Modeling domains using Bézier surfaces in plane boundary problems defined by the Navier–Lame equation with body forces

Bołtuć, Agnieszka; Zieniuk, Eugeniusz

doi:10.1016/j.enganabound.2011.04.005

Cited by 19 publications

(8 citation statements)

References 7 publications

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“…In [18] PIES for such equations without body forces has been developed, and in [22] PIES with body forces.…”

Section: Relations Describing the Linear Elastic Bodymentioning

confidence: 99%

“…The modification of such a domain, as in the case of curves, is very effective, since it bases on changing the position of selected control points of the surface. The mentioned way of modeling and modification has been used in the paper [22] to solve problems of elasticity with body forces.…”

Section: Pies and The Integral Identitymentioning

confidence: 99%

“…The next integrand in (3) is called the singular boundary solution and is presented by the expression [18,22] P Ã lj ðs 1 ; sÞ ¼ À 1 4pð1 À mÞg P 11 P 12 P 11 P 12 ; l; j ¼ 1; 2; . .…”

Section: Pies and The Integral Identitymentioning

confidence: 99%

“…The first integrand U Ã lj ðs 1 ; sÞ in (3) is called the fundamental boundary solution and takes into account (in its mathematical formalism) the shape of the boundary defined by any parametric functions C(s). The function U Ã lj ðs 1 ; sÞ for plane strain is presented in the following matrix form [18,22] U Ã lj ðs 1 ; sÞ ¼ À 1 8pð1 À mÞl ð3 À 4mÞ lnðgÞ À…”

Section: Pies and The Integral Identitymentioning

confidence: 99%

“…PIES for the Navier-Lamé equation with body forces has been developed in [22] and is presented by , l = 1, 2, . .…”

Section: Pies and The Integral Identitymentioning

confidence: 99%

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Numerical approximation strategy for solutions and their derivatives for two-dimensional solids

Bołtuć

Zieniuk

2015

Applied Mathematical Modelling

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a b s t r a c tThe paper presents the approximation strategy for solutions and derivatives of solutions of boundary value problems on the example of two-dimensional solids. The effectiveness of the proposed strategy lies in the fact that it gives possibility to calculate solutions and their derivatives continuously at all points of the boundary and the domain, irrespective of the method used to solve the boundary problem and regardless of the type of the problem. The strategy has been developed in order to: (1) improve the accuracy of solutions (displacement) and their derivatives (strains, stresses) in the vicinity of the boundary, where they are affected by errors, (2) make the ability to directly obtain the derivatives of solutions (strains, stresses) on the boundary, (3) avoid computing strongly singular integrals present in the integral identity used for obtaining solutions or their derivatives (e.g. stresses in plasticity problems). The different variants of the proposed strategy have been developed and their accuracy has been verified considering examples with analytical solutions.

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“…In [18] PIES for such equations without body forces has been developed, and in [22] PIES with body forces.…”

Section: Relations Describing the Linear Elastic Bodymentioning

confidence: 99%

Section: Pies and The Integral Identitymentioning

confidence: 99%

Section: Pies and The Integral Identitymentioning

confidence: 99%

Section: Pies and The Integral Identitymentioning

confidence: 99%

“…PIES for the Navier-Lamé equation with body forces has been developed in [22] and is presented by , l = 1, 2, . .…”

Section: Pies and The Integral Identitymentioning