Boundary Integral Methods for Thermoelasticity Problems

1986 ◽  
Vol 53 (2) ◽  
pp. 298-302 ◽  
Author(s):  
S. Sharp ◽  
S. L. Crouch
Keyword(s):  
Heat Flow ◽  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Thermally Induced ◽  
Flow Problems ◽  
Boundary Integral Methods ◽  
Integral Methods ◽  
Transient Heat Flow ◽  
Induced Stresses

The boundary integral method for solving transient heat flow problems is extended to calculate thermally induced stresses and displacements. These results are then corrected by means of an elastostatic solution to satisfy the boundary conditions.

scholarly journals Non-singular boundary integral methods for fluid mechanics applications

2012 ◽  
Vol 696 ◽  
pp. 468-478 ◽  
Author(s):  
Evert Klaseboer ◽  
Qiang Sun ◽  
Derek Y. C. Chan
Keyword(s):  
Stokes Flow ◽  
Integral Method ◽  
Practical Interest ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Singular Boundary ◽  
Boundary Integral Methods ◽  
Integral Methods ◽  
Weakly Singular ◽  
Principal Value

AbstractA formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad applicability of the approach is illustrated with a number of problems of practical interest to fluid and continuum mechanics including the solution of the Laplace equation for potential flow, the Helmholtz equation as well as the equations for Stokes flow and linear elasticity.

scholarly journals Springs, Formulas and Flatland:A Path to Boundary Integral Methods in Elasticity

2007 ◽  
Vol 1 (1) ◽  
Author(s):  
Frank J. Rizzo
Keyword(s):  
Boundary Value Problems ◽  
Computational Methods ◽  
Integral Method ◽  
Early Period ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Research Experience ◽  
Boundary Integral Methods ◽  
Long Period ◽  
Integral Methods

This memoir is about some embryonic thoughts and experiences with what is now often called the Direct Boundary Integral Method for boundary value problems in ‘classical elastostatics.’ It covers a very early period for me, from about 1954 to 1965, when I wrestled with relevant theoretical and mathematical issues, which I thought were important, primarily in the last two or three of those years. This was before I became aware of other contributors to the method, who are not mentioned here, and before they became aware of my work. So this is not a memoir largely filled with recollections of people and places; although I believe that subsequent interactions with fellow contributors and users of computational methods have become the most important part of my research experience. In any case, I understand that memoirs and papers of a more technical nature, written by some of those contributors, are part of these EJBE volumes. Those writings have bearing, no doubt, on the present memoir and much more, over a long period of time, and I look forward to reading them all....

A Fast Accurate Boundary Integral Method for Potentials on Closely Packed Cells

2013 ◽  
Vol 14 (4) ◽  
pp. 1073-1093 ◽  
Author(s):  
Wenjun Ying ◽  
J. Thomas Beale
Keyword(s):  
Integral Method ◽  
Fast Multipole Method ◽  
Surrounding Medium ◽  
Integral Kernel ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Poisson Solver ◽  
Integral Methods ◽  
Electric Potentials

AbstractBoundary integral methods are naturally suited for the computation of harmonic functions on a region having inclusions or cells with different material properties. However, accuracy deteriorates when the cell boundaries are close to each other. We present a boundary integral method in two dimensions which is specially designed to maintain second order accuracy even if boundaries are arbitrarily close. The method uses a regularization of the integral kernel which admits analytically determined corrections to maintain accuracy. For boundaries with many components we use the fast multipole method for efficient summation. We compute electric potentials on a domain with cells whose conductivity differs from that of the surrounding medium. We first solve an integral equation for a source term on the cell interfaces and then find values of the potential near the interfaces via integrals. Finally we use a Poisson solver to extend the potential to a regular grid covering the entire region. A number of examples are presented. We demonstrate that increased refinement is not needed to maintain accuracy as interfaces become very close.

A Combined Boundary Integral Method for Analysis of Crack Problems in Multilayered Elastic Media

2016 ◽  
Vol 08 (05) ◽  
pp. 1650070 ◽  
Author(s):  
Gongbo Long ◽  
Guanshui Xu
Keyword(s):  
Integral Method ◽  
Crack Tip ◽  
Boundary Integral ◽  
Thin Layers ◽  
Boundary Integral Method ◽  
Displacement Discontinuity ◽  
Elastic Media ◽  
Integral Methods ◽  
Crack Problems ◽  
Comparable Accuracy

An efficient and accurate elastic analysis based on boundary integral methods is presented for crack problems in inhomogeneous elastic media consisting of a set of individually uniform strata. The method combines the direct boundary integral method (DM) and the displacement discontinuity method (DDM) so that it shares both the efficiency of the DDM and the broad applicability of the DM. The DDM is implemented to construct the stiffness matrix in each layer, while the DM is used to characterize the effects of the interfaces. All the variables on the interfaces can then be eliminated through the continuity conditions, leading to the final system of equations consisting of variables on crack surfaces only. The concept of the crack tip element is also adopted for a better treatment of the crack tip singularity. The examples demonstrate that the combined method has comparable accuracy of DM but is more efficient, especially for the scaled thin layers in the application of practical hydraulic fracturing simulations.

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