Influência de não linearidades física e geométrica no comportamento de placas retangulares
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2022-06-28
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Universidade Federal de Goiás
Resumo
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.
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AGUIAR, D. M. O. Influência de não linearidades física e geométrica no comportamento de placas retangulares. 2022. 80 f. Dissertação (Mestrado em Geotecnia, Estruturas e Construção Civil) - Universidade Federal de Goiás, Goiânia, 2022.