The boundary element method for elasticity problems with concentrated loads based on displacement singular elements

Zhou, Wei; Ye, Qiang; Wang, Qiao; Feng, Y. T.; Chang, Xiaolin

doi:10.1016/j.enganabound.2018.11.016

Cited by 14 publications

(3 citation statements)

References 17 publications

(15 reference statements)

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“…Wang and Wang [43] obtained similar developments accounting for spline approximation in the boundary integration equation. Recently, Zhou et al [44] proposed singular logarithmic shape functions for approximating tractions and displacements along the element domain. In all cases, the validity and accuracy of the proposed methods require further improvements, which also motivated the developments presented herein.…”

Section: Introductionmentioning

confidence: 99%

The fracture failure of three-dimensional concrete structures subjected to concentrated loadings using the Boundary Element Method

Rocha

Leonel

2022

Rev. IBRACON Estrut. Mater.

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This study applies the Boundary Element Method (BEM) for the fracture failure modelling of three-dimensional concrete structures subjected to concentrated boundary conditions. The non-requirement of domain mesh by the BEM enables high accuracy in the domain fields assessment in addition to less complex remeshing procedures during crack propagation. However, concentrated boundary conditions often occur in fracture mechanics. The Lagrangian version of the BEM enforces such boundary conditions approximately by small length elements, which lead to numerical instabilities or even inaccurate problem representation. This study proposes a formulation for representing properly concentrated boundary conditions within the Lagrangian BEM framework. Nonlinear fracture mechanics describes the material failure processes herein. The classical cohesive crack approach governs the nonlinear energy dissipation processes, in which constant and tangent operators solve the resulting nonlinear system. Three applications demonstrate the accuracy of the proposed formulation, in which the BEM responses are compared against numerical and experimental results available in the literature.

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Section: Introductionmentioning

confidence: 99%

The fracture failure of three-dimensional concrete structures subjected to concentrated loadings using the Boundary Element Method

Rocha

Leonel

2022

Rev. IBRACON Estrut. Mater.

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“…In this context, the boundary element methods (BEM) and the method of fundamental solutions (MFS) are two representatives of this class of numerical approaches. BEM have been used to solve the two-dimensional Navier-Stokes equation (Sedaghatjoo et al, 2018), elasticity problems (Wei et al, 2019;Zhang et al, 2019), three-dimensional cracks in layered and graded half spaces (Xiao et al, 2019) and structural analysis of aircraft (Oliveira and Gomes, 2019), among many others.…”

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confidence: 99%

Solution of direct and inverse conduction heat transfer problems using the method of fundamental solutions and differential evolution

Basílio

Lobato

Arouca

2020

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Purpose The study of heat transfer mechanisms is an area of great interest because of various applications that can be developed. Mathematically, these phenomena are usually represented by partial differential equations associated with initial and boundary conditions. In general, the resolution of these problems requires using numerical techniques through discretization of boundary and internal points of the domain considered, implying a high computational cost. As an alternative to reducing computational costs, various approaches based on meshless (or meshfree) methods have been evaluated in the literature. In this contribution, the purpose of this paper is to formulate and solve direct and inverse problems applied to Laplace’s equation (steady state and bi-dimensional) considering different geometries and regularization techniques. For this purpose, the method of fundamental solutions is associated to Tikhonov regularization or the singular value decomposition method for solving the direct problem and the differential Evolution algorithm is considered as an optimization tool for solving the inverse problem. From the obtained results, it was observed that using a regularization technique is very important for obtaining a reliable solution. Concerning the inverse problem, it was concluded that the results obtained by the proposed methodology were considered satisfactory, as even with different levels of noise, good estimates for design variables in proposed inverse problems were obtained. Design/methodology/approach In this contribution, the method of fundamental solution is used to solve inverse problems considering the Laplace equation. Findings In general, the proposed methodology was able to solve inverse problems considering different geometries. Originality/value The association between the differential evolution algorithm and the method of fundamental solutions is the major contribution.

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“…The displacement singular elements proposed in [285] are adopted in this research since there is singularity caused by concentrated forces.…”

Section: The Transformation Matrixmentioning

confidence: 99%

A high-performance boundary element method and its applications in engineering

Liu¹

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The boundary element method for elasticity problems with concentrated loads based on displacement singular elements

Cited by 14 publications

References 17 publications

The fracture failure of three-dimensional concrete structures subjected to concentrated loadings using the Boundary Element Method

The fracture failure of three-dimensional concrete structures subjected to concentrated loadings using the Boundary Element Method

Solution of direct and inverse conduction heat transfer problems using the method of fundamental solutions and differential evolution

A high-performance boundary element method and its applications in engineering

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