Application of symbolic algebra to the analysisof plates on variable elastic foundation

Abstract

The analysis of plates on elastic foundation is very common in engineering. Usually the Winklermodel is adopted, and it is assumed that the foundation stiffness is constant over the area of the plate. In many cases, such as large foundation mats and in vertical slurry walls, the foundation stiffness varies and approximate solutions are found. Using symbolic algebra, an approximate finite element displacement method is introduced to analyse the problem of plates on a variable Winkler elastic foundation. It is proposed to add to the conventional plate element stiffness matrix, another matrix that will account for the effect of the variable foundation. The solution using this approach is compared to the solutions which were obtained using other approximation techniques. With the proposed method the convergence is much faster, with fewer elements, and saves computer and data preparation time.