Static analysis of gradient elastic 3-D solids by BEM

A boundary element method is developed for the static analysis of three - dimensional solids and structures with a gradient elastic material behavior that takes into account microstructural effects. A simplified version of Mindlin's general theory of linear gradient elasticity is employed. A variational statement is established to determine all possible boundary conditions (classical and due to gradient terms). The gradient elastic fundamental solution is explicitly derived and used to construct the boundary integral representation of the solution. It is found that, in addition to a boundary integral representation for the displacement, a second boundary integral representation for its normal derivative is also necessary. Explicit expressions for interior displacements and stresses in integral form are also presented. The system of the two boundary integral equations is solved numerically with the aid of a discretization of the surface of the body into quadratic quadrilateral elements. Numerical examples involving a cylindrical bar in tension and a sphere in radial deformation (in both interior and exterior versions) are solved to illustrate the method and demonstrate its high accuracy.