Static and dynamic convergence studies of a four‐noded membrane finite element with rotational degrees of freedom based on displacement superposition

Abstract

SUMMARYStatic and dynamic performance tests of a four-noded quadrilateral isoparametric membrane finite element enriched with rotational degrees of freedom (DOF) are presented. The formulation is based on displacement superposition whereby the in-plane displacements are decomposed additively into a regular, low-order contribution (governed by the nodal in-plane displacements) and a higher-order contribution (governed by the nodal in-plane rotations). The sensitivity of the element to element distortion and element aspect ratio is investigated. Comparisons with standard bilinear finite elements are made for static and dynamic loading case. It is demonstrated that the studied element exhibits an accuracy per DOF that is superior to the standard bilinear finite element.

Reciprocal mass matrices and a feasible time step estimator for finite elements with Allman's rotations

“…Further effort was made to construct mass matrices and test these formulations for modal and transient analyses. The consistent mass matrix (CMM) are presented in References 16,17 for a 3‐node triangle, in Reference 18 for a 4‐node quadrilateral and in in Reference 6 for a 4‐node tetrahedron element. A general construction for the lumped mass matrix (LMM) for elements with Allman's rotation is given in Reference 16.…”

“…Moreover, the scaling of the rotary inertia in LMM should be adjusted to the stabilization stiffness of the element. Therefore, CMM is preferred in implicit analysis 18,19 . Based on this profound research, finite elements with Allman's rotation made its way to academic finite element packages, for example, as 3‐node triangle TrPlaneStrRot in the open‐source code OOFEM 20 and commercial programs, for example, 4‐node tetrahedron (ELFORM = 4) and 8‐node hexahedron (ELFORM = 3) in LS‐DYNA.…”

4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortion

“…Since then, many efforts have been put on developing membrane elements with drilling DOFs. Recent attempts include but are not limited to the literatures …”

“…Recent attempts include but are not limited to the literatures. [50][51][52][53][54][55] In the present work, a simple but robust unsymmetric 4-node low-order quadrilateral membrane element with the drilling DOFs is developed. First, the test function of this element is assumed as a new kind of 2-dimensional isoparametric-based displacement field enriched by the drilling DOFs.…”

Four-Node Generalized Conforming Membrane Elements with Drilling DOFs Using Quadrilateral Area Coordinate Methods

“…Based on this assumption, the triangular element GT9 series and the quadrilateral element GQ12 series were developed. These elements all exhibit good performance [26], and among these models the quadrilateral element GQ12M8 is the best one.…”