Foundation Interaction Problems Involving an Elastic Half-Plane

摘要

Stress analysis problems involving interaction between a structure and its foundation often lead to extensive computational effort. This fact becomes obvious when finite-element methods are used to study problems where the foundation is idealized as an infinite elastic half-plane. Attempts to represent the half-plane by a finite size structure using many elements entail solving large systems of simultaneous equations at a considerable computational cost. This report presents a more computationally efficient procedure which employs the exact solution of the equations of elasticity for an elastic half-plane subjected to arbitrary surface loading. Complex variable formulations are shown to yield a compact solution for the stresses and displacements in a half-plane supporting several concentrated loads. This solution is also employed to compute flexibility and stiffness matrices relating the concentrated loads and the displacements at the points of application of the loads. The stiffness matrix derived in this manner is then employed to investigate a simple type of interaction problem where an Euler beam rests on an elastic half-plane and is subjected to external loading. The foundation interaction forces, as well as other quantities such as beam shear and moment, are also computed.