Estudo da validade da hipótese de Kirchhoff-Love na Teoria das Placas

Abstract

Equations and boundary conditions from the classical theory due to Kirchhoff-Love and the refined Reissner theory were obtained by using the linear theory of elasticity and standard energy variational principles. Analytical expressions of deflections and resultant stresses are treated for rectangular plates subjected to transverse uniformly distributed loadings considering the following boundary conditions: Case 1 - Four simply supported edges. Case 2 - Two simply parallel supported edges and two parallel clamped edges. Case 3 - Two simply parallel supported edges and two parallel free edges. We obtain numerical results which are presented in tables and graphs from a digital program by using analytical expressions. The analysis of the numerical results that we obtained by both theories allow us to stablish certain values for the relation h/a where h is the thickness of the plate and a the lenght of a side of the plate, from here on is not possible to use any more a classical theory due to Kirchhoff-Love. We analyse the perturbations which appear near to the boundary and corners of the plate, which arose from the difference between the two theories, according to the number of boundary conditions per each boundary. The equations of Hencky's theory are presented in appendix A.