scholarly journals Thermoelasticity if isotropic solids containing non-deformable thread-like inclusions

2019 ◽  
pp. 33-41
Author(s):  
Jaroslav Pasternak ◽  
Heorhiy Sulym ◽  
Nataliia Ilchuk
Keyword(s):  
Heat Conduction ◽  
Boundary Element Method ◽  
Numerical Solution ◽  
Boundary Element ◽  
Integral Equations ◽  
Numerical Example ◽  
Thermally Conducting ◽  
Isotropic Solids ◽  
Element Method

The paper derives integral equations of heat conduction and thermoelasticity of isotropic solids with non-deformable perfectly thermally conducting thread-like inclusions. It is observed that, in spite of the order of singularity, the integral equations obtained are hypersingular due to the symmetry of the kernels. Non-integral terms of these equations are derived. A boundary element method scheme for numerical solution of formulated problems is proposed. A numerical example is provided.

A Symmetric Galerkin Formulation of the Boundary Element Method for Acoustic Radiation and Scattering

1997 ◽  
Vol 05 (02) ◽  
pp. 219-241 ◽  
Author(s):  
Z. S. Chen ◽  
G. Hofstetter ◽  
H. A. Mang
Keyword(s):  
Boundary Element Method ◽  
Numerical Solution ◽  
Boundary Element ◽  
Integral Equations ◽  
Acoustic Radiation ◽  
Numerical Study ◽  
Three Dimensional ◽  
Galerkin Formulation ◽  
Thin Walled ◽  
Element Method

A symmetric Galerkin formulation of the Boundary Element Method for acoustic radiation and scattering is presented. The basic integral equations for radiation and scattering of sound are derived for structures, which may consist of a combination of a three-dimensional closed part and thin-walled parts. For the numerical solution of these integral equations a Galerkin-type numerical solution scheme is proposed. The evaluation of the weakly-singular and the hypersingular integrals, occurring in this formulation, is addressed briefly. An improved CHIEF-method is employed in order to prevent the singularity of the coefficient matrix of the algebraic system of equations at so-called irregular frequencies. Subsequently, an algorithm for the automatic determination of the number of nodal unknowns at intersections of thin-walled parts of a structure, or of thin-walled parts and the three-dimensional closed part of a structure, is described. The numerical study contains comparisons of analytical solutions for simple academic examples with the numerical results. In addition, a comparison of measured and computed results is presented for a structure, consisting of both a three-dimensional closed part and a thin-walled part.

scholarly journals Multiscale boundary element method for Poisson’s equation

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Nor Afifah Hanim Zulkefli ◽  
Su Hoe Yeak ◽  
Munira Ismail
Keyword(s):  
Boundary Element Method ◽  
Numerical Solution ◽  
Boundary Element ◽  
Poisson Equation ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Numerical Example ◽  
The Poisson Equation ◽  
Method Show ◽  
Element Method

This paper applied the multiscale boundary element method for the numerical solution of the Poisson equation. The multiscale technique coupling with boundary element method will be used to solve the problem of Poisson equation efficiently and faster. Numerical example is given to illustrate the efficiency of the propose method. The solution of proposed method will be compared with boundary element method and the former method show less iteration in computation.

scholarly journals Using Boundary Element Method to Calculate the Bending Center of General Section

2019 ◽  
Vol 267 ◽  
pp. 02010
Author(s):  
Xinyan Tang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Numerical Example ◽  
Torsion Function ◽  
Transverse Bending ◽  
General Section ◽  
Element Method

Using Siant — Venant bending theory, transverse bending of a general section cylinder, it comes down to solving two boundary integral equations of the same type, the bending function and additional torsion function of the cylinder are obtained. On this basis, using boundary element method to determine the bending center of general section. Finally, to illustrate the application of the method, a numerical example is given.

Mould cooling simulation for injection moulding using a fast boundary element method approach

2009 ◽  
Vol 224 (4) ◽  
pp. 653-662 ◽  
Author(s):  
H Zhou ◽  
Y Zhang ◽  
J Wen ◽  
S Cui
Keyword(s):  
Heat Conduction ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Injection Moulding ◽  
Heat Conduction Problem ◽  
Solution Time ◽  
Combination Method ◽  
Dynamic Allocation ◽  
Actual Problem ◽  
Element Method

The existing cooling simulations for injection moulding are mostly based on the boundary element method (BEM). In this paper, a fast BEM approach for mould cooling analysis is developed. The actual problem is decoupled into a one-dimensional transient heat conduction problem within the thin part and a cycle-averaged steady state three-dimensional heat conduction problem of the mould. The BEM is formulated for the solution of the mould heat transfer problem. A dynamic allocation strategy of integral points is proposed when using the Gaussian integral formula to generate the BEM matrix. Considering that the full and unsymmetrical influence matrix of the BEM may lead to great storage space and solution time, this matrix is transformed into a sparse matrix by two methods: the direct rounding method or the combination method. This approximated sparsification approach can reduce the storage memory and solution time significantly. For validation, six typical cases with different element numbers are presented. The results show that the error of the direct rounding method is too large while that of the combination method is acceptable.

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