Static and dynamic stability for geometrically nonlinear governing equations of elastic thin shallow shells

Autor:	Fan Jiashen
Rok vydání:	2001
Předmět:	Dynamic problem Geometrically nonlinear Deflection (engineering) Modeling and Simulation Modelling and Simulation Applied Mathematics Mathematical analysis Duffing equation Algebraic number Galerkin method Fourier series Cubic function Mathematics
Zdroj:	Applied Mathematical Modelling. 25(9):775-792
ISSN:	0307-904X
DOI:	10.1016/s0307-904x(01)00013-0
Popis:	In this study, the governing equations for large deflection of elastic thin shallow shells are deduced into an algebraic cubic equation to determine the unknown coefficient of the assumed deflection by applying Galerkin's method in combination with the algebraic polynomial and Fourier series. For the dynamic problem, the coefficient is replaced by an unknown function of time; after the same process is applied, the governing equations are deduced to be a nonlinear ODE of order two called the Duffing equation, and its analytical solution is known. The combination of the algebraic polynomial and Fourier series gives very rapid convergence in the asymptotic solutions.
Databáze:	OpenAIRE
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