The simple boundary element method for multiple cracks in functionally graded media governed by potential theory: a three-dimensional Galerkin approach

The simple boundary element method consists of recycling existing codes for homogeneous media to solve problems in non-homogeneous media while maintaining a purely boundary-only formulation. Within this scope, this paper presents a ‘simple’ Galerkin boundary element method for multiple cracks in problems governed by potential theory in functionally graded media. Steady-state heat conduction is investigated for thermal conductivity varying either parabolically, exponentially, or trigonometrically in one or more co-ordinates. A three-dimensional implementation which merges the dual boundary integral equation technique with the Galerkin approach is presented. Special emphasis is given to the treatment of crack surfaces and boundary conditions. The test examples simulated with the present method are verified with finite element results using graded finite elements. The numerical examples demonstrate the accuracy and efficiency of the present method especially when multiple interacting cracks are involved