Overhauser elements in boundary element analysis

Camp, Charles V.; Gipson, G. Steven

doi:10.1016/0895-7177(91)90053-a

Cited by 31 publications

(18 citation statements)

References 2 publications

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“…1016/j.ijsolstr.2006.04.008 necessity of replacing the continuous domains (or boundaries) with discrete ones, which in practice requires, particularly in complex boundary problems, an introduction of a large number of input data (nodes) and also resolving a considerable number of algebraic equation systems. Each day brings some original research work presenting new developments in the field and it would be impossible to mention all of them here (Camp and Gipson, 1991;Jonston, 1996Jonston, , 1997Sen, 1995;Liggett and Salmon, 1981;Durodola and Fenner, 1990;Gray and Soucie, 1993;Singh and Kalra, 1995). It should be noted, however, that the main idea behind all these papers is an attempt to improve existing BEM and FEM based on the traditional discretization of the domain or its boundary.…”

Section: Introductionmentioning

confidence: 95%

Non-element method of solving 2D boundary problems defined on polygonal domains modeled by Navier equation

Zieniuk

Bołtuć

2006

International Journal of Solids and Structures

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The paper presents a non-element method of solving boundary problems defined on polygonal domains modeled by corner points. To solve these problems a parametric integral equation system (PIES) is used. The system is characterized by a separation of the approximation of boundary geometry from the approximation of boundary functions. This feature makes it possible to effectively investigate the convergence of the obtained solutions with no need of performing the approximation of boundary geometry. The testing examples included confirm high accuracy of the solutions.

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Section: Introductionmentioning

confidence: 95%

Non-element method of solving 2D boundary problems defined on polygonal domains modeled by Navier equation

Zieniuk

Bołtuć

2006

International Journal of Solids and Structures

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“…The formula (14) is the transform of (9) to the boundary. In the particular case of a smooth boundary, D 0:5:…”

Section: Fourier Transform Of the Somigliana Identitymentioning

confidence: 99%

Modification of the boundary integral equation for the Navier–Lamé equations in 2D elastoplastic problems and its numerical solving

Zieniuk

Bołtuć

2017

Numerical Meth Engineering

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Summary The paper presents the generalization of the modification of classical boundary integral equation and obtaining parametric integral equation system for 2D elastoplastic problems. The modification was made to obtain such equations for which numerical solving does not require application of finite or boundary elements. This was achieved through the use of curves and surfaces for modeling introduced at the stage of analytical modification of the classic boundary integral equation. For approximation of plastic strains the Lagrange polynomials with various number and arrangement of interpolation nodes were used. Reliability of the modification was verified on examples with analytical solutions. Copyright © 2016 John Wiley & Sons, Ltd.

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“…The second meshing scheme represents a degenerate scheme which has previously been applied to conventional ÿrst-order Overhauser elements. 3 For both meshing strategies, exact solutions for the ÿrst and second tangential derivatives are obtained at nodes which are at least three away from the corner node. However, the ÿrst meshing strategy yields second tangential derivatives with magnitudes much greater than 100, as opposed to the expected magnitude of 2.…”

Section: Geometry With Cornersmentioning

confidence: 99%

“…One such technique has been developed by Overhauser 1 and has been used with interactive graphics. 2 Elements generated in this way have also been introduced into the BEM literature 3 and further extended to treat sharp corners. 4 Recently, the ideas of Overhauser were extended to create a set of higher-order basis functions, also C 1 -continuous from element to element.…”

Section: Introductionmentioning

confidence: 99%

C2-Continuous Elements for Boundary Element Analysis

Johnston¹

1997

Int. J. Numer. Meth. Engng.

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SUMMARYOverhauser's original idea of linearly blending two sets of quadratic C 0 -continuous basis functions to produce a set of C 1 -continuous basis functions is employed by linearly blending two sets of quadratic C 1 -continuous basis functions. The result is a set of eight basis functions which are C 2 -continuous from element to element and can be used for boundary element analysis where post-processing of the solution is required. Solutions to Laplace's equation in simple geometries are used to demonstrate the accuracy of the solutions obtained with the new elements. These new elements also provide more accurate values for the ÿrst and second derivatives of the solution in the tangential direction at all points on a smooth boundary and good approximations at corner points. ? 1997 by John Wiley & Sons, Ltd.

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Overhauser elements in boundary element analysis

Cited by 31 publications

References 2 publications

Non-element method of solving 2D boundary problems defined on polygonal domains modeled by Navier equation

Non-element method of solving 2D boundary problems defined on polygonal domains modeled by Navier equation

Modification of the boundary integral equation for the Navier–Lamé equations in 2D elastoplastic problems and its numerical solving

C2-Continuous Elements for Boundary Element Analysis

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