Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Positional description for nonlinear 2-D static and dynamic frame analysis by FEM with Reissner Kinematics

D.N. Maciel*, H.B. Coda
Escola de Engenharia de São Carlos, Universidade de São Paulo Av Trabalhador Sãocarlense, 400, São Carlos, SP 13566-960, Brazil

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This paper presents a simple formulation to treat large deflections in 2-D frames by the finite element method. The present formulation does not use the concept of displacement; it considers position as the real variable of the problem. The strain determination is done directly from the proposed positional concept. A non-dimensional space is created and relative configurations are used to directly calculate the strain energy and its derivatives at general points. The initial configuration is assumed as the basis of calculation, i.e. Hooke's law relates reference stress and engineering strain. Reissner Kinematics are employed, i.e. initial plane cross-sections remain plane after deformation and angles are independent of the slope of central line. Some static and dynamic examples are presented in order to show the accuracy of the proposed technique.

Keywords:  Geometric nonlinearity; Position description; Reissner Kinematics

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