Application of the boundary element method to plates on elastic foundations.

摘要

The boundary element method has emerged in the last two decades as a powerful numerical computational tool for the solution of plate bending problems. this thesis develops a general approach for the boundary element analysis of the interaction between elastic thin plates and elastic foundations. Foundation models studied include the elastic half-space, the Winkler foundation and edge supports. Corner lift-off and edge singularity conditions are considered.; In the analysis of plates on elastic foundations, the plate and the foundation are treated as two separate elastic bodies in unilateral contact at the interface. The behavior of the elastic plate under both the external loads and the contact pressure is modelled by the direct boundary integral equation formulation. The contact pressure between the plate and the foundation is modelled by contact elements. Boussinesq's solution is used to determine the flexibility matrix of the elastic half-space. The displacement compatibility conditions between the plate and the foundation are enforced at contact element nodes.; In the case of plates unilaterally edge supported, the contact pressure between the plate and the elastic edge supports are treated as the plate boundary variables, which are included in the boundary integral equation directly. Thus, no contact elements are required for this particular case of elastic foundation.