The Hellan–Herrmann–Johnson method for nonlinear shells

Neunteufel, Michael; Schöberl, Joachim

doi:10.1016/j.compstruc.2019.106109

Cited by 18 publications

(14 citation statements)

References 46 publications

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“…As discussed in [39,38] by introducing the averaged normal vector {ν} := ν L +ν R ν L +ν R the jump terms can be reordered yielding…”

Section: Curvature Computationmentioning

confidence: 99%

Numerical shape optimization of the Canham-Helfrich-Evans bending energy

Neunteufel¹,

Schöberl²,

Sturm³

2021

Preprint

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In this paper we propose a novel numerical scheme for the Canham-Helfrich-Evans bending energy based on a three-field lifting procedure of the distributional shape operator to an auxiliary mean curvature field. Together with its energetic conjugate scalar stress field as Lagrange multiplier the resulting fourth order problem is circumvented and reduced to a mixed saddle point problem involving only second order differential operators. Further, we derive its analytical first variation (also called first shape derivative), which is valid for arbitrary polynomial order, and discuss how the arising shape derivatives can be computed automatically in the finite element software NGSolve. We finish the paper with several numerical simulations showing the pertinence of the proposed scheme and method.

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“…As discussed in [39,38] by introducing the averaged normal vector {ν} := ν L +ν R ν L +ν R the jump terms can be reordered yielding…”

Section: Curvature Computationmentioning

confidence: 99%

Numerical shape optimization of the Canham-Helfrich-Evans bending energy

Neunteufel¹,

Schöberl²,

Sturm³

2021

Preprint

Self Cite

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“…To avoid shear locking effects we use the Kirchhoff-Love shell model introduced in [27]. The method is implemented in the NGS-Py interface, which is based on the finite element library Netgen/NGSolve 2 [33,34].…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Further, the forces are scaled appropriately with the thickness parameter t such that the deformations are in the same magnitude. Due to the nonlinear bending energy part in [27], however, the results may vary with respect to the thickness parameter. The reference values are computed by a very fine mesh and the error is computed by |result -reference|/|reference|.…”

Section: Numerical Examplesmentioning

confidence: 99%

Avoiding Membrane Locking with Regge Interpolation

Neunteufel,

Schöberl

2019

Preprint

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In this paper a novel method to overcome membrane locking of thin shells is presented. An interpolation operator into the so-called Regge finite element space is inserted in the membrane energy term to weaken the implicitly given kernel constraints. Due to the tangential-tangential continuity of Regge elements, the number of constraints is asymptotically halved on triangular meshes compared to reduced integration techniques. Provided the interpolant, this approach can be incorporated easily to any shell element. The performance of the proposed method is demonstrated by means of several benchmark examples.

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“…Recently, Neunteufel and Schöberl 20 adopted the hierarchic rotation approach to enhance their previously presented nonlinear Kirchhoff–Love shell element by transverse shear strains to obtain a Reissner–Mindlin shell element. The formulation is based on the mixed Hellan–Herrmann–Johnson method with a focus on membrane locking.…”

Section: Introductionmentioning

confidence: 99%

Transverse shear parametrization in hierarchic large rotation shell formulations

Thierer,

Oesterle,

Ramm

et al. 2024

Numerical Meth Engineering

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Consistent treatment of large rotations in common Reissner–Mindlin formulations is a complicated task. Reissner–Mindlin formulations that use a hierarchic parametrization provide an elegant way to facilitate large rotation shell analyses. This can be achieved by the assumption of linearized transverse shear strains, resulting in an additive split of strain components, which technically simplifies implementation of corresponding shell finite elements. The present study aims at validating this assumption by systematically comparing numerical solutions with those of a newly implemented hierarchic and fully nonlinear Reissner–Mindlin shell element.

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The Hellan–Herrmann–Johnson method for nonlinear shells

Cited by 18 publications

References 46 publications

Numerical shape optimization of the Canham-Helfrich-Evans bending energy

Numerical shape optimization of the Canham-Helfrich-Evans bending energy

Avoiding Membrane Locking with Regge Interpolation

Transverse shear parametrization in hierarchic large rotation shell formulations

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