Collocation BEM for 3D Lame Equation

Download CBEM_LAM, a package for solving the 3D Lamé equation based on a piecewise constant Collocation Boundary Element Method, and employing a boundary-only discretization technique.

Piecewise constant collocation method

The displacement and traction are assumed to be constant over each boundary element. It can be shown (see e.g. [2]) that the elastic potentials

and

due to a uniform distribution over a flat triangle can be employed to successfully compute and on . In addition, these potentials can be utilized to effectively calculate the displacement at interior points The analytic expressions for and over a flat triangle are given in [1]. Moreover, due to its boundary representation, the elastic Newton potential can also be effectively evaluated without the need of a volume-fitted mesh [2]. A brief description of the boundary-only discretization of the elastic Newton potential can be found in the user guide cbem_lamGuide.pdf provided in the package CBEM_LAM.

References

[1] S. Nintcheu Fata.
Explicit expressions for three-dimensional boundary integrals in linear elasticity.
J. Comput. Appl. Math., 235(15):4480-4495, 2011.
[2] S. Nintcheu Fata.
Boundary integral approximation of volume potentials in three-dimensional linear elasticity.
J. Comput. Appl. Math., 242(1):275-284, 2013.