Influência de não linearidades física e geométrica no comportamento de placas retangulares

• Main Author: Aguiar, Daniella Maria Oliveira
• Publication Date: 2022
• Format: Master thesis
• Language: por
• Source: Repositório Institucional da UFG
• Download full: http://repositorio.bc.ufg.br/tede/handle/tede/12217
• topic: Placas retangulares hiperelásticas; Modelo constitutivo neo-hookeano; Não linearidade física; Não linearidade geométrica; Hyperelastic rectangular plates; Neo-hookean constitutive law; Physical nonlinearity; Geometrical nonlinearity; ENGENHARIAS::ENGENHARIA CIVIL::CONSTRUCAO CIVIL

This work studies the influence of physical and geometric nonlinearities on the behavior of simply supported rectangular plates made of hyperelastic, isotropic, homogeneous, and incompressible material. In static analysis, geometrical nonlinearity is accounted for using two different theories to comparison - Novozhilov nonlinear theory and von Kármán nonlinear theory. The plate is under pressure loading that is described in two ways: distributed radial force (dead load) and displacement-dependent pressure (follower load or actual pressure). First the displacement field expansions are considered with three and twelve degrees of freedom, and then the Karhunen-Loève Method is applied to obtain a reduced order model. The pressuredisplacement responses are compared with those of other papers to validate the formulations. And, again using the pressure-displacement responses, the differences depending on the characteristics of the formulation employed are discussed and the solution obtained by the reduced order model is compared with the solution of the original system. In the dynamic analysis, the geometrical nonlinearity is described through von Kármán nonlinear theory, dead load pressure is applied, and the displacement field expansions are derived from the KarhunenLoève Method. The transverse frequency-displacement responses around various initial static configurations are examined. In both static and dynamic analyses, the physical nonlinearity is accounted for by the hyperelastic Neo-Hookean constitutive law, and the equations of motion are derived using Hamilton's Principle, the Rayleigh-Ritz method, and the local model method (MML). The Newton-Raphson method, adapted due to the MML, is used to solve the equations of motion. It is observed that the use of the reduced model gives satisfactory results and that the influence of nonlinearities, both physical and geometrical, are predominant when the plate is subjected to high amplitude displacements.