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2 Computer Assisted Mechanics and Engineering Sciences

2 2008

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The Trefftz finite elements modelling crack propagation

Sanecki H., Zieliński A.

Computer Assisted Mechanics and Engineering Sciences

2008

Vol. 15, No. 3/4

353-368

Investigation of crack propagation can sometimes be a crucial stage of engineering analysis. The T-element method presented in this work is a convenient tool to deal with it. In general, T-elements are the Trefftz-type finite elements, which can model both continuous material and local cracks or inclusions. The authors propose a special T-element in a form of a pentagon with shape functions analytically modelling the vicinity of the crack tip. This relatively large finite element can be surrounded by even larger standard T-elements. This enables easy modification of the rough element grid while investigating the crack propagation. Numerical examples proved that the "moving pentagon" concept enables easy automatic generation of the T-element mesh, which facilitates observation of crack propagation even in very complicated structures with many possible crack initiators occurring for example in material fatigue phenomena.

On the stability of hybrid equilibrium and Trefftz finite element models for plate bending problems

Maunder E. A. W.

Computer Assisted Mechanics and Engineering Sciences

2008

Vol. 15, No. 3/4

279-288

This paper is concerned with hybrid stress elements in the context of modelling the behaviour of plates subject to out of plane loading and based on Reissner-Mindlin assumptions. These elements are considered as equilibrium elements with statically admissible stress fields of which Trefftz fields form a special case. The existence of spurious kinematic modes in star patches of triangular elements is reviewed when boundary displacement fields are defined independently for each side. It is shown that for elements of moment degree > 1, the spurious modes for stars only exist at specific locations and/or for certain configurations. The kinematic properties of these modes are used to define sufficient conditions for the stability of a complete mesh of triangular elements. A method is proposed to check mesh stability, and introduce local modifications to ensure overall stability.