A six-node pentagonal assumed natural strain solid–shell element

Abstract A hybrid-mixed functionally graded material (FGM) piezoelectric four-node solid-shell element through the sampling surfaces (SaS) method is proposed. The SaS formulation is based on choosing inside the shell N SaS parallel to the middle surface in order to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. Such choice of unknowns with the use of Lagrange polynomials of degree N-1 in through-thickness interpolations of the displacements, strains, electric potential, electric field and material properties leads to a robust FGM piezoelectric shell formulation. The inner SaS are located at Chebyshev polynomial nodes that make it possible to minimize uniformly the error due to Lagrange interpolation. To implement the effective analytical integration throughout the element, the extended assumed natural strain (ANS) method is employed. As a result, the piezoelectric four-node solid-shell element exhibits a superior performance in the case of coarse meshes. To circumvent shear and membrane locking, the hybrid stress-strain solid-shell formulation via the Hu-Washizu variational principle is employed. The developed solid-shell element could be useful for the 3D stress analysis of FGMstructures because the SaS method allows obtaining the solutions with a prescribed accuracy, which asymptotically approach the exact solutions of electroelasticity as the number of SaS tends to infinity.

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Solid Shell Element and its Application in Roll Forming Simulation

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.340-341.347 ◽

2007 ◽

Vol 340-341 ◽

pp. 347-352 ◽

Cited By ~ 1

Author(s):

Da Yong Li ◽

Ying Bing Luo ◽

Ying Hong Peng

Keyword(s):

Degrees Of Freedom ◽

Shell Element ◽

Element Model ◽

Roll Forming ◽

Good Prospect ◽

Solid Shell ◽

Forming Process ◽

Forming Simulation ◽

Assumed Natural Strain ◽

Roll Forming Process

Solid shell element models which possess only translational degrees of freedom and are applicable to thin structure analyses has drawn much attention in recent years and presented good prospect in sheet metal forming. In this study, a solid shell element model is introduced into the dynamic explicit elastic-plastic finite element method. The plane stress constitutive relation is assumed to relieve the thickness locking and the selected reduced integration method is used to overcome volumetric locking. The assumed natural strain method is adopted to resolve shear locking and trapezoidal locking problem. Two benchmark examples and a stage of roll forming process are calculated, and the calculating results are compared with those by solid element model, which demonstrates the effectiveness of the element.

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New assumed natural strain formulation of the shallow shell element

Communications in Numerical Methods in Engineering ◽

10.1002/cnm.1640091206 ◽

1993 ◽

Vol 9 (12) ◽

pp. 989-1004 ◽

Cited By ~ 2

Author(s):

Rafi L. Muhanna

Keyword(s):

Shallow Shell ◽

Shell Element ◽

Natural Strain ◽

Strain Formulation ◽

Assumed Natural Strain

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Dynamic Analysis of Plates using a Improved Assumed Natural Strain Shell Element

Journal of the Korea Academia-Industrial cooperation Society ◽

10.5762/kais.2010.11.6.2284 ◽

2010 ◽

Vol 11 (6) ◽

pp. 2284-2291

Author(s):

Won-Hong Lee ◽

Sung-Cheon Han ◽

Weon-Tae Park

Keyword(s):

Dynamic Analysis ◽

Shell Element ◽

Natural Strain ◽

Assumed Natural Strain

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On the Assumed Natural Strain method to alleviate locking in solid-shell NURBS-based finite elements

Computational Mechanics ◽

10.1007/s00466-014-0978-4 ◽

2014 ◽

Vol 53 (6) ◽

pp. 1341-1353 ◽

Cited By ~ 37

Author(s):

J. F. Caseiro ◽

R. A. F. Valente ◽

A. Reali ◽

J. Kiendl ◽

F. Auricchio ◽

...

Keyword(s):

Finite Elements ◽

Solid Shell ◽

Natural Strain ◽

Assumed Natural Strain ◽

Strain Method

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Evaluation of the Enhanced Assumed Strain and Assumed Natural Strain in the SSH3D and RESS3 Solid Shell Elements for Single Point Incremental Forming Simulation

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.504-506.913 ◽

2012 ◽

Vol 504-506 ◽

pp. 913-918 ◽

Cited By ~ 4

Author(s):

Carlos Felipe Guzmán ◽

Amine Ben Bettaieb ◽

José Ilídio Velosa de Sena ◽

Ricardo J. Alves de Sousa ◽

Anne Marie Habraken ◽

...

Keyword(s):

Finite Element ◽

Incremental Forming ◽

Single Point ◽

Single Point Incremental Forming ◽

Solid Shell ◽

Shell Elements ◽

Enhanced Assumed Strain ◽

Natural Strain ◽

Assumed Strain ◽

Assumed Natural Strain

Single Point Incremental Forming (SPIF) is a recent sheet forming process which can give a symmetrical or asymmetrical shape by using a small tool. Without the need of dies, the SPIF is capable to deal with rapid prototyping and small batch productions at low cost. Extensive research from both experimental and numerical sides has been carried out in the last years. Recent developments in the finite element simulations for sheet metal forming have allowed new modeling techniques, such as the Solid Shell elements, which combine the main features of shell hypothesis with a solid-brick element. In this article, two recently developed elements -SSH3D element [1, 2] and RESS3 element [3]- implemented in Lagamine (finite element code developed by the ArGEnCo department of the University of Liège) are explained and evaluated using the SPIF line test. To avoid locking problems, the well-known Enhanced Assumed Strain (EAS) and Assumed Natural Strain (ANS) techniques are used. The influence of the different EAS and ANS parameters are analized comparing the predicted tool forces and the shape of a transversal cut, at the end of the process. The results show a strong influence of the EAS in the forces prediction, proving that a correct choice is fundamental for an accurate simulation of the SPIF using Solid Shell elements.

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Modeling and analysis of spiral actuators by exact geometry piezoelectric solid-shell elements

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x19880014 ◽

2019 ◽

Vol 31 (1) ◽

pp. 53-70

Author(s):

GM Kulikov ◽

SV Plotnikova ◽

E Carrera

Keyword(s):

Shell Element ◽

Middle Surface ◽

Solid Shell ◽

Modeling And Analysis ◽

Lagrange Polynomials ◽

Shell Elements ◽

Exact Geometry ◽

Piezoelectric Solid ◽

Assumed Natural Strain ◽

Shell Formulation

An exact geometry four-node piezoelectric solid-shell element through the sampling surfaces formulation is proposed. The sampling surfaces formulation is based on choosing inside the shell N – 2 sampling surfaces parallel to the middle surface and located at Chebyshev polynomial nodes to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. The bottom and top surfaces are also included into a set of sampling surfaces. Such choice of unknowns with the use of Lagrange polynomials of degree N – 1 in the through-the-thickness interpolations of displacements, strains, electric potential, and electric field yields a robust piezoelectric shell formulation. To implement efficient analytical integration throughout the solid-shell element, the extended assumed natural strain method is employed. The developed hybrid-mixed four-node piezoelectric solid-shell element is based on the Hu-Washizu variational principle and shows the excellent performance for coarse mesh configurations. It can be useful for the 3D stress analysis of piezoelectric shells with variable curvatures, in particular for the modeling and analysis of spiral actuators.

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