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CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 161
Different Enhanced Assumed Strain Formulations for Large Rotation Analysis of Shells B. Brank
Faculty of Civil and Geodetic Engineering, University of Ljubljana, Slovenia B. Brank, "Different Enhanced Assumed Strain Formulations for Large Rotation Analysis of Shells", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 161, 2006. doi:10.4203/ccp.83.161
Keywords: finite element shell modelling, fournode shell element, enhanced assumed strain method.
Summary
Since the initial work of Simo and Rifai [1] many finite elements based on the enhanced assumed strain (EAS)
method have been developed. As concerning shell formulations, the EAS method
has been basically been used in two different manners: (i) to obtain shell and solidshell
formulations that account for throughthethickness stretching, and (ii) to obtain
shell and solid shell elements with improved membrane performance. Many linear
and nonlinear EAS shell formulations (elements) have been presented, see for example VuQuoc and Tan [2] and the references therein.
In approach (i) the authors used the EAS method to introduce the throughthethickness stretching parameter. Doing so, they derived attractive higherorder sevenparameter shell or solidshell formulations, which are suitable for easy implementation of threedimensional hyperelastic and elastoplastic constitutive equations. On the other hand, in approach (ii) the authors used the EAS method to improve the inplane behaviour of higherorder shell or solidshell elements or the membrane behaviour of standard fiveparameter shell elements. In this work we conentrate on fiveparameter shell elements based on the shell theory with ReissnerMindlin kinematics. We are interested in a robust geometrically exact fournode quadrilateral finite element for nonlinear and large rotation analysis that can give good results even for coarse and distorted meshes. We look for an element that could be effectively used in nonlinear shell shape optimization problems, see for example Kegl and Brank [3], where many iterations are required to obtain an optimized shape, and meshes may become very distorted during the optimization process. To that end, performance of the shell fournode finite element, which uses an assumed natural strain (ANS) concept to avoid the shear locking and displacement formulation for the membrane and the bending parts of the corresponding functional, is improved by the use of the EAS method. Within the EAS method both the membrane and the bending strains of the element are enhanced. In order to check for an optimal fournode EASANS shell element, several possibilities for an enahncement of membrane and bending strains have been studied and coded. In contrast to the usual approach, we make an enhancement of both the membrane and the bending strains. Four, five or seven parameters are used to define enhanced membrane strains, and the same number of parameters is used to enhance the bending strains. For the transverse shear strains the ANS method is used. To obtain derivatives of the corresponding EAS functionals with respect to the independent finite element parameters, we used symbolic manipulation and an automatic differentiation tool developed by Korelc [4]. Numerical examples show that an enhancement of the bending strains does not improve the performance of a fournode shell finite element for a typical bending dominated problem. They also show that four enhancement parameters are not enough, and that five and seven enhancement parameters give equal numerical results. References
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