Numerical Solution of Rafts on Visco-Elastic Media Using Laplace Transforms.

摘要

In this paper problems of a raft on a viscoelastic half-space are converted to equivalent elastic problems by means of a Laplace transformation,and a numerical solution is obtained by finite element techniques. It is shown that the solution can be expressed in terms of an eigenvector expansion,and this solution is then transformed back to obtain a numerical solution to the original problem. One advantage of this form of solution is that it applies to any visco-elastic model,any relative raft-soil stiffness and any load pattern. The method allows an explicit solution to the original problem when the creep function can be modelled by springs and dashpots,and allows the solution of the problem to be reduced to a series of Volterra integral equations for the case of creep functions which cannot be modelled in this way. The method is illustrated by results for rectangular and circular rafts,and particular attention is paid to a realistic soil creep function which is asymptotic to a linear function of log time.