Implementação da Teoria de Reissner para placas com método dos elementos de contorno em ambiente computacional orientado a objetos

Abstract

The solution of linear problems of plates for isotropic and homogeneous materials must be satisfied within the context of the respective governing differential equations. Due to the diversities in the structural configuration, such as unusual boundary conditions, the analytical approach becomes more complex. This work deals with the formulation of the boundary integral equation of the bending plate problem taking into account the Reissner's theory and the numerical solution by means of the boundary element method (BEM). The Reissner's theory considers the strain energy not only from bending deformation but also from transversal shear deformation which leads to a partial differential equation of sixth order. It results in a more consistent numerical procedure in which three physical conditions along the boundary plate can be enforced. The implementation has been performed as an extension of a computational system based on object-oriented programming in Java called INSANE, developed at the Structural Engineering Department of UFMG. The current applications are focused in the analysis of at plate slabs with supports inside the domain, which is a very frequent problem in the design of structural reinforced concrete buildings. The efficiency and accuracy results obtained from several examples were compared with classical analytic solutions, numerical solution available in the literature and results of finite element analysis using Abaqus software as well.