![]() |
Computational & Technology Resources
an online resource for computational,
engineering & technology publications |
Civil-Comp Proceedings
ISSN 1759-3433 CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 254
Analytical Axisymmetric Finite Elements with Green-Lagrange Strains P. Pedersen
Department of Mechanical Engineering, Solid Mechanics, Danish Technical University, Lyngby, Denmark Full Bibliographic Reference for this paper
P. Pedersen, "Analytical Axisymmetric Finite Elements with Green-Lagrange Strains", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 254, 2004. doi:10.4203/ccp.79.254
Keywords: axisymmetric, analytical FE, Green-Lagrange strains, anisotropy, stiffness matrix.
Summary
Axisymmetric finite element analysis is of major importance in mechanical and
civil engineering. Pressure vessels, shafts, plates, shells, cylinders, etc. can
often be modeled axisymmetric, and some of these models can not adequately be
limited to strains that are linear depending on displacement gradients. The
present paper is a follow up on a similar paper [1],
restricted to plane problems.
Separating the dependence on the material constitutive parameters and on the stress-strain state from the dependence on the initial geometry and the displacement assumption, we obtain analytical secant and tangent element stiffness matrices. For the case of a linear displacement ring-element with triangular cross-section, closed form results are listed, directly suited for coding in a finite element program. As an example of application, numerical results for a circular plate problem show the indirect errors that may result from a linear strain model. The nodal positions of an element and the displacement assumption give six basic matrices that do not depend on material and stress/strain state, and thus are unchanged during the necessary iterations for obtaining a solution based on Green-Lagrange strain measure. The resulting stiffness matrices are especially useful in design optimization, because this enables analytical sensitivity analysis. Why these efforts to give an alternative stiffness evaluation, when well established numerical integration and fast computers can do the job? For research within optimal design the sensitivity analysis is of major importance. We need to answer questions like: Change in response for change in material parameters? Change in response for change in boundary shape? With the presented matrices these questions can be answered analytically without the difficult choice of a proper finite difference approach. For sensitivity analysis robustness is more important than computer-time, so saving computer-time is not the motivation. The present formulation follows the basic matrix approach in [2] for small strains. This means that the element geometry, the element orientation, the element nodal positions, and the displacement assumption are described by a few basic matrices that do not depend on material and stress/strain state. Material parameters and displacement gradients together give factors, so that linear combinations of the basic matrices determine the needed stiffness matrices.
As stated in textbooks, like in [4] and in
[3] a rigid rotation References
purchase the full-text of this paper (price £20)
go to the previous paper |
|