Estudo e desenvolvimento de código computacional para análise elástica-linear de vigas de Euler-Bernoulli sobre apoios elásticos contínuos via método dos elementos finitos

Abstract

The main focus of this work is a linear-elastic analysis of Euler-Bernoulli beams on continuum elastic foundation through Finite Element Method. It is presented the deduction of the stiffness matrix, with the contribution of the continuum elastic foundation, and the nodal loads vector for a beam element composed by two nodes, each one with two degrees of freedom: vertical displacement and cross-section rotation. The approximation functions that allows to discretize the fields of displacement along each element is a third degree function. Examples have been simulated to validate the computational code developed in this work. As results, the code generates the displacement and cross-section rotation along the beam, shear force, bending moment and support reactions.