Análise de vigas anisotrópicas, funcionalmente graduadas e compósitas laminadas apoiadas em base elática Winkler – Pasternak

Abstract

Beams supported on elastic foundations are widely used in engineering projects. Therefore, the analysis of the displacements suffered by them when supported on an elastic base is extremely important. It is also known that laminated composite beams, as well as functionally graded beams, can provide desirable properties such as stiffness and strength. Therefore, the present work presents solutions for the deflection of anisotropic, laminated and functionally graded composite beams on elastic foundations of the Winkler-Pasternak type, from the coupling between stretching, shearing, bending and twisting. The proposed formulation is based on the Euler-Bernoulli beam theory and the equations that describe the problem and the boundary conditions are derived from the principle of virtual work. The direct integration method can be used to decouple the deflections from axial displacement and torsion. Subsequently, the system of deflection equations decoupled in two principal directions is transformed into a first-order system. The solution of this system of equations is obtained through the parameters variation method, applying the fundamental matrix concept. The validation of the results found for the bending behavior of beams on elastic foundations is carried out by comparing them with the results available in the literature.