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Convected systems for curved structural elements
Author(s) -
Gattass Marcelo,
Abel John F.
Publication year - 1987
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620241109
Subject(s) - curvilinear coordinates , element (criminal law) , cartesian coordinate system , computation , lagrangian , finite element method , mathematics , coordinate system , geometry , mathematical analysis , algorithm , engineering , structural engineering , political science , law
This paper presents a new approach to the use of the updated Lagrangian formulation with convected systems. The development of this new method is similar to the updated Lagrangian formulation presented by Bathe et al. 4 The main difference is that here the tensors are written in their components in the curvilinear convected system, while Bathe, Ramm, and Wilson employ Cartesian components. A special form of the natural approach 5 is also introduced in this formulation to simplify the element computations. The matrices of a two‐dimensional curved beam‐column element are derived as an example of this new formulation. Finally, a numerical evaluation is performed to evaluate critically the new curved element and the method proposed here.