A posteriori error control and adaptivity of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml18" display="inline" overflow="scroll" altimg="si8.gif"><mml:mi>h</mml:mi><mml:mi>p</mml:mi></mml:math>-finite elements for mixed and mixed-hybrid methods

Petsche, Jan; Schröder, Jörg

doi:10.1016/j.camwa.2017.05.032

Cited by 6 publications

(3 citation statements)

References 19 publications

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“…According to Eqs. (42), (43) and (45), (46), the number of the unknown trial functions is 33 including the 21 stress coefficients 0σ k , 1σ k , 2σ k3 and the 6 displacement coefficients 0ûk , 0ûk , as well as the 6 rotation coefficients 0φ s , 1φ s , leading to a consistent shell model, see, for example, the consistency property of the displacement-based and stress-based shell theories, in [24,25,31,53,54]. In the next Section, a systematic process will be presented for the reduction in the number of variables.…”

Section: Dimensional Reduction Processmentioning

confidence: 99%

“…After having inserted Eqs. (22), (38) and the stress approximations (42)- (43), as well as the rotation approximation (46) and the transformed BC (53) in the latter equation and carrying out integrations with respect to the thickness coordinate ξ 3 , the integral expression becomes…”

Section: Weakly Imposed Rotational Equilibrium Equationmentioning

confidence: 99%

“…This idea was originally suggested in [18]. The structural FEs based on this approach are elaborated on 2D and 3D problems of linear elasticity in [3,8,12,27,46,50,56] and on cylindrical shell problems in [59,63], as well as [29] using first-order stress functions for the a priori satisfaction of the translational equilibrium equation.…”

Section: Introductionmentioning

confidence: 99%

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Dual-mixed hp-version axisymmetric shell finite element using NURBS mid-surface interpolation

Tóth

Burmeister

2020

Acta Mech

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A new, general hp-version axisymmetric finite element is derived for the boundary value problems of thin linearly elastic shells of revolution, applying a complementary strain energy-based three-field dual-mixed variational principle. For the interpolation of the mid-surface geometry, non-uniform rational B-splines-NURBS-is used. The independent field variables of the weak formulation are the a priori non-symmetric stress tensor, the displacement vector, and the infinitesimal skew-symmetric rotation tensor. The theoretical model of the shell formulation is based on a consistent dimensional reduction process and a systematic variablenumber reduction procedure. The inverse of the unvaried three-dimensional constitutive equation is employed since neither the classical kinematical assumptions nor the stress hypotheses are built in the mathematical model; namely, both the through-the-thickness variation and the normal stress to the shell mid-surface are not excluded. The new hp axisymmetric shell finite element is tested by a representative model problem for extremely thin and moderately thick, singly and doubly curved shells of negative and positive Gaussian curvature. Following from the numerical experiments, the constructed hp-shell finite element gives locking-free results not only for the displacement but also for the stresses.

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