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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 99
Edited by: B.H.V. Topping
Paper 187

Efficient Linear and Non-Linear Finite Element Formulation using a New Local Enhancement of Displacement Fields for Triangular Elements

L. Damkilde and R.R. Pedersen

Department of Civil Engineering, Aalborg University, Esbjerg, Denmark

Full Bibliographic Reference for this paper
L. Damkilde, R.R. Pedersen, "Efficient Linear and Non-Linear Finite Element Formulation using a New Local Enhancement of Displacement Fields for Triangular Elements", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 187, 2012. doi:10.4203/ccp.99.187
Keywords: incompatible element, material non-linear problems, geotechnics.

Finite elements are often formulated based on compatible displacement fields. For plane triangular elements this leads to a series of elements based on linear, quadratic or cubic variation of the in-plane displacements. The displacement fields become complete polynomial fields and the inter-element boundaries are fully compatible. The quadratic elements are considered robust and efficient. However, for example in geotechnical calculations with high material non-linearities the convergence rate is rather slow.

With plane rectangular elements a compatible displacement interpolation will not generate complete polynomial fields, and this may lead to the so-called shear loacking phenomenon. Shear locking arises from the incompleteness of the displacement field and can be avoided in different ways. One way is to reduce the order of integration, and in this way the differences in strain interpolation are avoided. Another more elegant and efficient method is to introduce local incompatible displacement fields which results in complete polynomial displacements fields. The local degrees of freedom are eliminated on the element level and therefore the computational costs are only marginal increased. The local incompatibilities fulfill the so-called patch test, and therefore the numerical results will converge to the exact solution for fine finite element meshes.

In this paper the well-known linear strain (LST) elements are locally enhanced resulting in a complete cubic displacement field interpolation. The extra degrees of freedom are eliminated locally and thereby the computational costs are not increased significantly. The shape functions are based on the authors previous work on compatible or nearly compatible shear flexible plate elements. The element formulation has been tested on linear cases with good results. Tests on non-linear problems also show an increased performance with improved accuracy especially for geotechnical problems.

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