boundary element method

http://orbilu.uni.lu/handle/10993/17878

http://hdl.handle.net/10993/17878

Sponsored by the National Science Foundation and the NSF Institute for Mathematics and its Applications, the University of Minnesota (Minneapolis, Minnesota, USA) is hosting a workshop on the boundary element method (BEM) April 23-26, 2012. This workshop consists of a two-day short course and a two-day colloquium on advances in the BEM with educational and industrial applications. Researchers and engineers from around the world, as well as students (both graduate and undergraduate) are invited to participate in this workshop.

Do you want to learn the boundary element method (BEM) and the latest fast solution methods from the experts around the world? If yes, come and attend the workshop on the BEM in September.

I am working on some boundary integral equation formulation and I am currently stuck with some mathematics. I wish anyone can help me out with this. 

I have an anisotropic (sometimes called generalized) biharmonic differential operator which  takes the form

L = k11 D1^4 +  k12 D1^2 D2^2 + k22 D2^4 

where D1 = d/dx, D2 = d/dy, my problem is two dimensional.

I need to find a fundamental solution (Green's function) for this operator, that is 

L(u) = -delta

where delta is Dirac delta function.

Might also be useful for simulating dislocation motion in a finite body.

Several sets of boundary integral equations for two dimensional elasticity are derived from Cauchy integral theorem.These equations reveal the relations between displacements and resultant forces, between displacements and tractions, and between the tangential derivatives of displacements and tractions on solid boundary.Special attention is given to the formulation that is based on tractions and the tangential derivatives of displacements on boundary, because its integral kernels have the weakest singularities.The formulation is further extended to include singular points, such as dislocations and line forces, in a finite body, so that the singular stress field can be directly obtained from solving the integral equations on the external boundary without involving the linear superposition technique often used in the literature. Body forces and thermal effect are subsequently included. The general framework of setting up a boundary value problem is discussed and continuity conditions at a non-singular corner are derived.  The general procedure in obtaining the elastic field around a circular hole is described, and the stress fields with first and second order singularities are obtained. Some other analytical solutions are also derived by using the formulation.