A boundary element method for solving 2-D and 3-D static gradient elastic problems Part II: Numerical implementation

The boundary element formulation for the static analysis of two-dimensional (2-D)and three-dimensional (3-D)solids and structures characterized by a gradient elastic material behavior developed in the first part of this work, is treated numerically in this second part for the creation of a highly accurate and efficient boundary element solution tool. The discretization of the body is restricted only to its boundary and is accomplished by the use of quadratic isoparametric three-noded line and eight-noded quadrilateral boundary elements for the 2-D and 3-D cases, respectively. Advanced algorithms are presented for the accurate and efficient numerical computation of the singular integrals involved. Numerical examples involving a cylindrical bar in tension and a cylinder and a sphere in radial deformation are solved by the proposed boundary element method and the results are found in excellent agreement with the derived by the authors analytical solutions. The bar and sphere problems are solved in a 3-D context, while the cylinder problem is solved in a 2-D context (plane strain). Both the exterior and interior versions of the cylinder and sphere problems are considered.