Estudo analítico-numérico de placas submetidas a ações pontuais e distribuídas em linha

Abstract

This work aims to discuss aspects of obtaining analytical and numerical solutions for plate problems, with or without elastic foundation support, subjected to point loads and/or line-distributed loads, using Kirchhoff and Mindlin plate theories. The analytical solutions for these problems were derived by manipulating the Dirac delta function (δ) for concentrated loads and the Heaviside function (H) for line distributions. Additionally, the strategies for obtaining the analytical solutions were based on the Levy and Navier methods. To enable numerical solutions for the plate problems, stiffness matrices associated with Winkler and Pasternak foundations were derived through mathematical manipulations compatible with the finite element formulations of DKT (Discrete Kirchhoff Triangle) and DST (Discrete Shear Triangle) elements, combined with linear or pseudo-consistent interpolations of transverse displacements within the element domain. Several analyzes were carried out involving different properties, boundary conditions and loading, the results of which were validated with analytical and/or numerical responses