Equilibrium considerations of the updated Lagrangian formulation of beam‐columns with natural concepts

1 November 1987

journal article
research article
Published by Wiley in International Journal for Numerical Methods in Engineering

Vol. 24 (11) , 2119-2141
https://doi.org/10.1002/nme.1620241108

Abstract

Bathe and co‐workers'^1,2 updated Lagrangian formulation is reviewed for a two‐dimensional beam‐column element. From this review a physical interpretation and properties are derived for the matrices of the method. A variant of Argyris and co‐workers'^4,5 natural concept is introduced in the updated Lagrangian formulation, and a new method to derive element matrices arises. A detailed derivation of the matrices of the twodimensional beam‐column element is presented to clarify further the UL formulations. Explicit expressions for these matrices, computed with the use of symbolic manipulation,¹⁷ are also presented to illustrate the concepts discussed. Finally, numerical results are shown to compare and evaluate different methods and matrices.

Keywords

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