A general high‐order finite element formulation for shells at large strains and finite rotations

Başar, Yavuz; Hanskötter, Ulrike; Schwab, Christoph

doi:10.1002/nme.591

Cited by 23 publications

(11 citation statements)

References 26 publications

(38 reference statements)

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“…The shell model is characterized by a Mindlin-Reissner kinematics with an extensible director [3]. Although arbitrary orders of shell kinematics can be used in the following, a linear kinematics is considered for the description of thickness changes in this paper.…”

Section: Higher-order Finite Shell Element Formulationmentioning

confidence: 99%

“…Using the proposed linear finite shell element kinematics, the Green-Lagrange strain tensor E can be decomposed into membrane, shear and transversal parts with respect to the thickness coordinate 3 as follows:…”

Section: Eas Concept For Low-order Shell Elementsmentioning

confidence: 99%

“…[1,2] and references therein). The p-version of the finite element formulation using a linear Mindlin-Reissner-type shell kinematics with extensible director is frequently used as an efficient alternative to the h-version since locking effects are avoided a priori [3]. However, in case of incompressible material behavior, higher-order shell elements also suffer from volumetric locking 1417 as volume or low-order shell elements do.…”

Section: Introductionmentioning

confidence: 99%

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EAS concept for higher‐order finite shell elements to eliminate volumetric locking

Hommel¹,

Meschke²

2008

Numerical Meth Engineering

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SUMMARYThe deficiency of volumetric locking phenomena in finite elements using higher-order shell element formulations based on Lagrangean polynomials and a linear finite shell kinematics cannot be avoided by the existent enhanced assumed strain (EAS) concept established for low-order elements. In this paper a consistent modification of the EAS concept is proposed to extend its applicability to higher-order shell elements. This modification, affecting the transversal normal strain for polynomial orders p>1, eliminates pathological modes caused by volumetric locking. The efficiency of the proposed extended EAS method is demonstrated by means of eigenvalue analyses and two representative numerical examples.

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Section: Higher-order Finite Shell Element Formulationmentioning

confidence: 99%

Section: Eas Concept For Low-order Shell Elementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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EAS concept for higher‐order finite shell elements to eliminate volumetric locking

Hommel¹,

Meschke²

2008

Numerical Meth Engineering

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“…Despite the computational effort required, the use of fully integrated finite elements of higher orders tends to mitigate most types of locking, increasing the reliability of the formulation (see, for instance, [2], [3], [4] and [5]). High-order shell finite elements are successfully employed, for example, in [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…One contribution of this paper is to cover the lack in the assessment of the seven-parameter shell performance under large-strain problems. In [6] and [9], for example, high-order hyperelastic shells with linear strain rate across the thickness are employed, but only the Saint Venant-Kirchhoff model is used in the numerical examples. Moreover, the present finite element formulation can be easily implemented in a computer code for any order of approximation.…”

Section: Introductionmentioning

confidence: 99%

A shell finite element formulation to analyze highly deformable rubber-like materials

Pascon

Coda

2013

Lat. Am. j. solids struct.

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In this paper, a shell finite element formulation to analyze highly deformable shell structures composed of homogeneous rubberlike materials is presented. The element is a triangular shell of anyorder with seven nodal parameters. The shell kinematics is based on geometrically exact Lagrangian description and on the ReissnerMindlin hypothesis. The finite element can represent thickness stretch and, due to the seventh nodal parameter, linear strain through the thickness direction, which avoids Poisson locking. Other types of locking are eliminated via high-order approximations and mesh refinement. To deal with high-order approximations, a numerical strategy is developed to automatically calculate the shape functions. In the present study, the positional version of the Finite Element Method (FEM) is employed. In this case, nodal positions and unconstrained vectors are the current kinematic variables, instead of displacements and rotations. To model near-incompressible materials under finite elastic strains, which is the case of rubber-like materials, three nonlinear and isotropic hyperelastic laws are adopted. In order to validate the proposed finite element formulation, some benchmark problems with materials under large deformations have been numerically analyzed, as the Cook's membrane, the spherical shell and the pinched cylinder. The results show that the mesh refinement increases the accuracy of solutions, high-order Lagrangian interpolation functions mitigate general locking problems, and the seventh nodal parameter must be used in bending-dominated problems in order to avoid Poisson locking.Keywo rds large deformation analysis; homogeneous rubber-like materials; shell finite elements.

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A semi‐local spectral/hp element solver for linear elasticity problems

Bittencourt

Karniadakis

2014

Numerical Meth Engineering

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SUMMARYWe develop an efficient semi‐local method for speeding up the solution of linear systems arising in spectral/hp element discretization of the linear elasticity equations. The main idea is to approximate the element‐wise residual distribution with a localization operator we introduce in this paper, and subsequently solve the local linear system. Additionally, we decouple the three directions of displacement in the localization operator, hence enabling the use of an efficient low energy preconditioner for the conjugate gradient solver. This approach is effective for both nodal and modal bases in the spectral/hp element method, but here, we focus on the modal hierarchical basis. In numerical tests, we verify that there is no loss of accuracy in the semi‐local method, and we obtain good parallel scalability and substantial speed‐up compared to the original formulation. In particular, our tests include both structure‐only and fluid‐structure interaction problems, with the latter modeling a 3D patient‐specific brain aneurysm. Copyright © 2014 John Wiley & Sons, Ltd.

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A general high‐order finite element formulation for shells at large strains and finite rotations

Cited by 23 publications

References 26 publications

EAS concept for higher‐order finite shell elements to eliminate volumetric locking

EAS concept for higher‐order finite shell elements to eliminate volumetric locking

A shell finite element formulation to analyze highly deformable rubber-like materials

A semi‐local spectral/hp element solver for linear elasticity problems

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