An Hp-Adaptive Hierarchical Formulation for the Boundary Element Method Applied to Elasticity in Two Dimensions

Pessolani, Raul Bernardo Vidal

doi:10.1590/s0100-73862002000100001

Cited by 10 publications

(2 citation statements)

References 7 publications

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“…In DIBEM, since the fundamental solution also composes the kernel to be interpolated, for the source point ξ to have the same position as the field points X, it is necessary to perform a regularization procedure, like the one proposed by Hadamard (Pessolani, 2002). In this sense, the following procedure is performed on the integral term of the right-hand side of equation (1):…”

Section: Direct Interpolationmentioning

confidence: 99%

Comparisons between direct interpolation and reciprocity techniques of the boundary element method for solving two-dimensional Helmholtz problems

Balista,

Loeffler,

Lara

et al. 2023

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PurposeThis work compares the performance of the three boundary element techniques for solving Helmholtz problems: dual reciprocity, multiple reciprocity and direct interpolation. All techniques transform domain integrals into boundary integrals, despite using different principles to reach this purpose.Design/methodology/approachComparisons here performed include the solution of eigenvalue and response by frequency scanning, analyzing many features that are not comprehensively discussed in the literature, as follows: the type of boundary conditions, suitable number of degrees of freedom, modal content, number of primitives in the multiple reciprocity method (MRM) and the requirement of internal interpolation points in techniques that use radial basis functions as dual reciprocity and direct interpolation.FindingsAmong the other aspects, this work can conclude that the solution of the eigenvalue and response problems confirmed the reasonable accuracy of the dual reciprocity boundary element method (DRBEM) only for the calculation of the first natural frequencies. Concerning the direct interpolation boundary element method (DIBEM), its interpolation characteristic allows more accessibility for solving more elaborate problems. Despite requiring a greater number of interpolating internal points, the DIBEM has presented higher-quality results for the eigenvalue and response problems. The MRM results were satisfactory in terms of accuracy just for the low range of frequencies; however, the neglected higher-order primitives impact the accuracy of the dynamic response as a whole.Originality/valueThere are safe alternatives for solving engineering stationary dynamic problems using the boundary element method (BEM), but there are no suitable comparisons between these different techniques. This paper presents the particularities and detailed comparisons approaching the accuracy of the three important BEM techniques, aiming at response and frequency evaluation, which are not found in the specialized literature.

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Section: Direct Interpolationmentioning

confidence: 99%

Comparisons between direct interpolation and reciprocity techniques of the boundary element method for solving two-dimensional Helmholtz problems

Balista,

Loeffler,

Lara

et al. 2023

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show abstract

“…No MECID, uma vez que a solução fundamental também compõe o núcleo a ser interpolado, para que o ponto fonte 𝜉 tenha a mesma posição que os pontos campo 𝑋, é necessário realizar um procedimento de regularização, como o proposto por Hadamard [16]. Neste sentido, o procedimento seguinte é realizado no termo integral do lado direito da Eq.…”

Section: Técnica Da Dupla Reciprocidadeunclassified

Comparação entre as técnicas de interpolação direta e dupla reciprocidade na solução do problema de autovalor

Balista¹,

Neto²,

Lara³

2022

BJDV

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O presente trabalho apresenta os princípios matemáticos e compara duas técnicas do Método dos Elementos de Contorno que usam funções de base radial para resolver a integral relacionada ao termo reativo da Equação de Helmholtz. Assim, em um primeiro momento, apresenta-se a técnica da Dupla Reciprocidade, a qual usa procedimentos relacionados com a aplicação de princípios de reciprocidade para transformar a integração do domínio em integral de contorno. Em um segundo momento, a apresenta-se a técnica da Interpolação Direta, que se baseia em um procedimento de interpolação, no qual todo o núcleo do integral do domínio é aproximado. A comparação entre as duas técnicas é realizada por meio da análise de precisão das frequências naturais, encontradas pela solução dos problemas de autovalor. Um exemplo clássico foi escolhido para a avaliação dos resultados.

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Application of Boundary Element Method superposition technique for solving natural frequencies in piecewise homogeneous domains

Barbosa

Loeffler

2020

Computers & Mathematics with Applications

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An Hp-Adaptive Hierarchical Formulation for the Boundary Element Method Applied to Elasticity in Two Dimensions

Cited by 10 publications

References 7 publications

Comparisons between direct interpolation and reciprocity techniques of the boundary element method for solving two-dimensional Helmholtz problems

Comparisons between direct interpolation and reciprocity techniques of the boundary element method for solving two-dimensional Helmholtz problems

Comparação entre as técnicas de interpolação direta e dupla reciprocidade na solução do problema de autovalor

Application of Boundary Element Method superposition technique for solving natural frequencies in piecewise homogeneous domains

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