Boundary Element Analysis of Gradient Elastic Problems

A boundary element method (BEM), suitable for solving two dimensional (2D) and three dimensional (3D) gradient elastic problems under static loading, is presented. The simplified Form-II gradient elastic theory (a simple version of Mindlin’s Form II general gradient elastic theory) is employed and the corresponding fundamental solution is exploited for the formulation of the integral representation of the problem. Three noded quadratic line and eight noded quadratic quadrilateral boundary elements are utilized and the discretization is restricted only to the boundary. The boundary element methodology is explained and presented. The importance of satisfying the correct boundary conditions, being compatible with Mindlin’s theory is demonstrated with a simple example. Three numerical examples are reported to illustrate the method and exhibit its merits.