Computer Implementation of Boundary-Element <Emphasis FontCategory="NonProportional">Algorithms</Emphasis>: Fid-Bau Portal

Computer Implementation of Boundary-Element Algorithms

Aleynikov†, Sergey M.

Abstract This chapter deals with practical implementation of the developed numerical algorithms and substantiation of the reliability of the numerical solutions. It presents the general characteristics and structure of the Rostwerk software package for investigating three-dimensional stress-strained states of elastic bases corresponding to the interaction of foundation structures with soil under force factors of general kind. Procedures for creating input databases are described in detail. Algorithms and modules for automatic formation of boundary element grids in plane and in space are presented. An original algorithm for triangulation of flat single – and multiply connected domains, bounded by straight line segments or circle arcs, is described. An algorithm of generation (according to the given triangulation) of dual polygonal boundary element grids of Dirichlet cell type is considered. The created object library of boundary element modules, partitioned into boundary elements, enabling spatial discretization of complex-shaped surfaces of foundation structures, is described. Specific features of solving the systems of linear algebraic equations with asymmetric and close-packed matrices, arising in boundary element analysis, are considered. For solving such systems by direct (Gauss type) methods a special scaling procedure is applied, improving the conditioning of matrices for the finite-dimensional algebraic analogue of a contact problem. The data about the reliability of the numerical solutions are presented. The boundary-element method accuracy and efficiency are demonstrated by the examples of the solved test problems for flat punches of circular, annular and polygonal shapes. Boundary-element solutions for spatial contact problems concerning a rigid spherical inclusion and a cylindrical deepened punch in an elastic half-space are obtained. The final part of the chapter gives the results for numerical-and-analytical solution of the spatial contact problem on impressing a deepened conical punch into an elastic half-space. The method of determination of the deformation modulus from tests for deepened conical indenters with different angles by static loading is substantiated theoretically.