Original scientific paper

Errors in modelling high order gradient fields using reciprocity based FEM

Vladimír Kompiš ; Faculty of Mechanical Engineering, University of Žilina, Žilina, Slovakia
Lenka Jakubovičová ; Faculty of Mechanical Engineering, University of Žilina, Žilina, Slovakia

Abstract

In this paper errors in displacement and stress fields in reciprocity based finite elements are studied in examples of modelling of high order gradient fields using quadratic elements. In the reciprocity based FE formulation Trefftz polynomial functions are used to formulate stiffness matrices by boundary integral equations. This leads to a nonsingular boundary integral formulation in which tractions and displacements on the element boundaries are expressed by the reciprocity relation. The displacements are chosen to be compatible between the elements and weak satisfaction of interelement equilibrium defines the total system of equations in the discretized form. The simple error estimator used in isoparametric elements is compared with the exact error distribution. It is shown that this error estimator is not reliable for elements in which the governing equations are not satisfied inside the element. The results also show the importance of inclusion of boundary conditions for an effective recovery algorithm for stress.

Keywords

error estimator, Trefftz polynomial functions, reciprocity based FEM, high order gradient fields

Hrčak ID:

318824

URI

https://hrcak.srce.hr/318824

Publication date:

15.6.2000.

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