Ανάλυση ελαστικά εδραζόμενων δοκών με τη μέθοδο των πεπερασμένων στοιχείων

Abstract

This diploma thesis studies the behavior of beams resting on elastic foundation. It provides a brief overview of the foundation models based on Winkler s original foundation model, as well as a detailed analysis of beams resting on Winkler’s foundation using the finite element method. The numerical implementation is achieved by the finite element method and developing for this purpose a process in EXCEL. The analysis of beams resting on elastic medium has attracted a considerable attention for a prolonged period of time. Many engineering mechanics problems have been modeled as beams resting on an elastic medium. Typical examples are the combination of footings and mat foundations, laterally loaded piles, railway tracks, etc. The solution of beams resting on elastic foundation is a statically indeterminate problem in mechanics. In this case, we have the beam on an elastic base along its entire bottom surface or just a part of it. In some cases, the theoretical approach and its solution may become very complicated or impossible, so alternatively the problems can be solved by numerical methods such as the finite element method (FEM) or the boundary element method (BEM). In the thesis at hand, the analysis of beams on elastic foundation is performed using the finite element method (FEM). The beam system is discretized into elements, allowing a movement and a rotation at each node using the theory of small deformations. Several examples are presented and complex frame structures have been \nstudied in order to demonstrate the effect of the elastic foundation on the behavior of the whole model.