A new shell element accounting for through-thickness deformation

El-Abbasi, N.; Meguid, S. A.

doi:10.1016/s0045-7825(99)00348-5

Cited by 71 publications

(62 citation statements)

References 30 publications

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“…The shell su ers large displacements but strains and rotations are relatively small (see Reference [65]). The test is very popular and has been studied in References [4,5,60,65,69,70,73,77,[79][80][81]. The Figure 24 shows the non-deformed mesh and a deformed mesh of the total hemisphere model.…”

Section: Non-linear Problemsmentioning

confidence: 99%

“…For the solution of shell problems with shell elements, the comparison is not so conclusive. In terms of versatility, the so-called solid-shell elements [1][2][3][4][5][6][7] which only adopt displacement variables at the nodes and do not preclude the use of general 3D constitutive models, can be e ective in modelling shell intersections and allow a natural coupling with 3D elements. However, for problems containing thick geometries such as bulk forming problems, solid elements should be used.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of 3D problems using a new enhanced strain hexahedral element

Areias¹,

Sá²,

Curnis³

et al. 2003

Numerical Meth Engineering

119

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SUMMARYThe now classical enhanced strain technique, employed with success for more than 10 years in solid, both 2D and 3D and shell ÿnite elements, is here explored in a versatile 3D low-order element which is identiÿed as HIS. The quest for accurate results in a wide range of problems, from solid analysis including near-incompressibility to the analysis of locking-prone beam and shell bending problems leads to a general 3D element. This element, put here to test in various contexts, is found to be suitable in the analysis of both linear problems and general non-linear problems including ÿnite strain plasticity. The formulation is based on the enrichment of the deformation gradient and approximations to the shape function material derivatives. Both the equilibrium equations and their variation are completely exposed and deduced, from which internal forces and consistent tangent sti ness follow. A stabilizing term is included, in a simple and natural form. Two sets of examples are detailed: the accuracy tests in the linear elastic regime and several ÿnite strain tests. Some examples involve ÿnite strain plasticity. In both sets the element behaves very well, as is illustrated in numerous examples.

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Section: Non-linear Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of 3D problems using a new enhanced strain hexahedral element

Areias¹,

Sá²,

Curnis³

et al. 2003

Numerical Meth Engineering

119

View full text Add to dashboard Cite

show abstract

“…Although many shell finite element procedures using kinematical assumptions of higher order (in the transverse direction) than the Reissner-Mindlin assumptions have already been proposed and discussed, see e.g. [4,12,14], a mathematical analysis of the pinching locking phenomenon leading to efficient mathematically-substantiated treatments is missing, and this is the objective of the present paper.…”

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confidence: 99%

The treatment of “pinching locking” in3D-shell elements

Chapelle¹,

Ferent²,

Tallec

2003

ESAIM: M2AN

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Abstract. We consider a family of shell finite elements with quadratic displacements across the thickness. These elements are very attractive, but compared to standard general shell elements they face another source of numerical locking in addition to shear and membrane locking. This additional locking phenomenon -that we call "pinching locking" -is the subject of this paper and we analyse a numerical strategy designed to overcome this difficulty. Using a model problem in which only this specific source of locking is present, we are able to obtain error estimates independent of the thickness parameter, which shows that pinching locking is effectively treated. This is also confirmed by some numerical experiments of which we give an account.Mathematics Subject Classification. 65N30, 74K25.

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“…The initial unit normal vector n 0 (equation 4), the vector g 1 (equation 6) and the rate a (equation 6) are also interpolated via their corresponding nodal values and shape functions: for linear approximation order, the shell elements can be curved. As in the study of [9], there are seven parameters -or degrees of freedom -per node (L): three current positions of the shell mid- formulations, which can also numerically describe thickness change and linear strain across the thickness direction are presented by [14], [28], [29], [30], [31], [5] and [9], among others. Regarding Nonlinear Continuum Mechanics strain measures, the following Lagrangian quantities are used in this paper:…”

Section: Finite Element Mappingmentioning

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 new shell element accounting for through-thickness deformation

Cited by 71 publications

References 30 publications

Analysis of 3D problems using a new enhanced strain hexahedral element

Analysis of 3D problems using a new enhanced strain hexahedral element

The treatment of “pinching locking” in3D-shell elements

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

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