Physically stabilised displacement-based ANS solid-shell element

Edem, I.B.; Gosling, Peter

doi:10.1016/j.finel.2013.05.009

Cited by 8 publications

(6 citation statements)

References 50 publications

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“…The displacement responses of the internal nodes are summarized in Table III. They meet well with the theoretical solutions in Equation (42). The computed stress values at both the top and bottom surfaces are also in perfect agreement with the following theoretical stress state: xx D yy D˙0:6667; xy D˙0:2000…”

Section: Bending Patch Testsupporting

confidence: 84%

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A new reduced integration solid‐shell element based on EAS and ANS with hourglass stabilization

Liu

Zhang

et al. 2015

Numerical Meth Engineering

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Summary In this paper, a novel reduced integration eight‐node solid‐shell finite element formulation with hourglass stabilization is proposed. The enhanced assumed strain method is adopted to eliminate the well‐known volumetric and Poisson thickness locking phenomena with only one internal variable required. In order to alleviate the transverse shear and trapezoidal locking and correct rank deficiency simultaneously, the assumed natural strain method is implemented in conjunction with the Taylor expansion of the inverse Jacobian matrix. The projection of the hourglass strain‐displacement matrix and reconstruction of its transverse shear components are further employed to avoid excessive hourglass stiffness. The proposed solid‐shell element formulation successfully passes both the membrane and bending patch tests. Several typical examples are presented to demonstrate the excellent performance and extensive applicability of the proposed element. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: Bending Patch Testsupporting

confidence: 84%

“…In order to improve the bending performance and achieve the locking-free property of the solid-shell formulation, the ANS method [20,28,41,42] is incorporated in this work for the normal thickness strain and transverse shear strains.…”

Section: Assumed Natural Strain Methodsmentioning

confidence: 99%

A new reduced integration solid‐shell element based on EAS and ANS with hourglass stabilization

Liu

Zhang

et al. 2015

Numerical Meth Engineering

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“…They can be easily combined with various fully 3D constitutive models (e.g., orthotropic elastic behavior, plastic behavior), without any further assumptions, such as plane-stress assumptions. Based on the reduced-integration technique (see, e.g., [ 9 ]), they are often combined with advanced strategies to alleviate locking phenomena, such as the assumed-strain method (ASM) (see, e.g., [ 4 ]), the enhanced assumed strain (EAS) formulation (see, e.g., [ 10 ]), and the assumed natural strain (ANS) approach (see, e.g., [ 11 ]). Several FE formulations for the analysis of thin FGM structures have been developed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Quadratic Solid–Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates

Chalal

Abed‐Meraim

2018

Materials

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In the current contribution, prismatic and hexahedral quadratic solid–shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as the only degrees of freedom. Also, the in-plane reduced-integration technique is combined with the assumed-strain method to alleviate various locking phenomena. Furthermore, an arbitrary number of integration points are placed along a special direction, which represents the thickness. The developed elements are coupled with functionally graded behavior for the modeling of thin FGM plates. To this end, the Young modulus of the FGM plate is assumed to vary gradually in the thickness direction, according to a volume fraction distribution. The resulting formulations are implemented into the quasi-static ABAQUS/Standard finite element software in the framework of large displacements and rotations. Popular nonlinear benchmark problems are considered to assess the performance and accuracy of the proposed SHB elements. Comparisons with reference solutions from the literature demonstrate the good capabilities of the developed SHB elements for the 3D simulation of thin FGM plates.

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“…It should be noted that some versions of the well-established Solid-Shell finite element approach [23][24][25][26][27][28][29][30] precedes our formulation on using vectors instead of rotations to solve shells problems; therefore our approach is classified as a Solid-Shell-like formulation. There are two main differences between these formulations.…”

Section: Introductionmentioning

confidence: 99%

A FEM continuous transverse stress distribution for the analysis of geometrically nonlinear elastoplastic laminated plates and shells

Coda

Sampaio

Paccola

2015

Finite Elements in Analysis and Design

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Physically stabilised displacement-based ANS solid-shell element

Cited by 8 publications

References 50 publications

A new reduced integration solid‐shell element based on EAS and ANS with hourglass stabilization

A new reduced integration solid‐shell element based on EAS and ANS with hourglass stabilization

Quadratic Solid–Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates

A FEM continuous transverse stress distribution for the analysis of geometrically nonlinear elastoplastic laminated plates and shells

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