Enrichment of linear hexahedral finite elements using rotations of a virtual space fiber

Abstract

SUMMARYThe present paper deals with the enrichment of 3D low‐order finite elements. The used concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. A consistent stiffness matrix is obtained, allowing a better approximation of the actual solution compared with that resulting from low‐order finite elements. Implemented for two eight‐node hexahedral elements, the performance of the space fiber rotation concept is assessed by running some classical beam, plate, and shell benchmarks, and the obtained results are compared especially with those given by linear eight‐node and quadratic 20‐node hexahedral elements. In particular, it is shown that the developed elements accuracy is significantly superior to that of the classical eight‐node hexahedral element and close to that of the classical 20‐node hexahedral element. Copyright © 2013 John Wiley & Sons, Ltd.

A specific finite element procedure for the analysis of elastic behaviour of short fibre reinforced composites. The Projected Fibre approach

“…Future developments also concern the extension to 3D cases of the PF approach with taking into account as mentioned before of the damage behaviour, and an adapted version of the accurate 8-node Space Fibre Rotation (SFR) element [25,26].…”

An Eight-Node Hexahedral Finite Element with Rotational DOFs for Elastoplastic Applications

“…Hence, the SFR concept adds rotational DOFs along with the classical displacement ones. Ayad et al [26] adopted the SFR concept to formulate two eight-node hexahedral elements SFR8 and SFR8I. The response of these two elements in the linear static regime was examined through a series of benchmarks where the findings show a better accuracy than the classical first order hexahedral element and close to the quadratic 20-node hexahedral element.…”

A Four-Node Tetrahedral Finite Element Based on Space Fiber Rotation Concept

“…The so-called Space Fiber Rotation (SFR) concept was firstly introduced by Ayad [8] and later by Meftah [9] to enhance the accuracy of first-order finite elements. This SFR concept was then adapted to 3D elastic structures by Meftah et al [10] by developing a 3D six-node prismatic solid element, named SFR6, and by Ayad et al [11] by introducing two 3D eight-node hexahedral solid elements named SFR8 and SFR8I (with incompatible mode). One would like to recall that the present concept was firstly derived from 2D and extended later for 3D virtual rotations of a nodal fiber that improves the approximation of the displacement vector.…”

“…Furthermore, in the work of Meftah et al [12], an extension of the SFR eight-node hexahedral elements SFR8 and SFR8I, was proposed to account for geometrically nonlinear problems. Moreover, Meftah et al [13] developed a multilayered extension of the eight-node hexahedral element named SFR8M to study composite laminate structures. In particular, it was shown that these 3D SFR solid elements yield results that are significantly better than those of the classical first-order wedge and hexahedral elements and globally close to those of the classical quadratic elements.…”

“…In particular, it was shown that these 3D SFR solid elements yield results that are significantly better than those of the classical first-order wedge and hexahedral elements and globally close to those of the classical quadratic elements. It should be noted that the SFR solid elements maintain a good performance especially for coarse and distorted meshes [9][10][11][12][13][14].…”