The linear strain field of 4-node tetrahedral finite elements created using strain smoothing method

Abstract

One of the goals of this research was the analysis of the strain-smoothed element method, as presented in Lee et al. (2018). The method was applied to the linear tetrahedral finite elements, with the purpose of overcoming a very stiff behavior, which is specifically expressed in bending problems. Using this method, the linear strain field is created within the element itself, considering the constant strains of the surrounding elements. Accordingly, the obtained element achieves greater precision and less stress discontinuity on the borders between the elements. The efficiency of such a method is reflected in the fact that special smoothing domains are not created and that linearity of the strain field is achieved without the introduction of additional parameters and degrees of freedom. Additionally, we conducted a comparative analysis of performances of the linear tetrahedral finite elements implemented within the program packages PAK and Nastran, as compared to the element suggested in Lee et al. (2018). By presenting concrete examples of bending problems, it was shown that the constant strain field of a linear tetrahedral finite element requires a very dense mesh so that the approximation of linear strain field of the bending problem would be accurate enough. The element with the corrected strain field achieves a higher level of accuracy and significantly faster convergence compared to the element with constant strains. Therefore, by applying the suggested smoothing method the domain of the linear tetrahedral finite element practical application is expanded.