresses and error indicators

Use of the tangent derivative boundary integral equations for the efficient computation of stresses and error indicators

New approaches for error estimation and adaptivity for 2D potential boundary element methods

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