Dynamic Boundary Element Analysis of Machine Foundations

Abstract

The central theme of this thesis is the further development of boundary element methods for the analysis of three-dimensional machine foundations, pertaining to various (translational and rotational) modes of vibration and, in particular, to high frequency response. Surface and embedded rectangular foundations are considered. The soil is assumed to behave approximately as a linear elastic material for small amplitudes of strain. The problem is formulated and solved in the frequency domain. This work includes rigorous theoretical studies, effective numerical techniques for the solution of the boundary integral equations, and efficient computer implementation of the algorithm. The derivation of the boundary integral formulation is reviewed and the dynamic fundamental solutions are examined in detail. The particular fundamental solutions for incompressible media has been derived in order to deal more effectively with these materials. Advanced integration schemes for non-singular and singular integrals have been developed in order to improve the computational accuracy and efficiency of the boundary element analysis. A novel infinite boundary element for dynamic analyses has been developed, which provides an efficient means for including far-field effects, without the necessity of explicit discrete representation outside the near field. The implementation and vectorization of the computer program using the IBM 3090-150 Vector Facility is described. Various numerical results for rectangular foundations are presented in order to illustrate the potential of the infinite boundary element formulation. Included among these are new results pertaining to the high frequency response of machine foundations