# The Solution of Foundation Mat Problems by Finite-Element Methods

*Synopsis
In the finite-element method of structural analysis stiffness matrices are derived after a displacement form has been assumed. These element stiffness matrices are then combined in order to get the solution for the whole structure. For isotropic and orthotropic plates several authors 1-4 have derived satisfactory element stiffness matrices for plates supported in various ways. This present paper extends the range of the method by deriving stiffness matrices for plates, which include the effect of an elastic foundation, for two of the assumed displacement forms. A stiffness matrix
for a beam on an elastic foundation is also presented. The effect of the foundation is assumed to consist of two parts: (a) the spring type reaction which is directly proportional to the displacement and (b) a spring-coupling action which simulates shear resistance in the foundation. The correctness of the stiffness matrices is adduced by comparison of calculated results obtained by their use with experimentally obtained values and, where possible, with values calculated by other theoretical methods. Brief details are given of an Algol computer programme which has been specially written for finite-element problems and which is capable of dealing with large-order matrices.
R.T. Severn*

Author(s): Severn, R T

Keywords: analysis;finite element methods;plates;stiffness