Vol.2, No 7/2, 1997 pp. 513 - 523
UDC: 531.22; 624.042.1; 687.053.4

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STRESS RECOVERY PROCEDURE BASED ON THE KNOWN DISPLACEMENTS
Dubravka Mijuca*, Zoran Drašković**, Mladen Berković*
* Faculty of Mathematics, Belgrade, Yugoslavia
** Institute of Mathematics, Belgrade, Yugoslavia
e–mail: dmijuca@matf.bg.ac.yu, mberkovic@matf.bg.ac.yu

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Abstract. Finite element method provides only the numerical simulation of a real behaviour of the observed physical problem. Hence, it is particularly important to have a reliable stress recovery technique and also the tools for error estimates of calculated stresses. In this paper a stress recovery procedure, based not on the conventionally calculated stresses but on the displacements, is studied in detail. Another useful property of the proposed approach is that all expressions are coordinate independent. These features have the following implications. First, a global continuous stress field is obtained directly from displacements and second, there is a possibility to use different coordinate systems at each global node.
Along with a basic demand for reliability of a mathematical model, there is also an important question of a solution time needed for the accuracy required. It has been shown by the numerical evidence that proposed procedure evidently increases the quality of finite element (FE) solution and, for finer meshes, can even reduce the solution time, at least compared with the simplest form of stress averaging, i.e. the arithmetic mean of nodal stresses from neighbouring elements.

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POUZDANO IZRAČUNAVANJE NAPONA U METODI KONAČNIH ELEMENATA U radu je predstavljena pouzdana, globalna, koordinatno nezavisna metoda izračunavanja kontinualne naponske slike modela opterećenog tela. Metoda se bazira na poznatim pomeranjima, koja mogu da budu određena eksperimentalno, teorijski ili numerički.