Aplicação do polinômio de Hermite-Caos para a determinação da carga de instabilidade paramétrica de cascas cilíndricas com incerteza nos parâmetros físicos e geométricos
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2014-04-04
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Universidade Federal de Goiás
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The present study aims to investigate the influence of uncertainties in physical and geometric parameters to obtain the load parametric instability of cylindrical shell, using the Galerkin method with the stochastic polynomial Hermite-Caos. The nonlinear equations of motion of the cylindrical shell are deduced from their functional power considering the strain field proposed by Donnell´s nonlinear shallow shell theory. The uncertainties are considered as random parameters with probability density function known in the partial differential equation of motion of the cylindrical shell, which it becomes a stochastic partial differential equation due to the presence of randomness. First, the discretization of the stochastic problem is performed using the stochastic Galerkin method together with polynomial Hermite-Chaos, to transform the stochastic partial differential equation into a set of equivalent deterministic partial differential equations, which take into account the randomness of the system. Then, the discretization of the lateral field displacement is made by a perturbation procedure, indicating the nonlinear vibration modes which couple to the linear vibration mode. The set of partial differential equations is transformed into a deterministic system of equations deterministic ordinary second order in time. Uncertainty is considered in one of its parameters: the Young modulus, thickness and amplitude of initial geometric imperfection. Then we analyze the influence of randomness in two parameters simultaneously: the thickness and the Young modulus. Once obtained the system of ordinary differential equations deterministic containing the randomness of the parameters, the integration over discrete time system is made from the Runge- Kutta fourth order to obtain results as the time response, bifurcation diagrams and
boundaries of instability which are compared with deterministic analysis, indicating that
polynomial Hermite-Chaos is a good numerical tool for predicting the load parametric
instability without the need to perform a process of sampling.
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BRAZÃO, A. F. Aplicação do polinômio de Hermite-Caos para a determinação da carga de instabilidade paramétrica de cascas cilíndricas com incerteza nos parâmetros físicos e geométricos. 2014. 93 f. Dissertação (Mestrado em Geotecnia, Estruturas e Construção Civil) - Universidade Federal de Goiás, Goiânia, 2014.