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bdryelem - EN224 Linear Elasticity Division of Engineering...

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EN224: Linear Elasticity Division of Engineering 3.3 The Boundary Element Method There is an important application of the singular solutions developed in Section 3.2. It is generally very difficult to find exact solutions to boundary value problems in linear elasticity, and we often resort to numerical techniques to obtain approximate solutions. The boundary element method is a particularly efficient numerical method, particularly for problems where no body forces act on the solid. There are two common varieties of the boundary element method: these are known as the so called `direct and `indirect formulations. The Indirect Boundary Element Method Suppose that we seek With on , Now, suppose we were to regard our region as a subregion of an infinite solid. Perhaps we could find a distribution of body forces in an infinite solid that would somehow satisfy all our boundary conditions? Surprisingly, this approach turns out to work, and is the basis for the indirect boundary element method. In fact, it turns out that one only needs to distribute body forces inside and on its boundary. Following standard Generated by www.PDFonFly.com at 1/10/2010 9:43:25 PM URL: http://www.engin.brown.edu/courses/en224/bdryelem/bdryelem.html
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notation, we will let denote this unknown body force distribution. We must clearly set within the solid. There is no simple way to determine on the boundary, but we note that we can express the displacement and stress fields in the solid as where denotes the normalized Kelvin state.
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