Vol.2, No 7/2, 1997 pp. 513 - 523

UDC: 531.22; 624.042.1; 687.053.4

**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

**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.

**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.