Boundary integral, volume integral and combined formulations

1995 ◽  
pp. 353-394
Author(s):  
Nathan Ida
Keyword(s):  
Boundary Integral ◽  
Volume Integral

scholarly journals Thermal Stress Analysis of 3D Anisotropic Materials Involving Domain Heat Source by the Boundary Element Method

2019 ◽  
Vol 35 (6) ◽  
pp. 839-850
Author(s):  
Y. C. Shiah ◽  
Nguyen Anh Tuan ◽  
M.R. Hematiyan
Keyword(s):  
Boundary Element Method ◽  
Heat Source ◽  
Boundary Element ◽  
Thermal Stresses ◽  
Quadratic Function ◽  
Boundary Integral ◽  
Volume Integral ◽  
Direct Evaluation ◽  
Volume Heat ◽  
Element Method

ABSTRACTIn engineering applications, it is pretty often to have domain heat source involved inside. This article proposes an approach using the boundary element method to study thermal stresses in 3D anisotropic solids when internal domain heat source is involved. As has been well noticed, thermal effect will give rise to a volume integral, where its direct evaluation will need domain discretization. This shall definitely destroy the most distinctive notion of the boundary element method that only boundary discretization is required. The present work presents an analytical transformation of the volume integral in the boundary integral equation due to the presence of internal volume heat source. For simplicity, distribution of the heat source is modeled by a quadratic function. When needed, the formulations can be further extended to treat higher-ordered volume heat sources. Indeed, the present work has completely restored the boundary discretization feature of the boundary element method for treating 3D anisotropic thermoelasticity involving volume heat source.

A Volume Integral Equation Technique for Multiple Inclusion and Crack Interaction Problems

1997 ◽  
Vol 64 (1) ◽  
pp. 23-31 ◽  
Author(s):  
Jungki Lee ◽  
Ajit Mal
Keyword(s):  
Integral Equation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Interfacial Stress ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Integral Methods ◽  
Multiple Inclusion ◽  
Interface Layers ◽  
Volume Integral Equation Method

A volume integral equation method is introduced for the solution of elastostatic problems in heterogeneous solids containing interacting multiple inclusions, voids, and cracks. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions and cracks. The influence of interface layers on the interfacial stress field is investigated. The stress intensity factors for microcracks in the presence of interacting inclusions or voids are also calculated for a variety of model geometries. The accuracy and efficiency of the method are examined through comparison with results obtained from analytical and boundary integral methods.

Boundary Element Analysis of Interior Thermoelastic Stresses in Three-Dimensional Generally Anisotropic Bodies

2016 ◽  
Vol 32 (6) ◽  
pp. 725-735 ◽  
Author(s):  
Y.-C. Shiah ◽  
J.-Y. Chong
Keyword(s):  
Integral Equation ◽  
Stress Analysis ◽  
Boundary Element ◽  
Thermoelastic Stress ◽  
Boundary Integral ◽  
Thermoelastic Stress Analysis ◽  
Volume Integral ◽  
Element Analysis ◽  
Anisotropic Bodies ◽  
Thermoelastic Stresses

AbstractThis paper is to present the treatment of internal thermoelastic stress analysis in 3D anisotropic bodies by the boundary element method (BEM). Fundamentally, thermal effects will give rise to an additional volume integral in the boundary integral equation (BIE). By applying the fundamental solutions represented by Fourier series, the volume integral has been analytically transformed to the boundary. For the present work, spatial differentiations of the integral equation are performed to give displacement gradients at internal points of interest. This differentiated integral equation is further implemented to perform thermoelastic stress analysis inside 3D anisotropic bodies. This analysis is particularly important in engineering applications when thermoelastic stresses concentrations are present inside the bodies. The present work is the first BEM implementation for this study by the transformed BIE. In the end, two benchmark examples are tested to demonstrate the applicability of the present BEM treatment.

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