Estudo das descrições Lagrangiana e Euleriana na análise não-linear geométrica com o emprego do Método dos Elementos Finitos

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Study of the Lagrangian and Eulerian descriptions in geometrical nonlinear analysis with use of the finite element method

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Author(s):	Cristina Ferreira de Paula Total Authors: 1
Document type:	Master's Dissertation
Press:	São Carlos.
Institution:	Universidade de São Paulo (USP). Escola de Engenharia de São Carlos (EESC/SBD)
Defense date:	1997-05-12
Examining board members:	Sergio Persival Baroncini Proença; Marcio Roberto Silva Corrêa; Carlos Eduardo Nigro Mazzilli
Advisor:	Sergio Persival Baroncini Proença
Abstract
In this work, several conceptual aspects related to the mechanic-mathematical modeling for description of the geometrical nonlinear stuctural behavior are studied. First of all the Principle of Virtual Work is presented in order to characterize the equilibrium in the displaced position. Then, from the use of finite element method one analyses the Lagrangian and Eulerian forms which result from the adopted description of the motion. Stability of the structural response is treated by discussing the concepts of limit and bifurcation points. Finally, the incremental procedures in combination with the Newton schemes for solution of nonlinear equations and characterization of the singular points of equilibrium are studied. The numerical applications are related to the analysis of simple linear structures. (AU)