CORRECTION OF THE STRAIN FIELD OF LINEAR TETRAHEDRAL FINITE ELEMENT USING STRAIN SMOOTHING METHOD

Abstract

The purpose of this paper was analyzing the performance of the linear tetrahedral finite element. As 4-node tetrahedrons are low-order elements that have a very stiff behavior with a constant strain field in bending problem analysis, this paper presents the Strain Smoothed Element Method [1], which gives considerably better performances of the linear elements comparing to standard formulation, without introducing significant changes in FEM. Taking constant strains of the adjacent elements into consideration, using this method the linear strain field is created in the observed element, which achieves greater precision and hence lowering the discontinuity of the stress on the borders between elements. In the second part of the paper, numerical examples that encompass two plane stress problems were used to examine the performances of the linear tetrahedral element, which has already been implemented within the program package PAK, in comparison with the performances of the element with a corrected strain field, shown in [1]. As mentioned problems that we encounter in modeling with linear elements are overcome in practice with higher order approximation, performance of tetrahedral element with parabolic interpolation of the displacement field is also analyzed with numerical examples. The comparatively presented results obtained from the program packages PAK and Nastran display great agreement of these two software packages and significantly bigger precision of elements with a corrected strain field compared to the constant strain element. Upon comparing the parabolic and corrected elements, a better behavior was observed in the parabolic element. However, as this is an element that has greater number of degrees of freedom, the obtained results are fully justified.