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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 24
ADVANCES IN NON-LINEAR FINITE ELEMENT METHODS
Edited by: B.H.V. Topping and M. Papadrakakis
Paper II.4

A Numerical Approach to Exact Finite Elements in Nonlinear Analysis of Bar Structures

Z. Waszczyszyn and M. Janus-Michalska

Institut Metod Komputerowych w Inzynieri Ladowej, Cracow University of Technology, Poland

Full Bibliographic Reference for this paper
Z. Waszczyszyn, M. Janus-Michalska, "A Numerical Approach to Exact Finite Elements in Nonlinear Analysis of Bar Structures", in B.H.V. Topping, M. Papadrakakis, (Editors), "Advances in Non-Linear Finite Element Methods", Civil-Comp Press, Edinburgh, UK, pp 47-53, 1994. doi:10.4203/ccp.24.2.4
Abstract
Exact Finite Elements (EFE) are formulated without "a priori" assumed shape functions. Matrices of EFE are obtained as a result of numerical integration of a complete set of field equations which constitute 2-Point Boundary Value Problem (2P-BVP). EFEs have been successfully applied to the linear buckling analysis of bar structures and axisymmetric plates and shells. In the paper incremental set of ordinary differential equations of 2P-BVP has been formulated for finite deflections of elastic and elastic-plastic framed structures. Numerical analysis points out great efficiency of EFEs in case of elastic columns, beams and frames under spatially fixed and follower loads. First results obtained for elastic-plastic structures reveal great possibilities of EFEs application.

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