Finite Element Static Analysis of Slabs on Elastic Foundation

Abstract

The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for partial differential equations. It uses subdivision of whole problem domain into simpler parts, called finite elements, and variational methods from the calculus of variations to solve the problem by minimizing the associated error function. Analogous to the idea that connecting many tiny straight lines can approximate a larger circle, FEM encompasses methods for connecting many simple element equations over many small subdomains, named finite elements, to approximate a more complex equation over a larger domain. Concrete building slabs (plates), upheld directly by the soil medium, is a common construction form. It is utilized as a part of private, business, mechanical, and institutional structures. In some of these structures, substantial slab loads occur, for example, in libraries, grain stockpiling structures, distribution centres, and so forth. A mat foundation, which is usually utilized as a part of the supporting of multi-story building sections, is another illustration of a vigorously loaded concrete slab supported directly by the soil medium. In every one of these structures, it is vital to compute slab displacements and consequent stresses with a worthy level of precision so as to guarantee a sheltered and practical configuration. This project presents a finite element static analysis for estimating the structural behaviour of plates resting on elastic foundations, described by the Winkler’s Model. A Matlab program computing the displacement and stresses for slabs on elastic foundation has been presented in the appendix.