A Comprehensive Comparative Review of Various Advanced Finite Elements to Alleviate Shear, Membrane and Volumetric Locking

Abstract

Finite element analysis (FEA) is an extensively exercised numerical procedure to address numerous problems in several engineering fields. However, the accuracy of conventional FEA solutions is significantly affected in specific circumstances where the problem demands near-incompressibility or incompressibility of domain or analysis of thin structural geometries. Over time, several advanced FE models are developed to improve the quality of solutions in stated situations. However, the extensive comparative aspects of these methods are spared limited attention. In the present paper, a comprehensive review and comparison of the selected FE models have been presented. The detailed implementation procedure, along with the relative efficacy of the methods, has been derived for selective reduced integration (SRI), enhanced assumed strain (EAS), assumed natural strain (ANS), and a specific class of hybrid stress elements alongside the conventional FE formulation. The quality of results is assessed by evaluating the relative error norms in displacement and stress on well-established benchmark numerical examples. Furthermore, the paper investigates the methods for several parameters that include the method’s best-suited environment, robustness, and efficiency. The findings in the paper provide an elaborate understanding of the optimal choice of the method in locking-dominated problems.