Stress analysis of thin and thick plates on elastic foundations using boundary and finite element methods

摘要

In this work an attempt has been made to derive a fullfinite element and boundary element theory for the analysis ofthin and thick plates on elastic foundations. A new high ordershear finite element capable of the analysis of thin thick plateshas been derived using Hermitian and Lagrangian shape functions.Different new boundary element derivations for the analysis ofthin plates on elastic foundations are introduced using 3degrees-of-freedom per node. A full new derivation of boundaryelements for thick plates on elastic foundations using complexBessel functions is presented. Fourier and Hankel integraltransforms have been employed for the derivation of differentfundamental solutions required for boundary element analysis.Several techniques for dealing with singular and divergentintegrals encountered with boundary integral equations weredeveloped including the use of "Modified Kelvin Functions" andfictitious boundary concept. some case studies with differentloading and boundary conditions were tested and proved that thenew derivations presented in this work are correct and reliablefor the analysis of thin and thick plates on elastic foundations.