Boundary elements and the analog equation method for the solution of elastic problems in 3-D non-homogeneous bodies

• The elastic problem in 3D domains with functionally varying elastic properties is solved.
• The Boundary Elements and the Analog Equation Method is employed.
• ATPS-2D Radial Basis Functions are used to interpolate domain unknowns.
• Quadratic isoparametric boundary elements has been used.
• Accuracy and stability of the numerical procedure is investigated.

The application of the Boundary Element Method (BEM) to elastostatic problems involving 3D non-homogeneous materials like Functionally Graded Materials (FGMs) is presented in this paper. The Analog Equation Method (AEM) is used to transform the original problem into a new problem with unknown fictitious source but known Fundamental Solution. By means of this transformation a system of uncoupled Domain/Boundary Integral Equations (D/BIEs) is first obtained, combining standard Boundary Element discretization and Radial Basis Functions (RBFs) approximation for the fictitious source. The application of the original differential operator to the displacement BIE provides the extra equations to compute the unknown fictitious source. The boundary character of the method is maintained since the integrals involved in the equations are limited only to the boundary since the RBFs are selected in such a way that the corresponding analog equation could be solved analytically. Numerical examples for three-dimensional problems in continuously non-homogeneous, isotropic and linear elastic FGMs are presented and discussed.