Triple-reciprocity Boundary Element Method Research Articles

Calculation of singular integrals on elements of three-dimensional problems by triple-reciprocity boundary element method

Accurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique. In this paper, a new technique is considered to evaluate the weak singular integrals that arise in the solution of three-dimensional Laplace's equation. This new application of the triple-reciprocity boundary element method is proposed for the calculation of singular integrals. A formulation of the boundary element method is utilized, and a method for the direct numerical integration of the two-dimensional surface using a two-dimensional interpolation method is proposed. In numerical integral calculation, the numerical integration of arbitrary shape is possible, and integration in the case of two-dimensional integration is approximately changed into a one-dimensional integration by using the Green's second identity. In the introduced line integral, there is no singularity. To evaluate the efficiency of this method, several numerical examples are given.

Precision controllable Gaver–Wynn–Rho algorithm in Laplace transform triple reciprocity boundary element method for three dimensional transient heat conduction problems

In this paper, Laplace transform triple reciprocity boundary element method (LT-TRBEM) is employed to solve the three dimensional transient heat conduction problems. In order to improve the accuracy of the Laplace inversion using Gaver-Wynn-Rho (GWR) algorithm in non-multi-precision computational environment, a precision controllable GWR (PCGWR) algorithm is proposed in the current study. The inversion parameter NL will be selected automatically according to inverse transform accuracy. Solutions with very poor precision in GWR will be identified and eliminated by PCGWR to guarantee the inverse transform accuracy. In LT-TRBEM, there is a non-integral term containing fundamental solution in the boundary integral equation (BIE) for domain points. The value of it is infinite and cannot be calculated directly. In order to supplement this shortcoming, a computable BIE for domain points is proposed, the term with infinite value is converted into a known amount of boundary integral. So, we can calculate the domain points’ temperature successfully, and LT-TRBEM can be employed in problems with discontinuous boundary conditions. Three numerical examples were included to demonstrate the performance of the proposed approach. In summary, LT-TRBEM combined with the PCGWR and the new BIE for domain points can capture the transient heat conduction responses efficiently and accurately.

An improved implementation of triple reciprocity boundary element method for three-dimensional steady state heat conduction problems

The domain integrals caused by heat generation appearing in the boundary integral equation (BIE) of steady state heat conduction problems can be converted into boundary integrals by triple reciprocity method (TRM). However, the current triple reciprocity approximation (TRA) of domain functions is time-consuming and its accuracy is not stable in different geometric models, due to the need to solve a combination equation, whose degree of freedom is twice the number of boundary nodes plus the number of domain interpolation points. Therefore, a new formula of TRA is proposed in the current study to save computing time and storage space and improve accuracy. In the new proposed TRA formula, the combination equation is transferred into three equations that are solved in sequence. Four numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method. Results show that although the new TRA formulation is equivalent to the original one, the approximation results are quite different, especially for non-thin structures. Particularly, the improved formula of TRA can save computing time and storage space, and get better accuracy. The improved triple reciprocity BEM is a useful approach to analyze the three-dimensional steady heat conduction problems more efficiently and accurately.

Numerical integration to obtain moment of inertia of nonhomogeneous material

The moment of inertia of a continuous object with an arbitrary shape made of a nonhomogeneous material is usually calculated by dividing it into small domains. However, it is a burdensome process to specify the density of the small domains. When the Monte Carlo method is used in the case of an arbitrary shape, the computation time increases. In this paper, a technique of easily calculating the moment of inertia of a 3D nonhomogeneous material using boundary integral equations is proposed. It is also shown how to calculate the mass, primary moment, and center of mass of an arbitrary object made of a nonhomogeneous material. A technique employed in the triple-reciprocity boundary element method is used to evaluate integral. In this paper, a formulization of the boundary element method is utilized, and a technique for the direct numerical integration of the three-dimensional domain using a three-dimensional interpolation method without carrying out domain division is proposed. To investigate the efficiency of this technique, several numerical examples are given.

Meshless large plastic deformation analysis considering with a friction coefficient by triple-reciprocity boundary element method

Meshless large plastic deformation analysis considering with a friction coefficient by triple-reciprocity boundary element method

109 三重相反境界要素法による不均質材の二次元メッシュレス熱応力解析(GS1,3 材料力学(1),研究討論セッション)

109 三重相反境界要素法による不均質材の二次元メッシュレス熱応力解析(GS1,3 材料力学(1),研究討論セッション)

M409 三重相反境界要素法による不均質材の三次元メッシュレス熱応力解析(GS1,3 材料力学(6),修士研究発表セッション)

M409 三重相反境界要素法による不均質材の三次元メッシュレス熱応力解析(GS1,3 材料力学(6),修士研究発表セッション)

Three-dimensional heat conduction analysis of inhomogeneous materials by triple-reciprocity boundary element method

Homogeneous heat conduction can be easily analyzed by the boundary element method. However, domain integrals are generally necessary to solve the heat conduction problem in non-homogeneous and functionally gradient materials. This paper shows that the three-dimensional heat conduction problem in non-homogeneous and functionally gradient materials can be solved approximately without the use of a domain integral by the triple-reciprocity boundary element method. In this method, the distribution of domain effects is interpolated using integral equations. A new computer program is developed and applied to several problems.

三重相反境界要素法による不均質材のメッシュレス応力解析

In general, internal cells are required to solve nonhomogeneous elastic problems using a conventional boundary element method (BEM). However, in this case, the merit of the BEM, which is an ease of data preparation, is lost. In this study, it is shown that two-dimensional nonhomogeneous elastic problems of functionally gradient materials can be solved without the use of internal cells, using the triple-reciprocity BEM. The triple-reciprocity BEM can be applied to thermo-elastoplastic problems with arbitrary heat generation and to three-dimensional elastoplastic problems without internal cells. In this paper, Young's modulus and Poisson's ratio are variable in nonhomogeneous elastic materials. In this method, boundary elements and arbitrary internal points are used. The distribution of fictitious body force generated by a nonhomogeneous material is interpolated using boundary integral equations. This interpolation corresponds to a thin plate spline. In this paper, elastic analysis is carried out for laminated materials, porous materials and a particle-dispersed composite as special cases of functionally gradient materials. In the case of composite materials or a layer structure, the distribution of Lame's constant is not continuous. However, the same interpolation method can be used for special case of nonhomogeneous material. A new computer program is developed and applied to several nonhomogeneous elastic problems to clearly demonstrate the theory.

三重相反境界要素法による不均質材のメッシュレス熱応力解析

三重相反境界要素法による不均質材のメッシュレス熱応力解析

109 三重相反境界要素法による不均質材のメッシュレス三次元応力解析(GS-1 計算・固体力学)

109 三重相反境界要素法による不均質材のメッシュレス三次元応力解析(GS-1 計算・固体力学)

417 三重相反境界要素法による遠心力を伴うメッシュレス三次元弾塑性解析(GS-1,3,12 計算力学(2))

417 三重相反境界要素法による遠心力を伴うメッシュレス三次元弾塑性解析(GS-1,3,12 計算力学(2))

2002 三重相反境界要素法による不均質材のメッシュレス応力解析

不均質材の弾性解析を行う場合,従来の境界要素法では内部セルを用いて行う.内部セルを使用しない方法がいろいろ提案されているが,完全な手法がない.二重相反境界要素法では,多くの種類のあるRBFの選択に工夫が必要である.内部セルを使用しない方法が提案されているが,ポアソン比は一定である必要がある.一方,著者は,三重相反境界要素法により,セルを用いないで任意の物体力を伴う二次元弾性問題を解析する方法を提案している.本論文では多重相反境界要素法により,傾斜機能材や複合材などの不均質材をメッシュレスで解析する方法を示す本手法では,ポアソン比も任意の分布でよく,さらに複合材の計算のための行列式が非常に小さくできることを示す境界積分方程式を用いて疑似物体力を補間し,この補闇値を用いて精度よく解析する方法を示す.本手法では境界上および,領域内の幾つかの任意点での物性値を使用する.また,計算例により本手法の有効性を示した.

Axial symmetric stationary heat conduction analysis of non-homogeneous materials by triple-reciprocity boundary element method

The heat conduction problems in homogeneous media can be easily solved by the boundary element method. The spatial variations of heat sources as well as material coefficients gives rise to domain integrals in integral formulations for solution of boundary value problems in functionally gradient materials (FGM), since the fundamental solutions are not available for partial differential equations with variable coefficients, in general. In this paper, we present the development of the triple reciprocity method for solution of axial symmetric stationary heat conduction problems in continuously non-homogeneous media with eliminating the domain integrals. In this method, the spatial variations of domain “sources” are approximated by introducing new potential fields and using higher order fundamental solutions of the Laplace operator.

Three-dimensional unsteady thermal stress analysis by triple-reciprocity boundary element method

Abstract The conventional boundary element method (BEM) requires a domain integral in unsteady thermal stress analysis with heat generation and/or an initial temperature distribution. In this paper, it is shown that the three-dimensional unsteady thermal stress problem can be solved effectively using the triple-reciprocity boundary element method without internal cells. In this method, the distributions of heat generation and initial temperature are interpolated using integral equations and higher order time-dependent fundamental solutions. A new computer program was developed and applied for solving several test problems.

Deformation analysis of thin plate with distributed load by triple-reciprocity boundary element method

Abstarct In general, internal cells are required to solve the deformation of a thin plate with an arbitrary distributed load using a conventional boundary element method (BEM). However, in this case, the merit of the BEM, which is the easy preparation of data, is lost. In this paper, it is shown that the deformation analysis of a thin plate with an arbitrary distributed load can be performed without the use of internal cells using the triple-reciprocity BEM. The distribution of an arbitrary load is interpolated using boundary integral equations. The problem of the thin plate, in accordance with Kirchhoff's theory, is formulated by means of two coupled Poisson equations, which are expressed in integral form using the second theorem of Green in the classical way. A new computer program was developed and applied to several problems.

Meshless Unsteady Thermo-Elastoplastic Analysis by Triple-Reciprocity Boundary Element Method

Meshless Unsteady Thermo-Elastoplastic Analysis by Triple-Reciprocity Boundary Element Method

601 三重相反境界要素法による非定常熱伝導解析(OS6.境界要素法の高度化と最新応用(1),OS・一般セッション講演)

601 三重相反境界要素法による非定常熱伝導解析(OS6.境界要素法の高度化と最新応用(1),OS・一般セッション講演)

三重相反境界要素法による非定常熱弾塑性解析

三重相反境界要素法による非定常熱弾塑性解析

Three-Dimensional Unsteady Thermal Stress Analysis by Triple-Reciprocity Boundary Element Method

Three-Dimensional Unsteady Thermal Stress Analysis by Triple-Reciprocity Boundary Element Method