High-performance unsymmetric 3-node triangular membrane element with drilling DOFs can correctly undertake in-plane moments

Abstract

Purpose This paper aims to propose a simple but robust three-node triangular membrane element with rational drilling DOFs for efficiently analyzing plane problems. Design/methodology/approach This new element is developed within the general framework of unsymmetric FEM. The element test functions are determined by using a conforming displacement field which is slightly different with the classical Allman’s interpolations, while a self-equilibrated stress field formulated based on the analytical airy stress solutions is adopted as the trial functions. To ensure the correctness between the drilling DOFs and the true rotations in elasticity, reasonable constraints are introduced through the penalty function method. Moreover, the special quadrature strategy is used for operating related integrations for future enrichment of element behavior. Findings Numerical benchmark tests reveal that this new triangular membrane element has exceptional prediction capabilities. In particular, this element can correctly reproduce a rigid body rotation motion and correctly undertake the external in-plane twisting moments; thus, it is a reasonable choice for being used to formulate flat shell elements or to be connected with other kind of elements with physical rotational DOFs. Originality/value This work provides a new approach for developing high-performance lower-order elements with simple formulations and good numerical accuracies.

Some advances in high-performance finite element methods

“…Thus, the MacNeal's theorem is perfectly broken through. Furthermore, unsymmetric three-node triangular and four-node quadrilateral membrane elements with drilling DOFs that can exhibit excellent performances were also proposed by Shang et al (2018a), Shang and Ouyang (2018), respectively.…”

Extension of the unsymmetric 8-node hexahedral solid element US-ATFH8 to geometrically nonlinear analysis

“…Thus, they are not suitable for the practical situations (Ooi et al , 2008). By introducing the analytical trial function method and the generalized conforming technique (Long et al , 2009), Cen et al proposed a series of new unsymmetric elements (Cen et al , 2015a; Zhou et al , 2017; Huang et al , 2018; Li et al , 2018; Shang et al , 2018a, 2018b) which can eliminate all original defects and greatly improve precisions. The test functions and trial functions for displacement fields are different in the unsymmetric finite element method, just like the Petrov–Galerkin formulations.…”

An unsymmetric 8‐node plane element immune to mesh distortion for linear isotropic hardening material

“…[29][30][31] A series of related elements has been proposed by Cen et al, such as plane 4-node, 8-DOF quadrilateral element US-ATFQ4, 32,33 3D 8-node, 24-DOF hexahedral solid element US-ATFH8, 34 the 8-node, 24-DOF hexahedral solid-shell element US-ATFHS8, 35,36 and so on. 37,38 These novel unsymmetric elements have exhibited great advantages and showed excellent performance in case of anti-buckling edge distortion mesh and have not brought significant additional computational effort. Although the developed distortion-immune elements have achieved great success in linear and geometric nonlinear problems.…”