Derivation of a dual-mixed hp-finite element model for axisymmetrically loaded cylindrical shells

Kocsán, Lajos György

doi:10.1007/s00419-011-0530-3

Cited by 6 publications

(4 citation statements)

References 31 publications

(45 reference statements)

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“…The theoretical results presented in this paper were motivated by the facts that (i) robust and effective multi-field dual-mixed hp finite elements based on non-symmetric stress field are managed to be developed for elastostatic problems of thin cylindrical shells in [36,62,64], and (ii) the limited applicability of the principle of complementary virtual work to time-dependent problems. The question comes up how to extend the multi-field dual-mixed variational functionals using non-symmetric stresses to model time-dependent elasticity problems.…”

Section: Introductionmentioning

confidence: 99%

Multi-field Dual-Mixed Variational Principles Using Non-symmetric Stress Field in Linear Elastodynamics

Tóth

2015

J Elast

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Three types of multi-field dual-mixed variational principles using a priori non-symmetric stress field will be derived for dynamic problems of linearly elastic solids. Starting from the functional of complementary Hamilton's principle it is shown how this variational formulation is modified with applying the Lagrange multiplier technique, to obtain a new four-field dual-mixed functional. The independent fields of this functional will be the displacement vector, the non-symmetric stress tensor, the skew-symmetric rotation tensor and the momentum vector. Then we present how to treat appropriately the six different types of initial conditions in a weak and/or strong sense by adding a new integral expression to the four-field functional. Modifying this functional through a Legendre transformation results in a new complementary energy-based five-field dual-mixed functional which allows the momentum-and velocity vectors to be independently approximated. A complementary energy-based three-field dual-mixed variational formulation is obtained by eliminating the momentum-and velocity fields through the strong enforcement of the kinematic equation and the impulse-velocity relation from the five-field principle.

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Section: Introductionmentioning

confidence: 99%

Multi-field Dual-Mixed Variational Principles Using Non-symmetric Stress Field in Linear Elastodynamics

Tóth

2015

J Elast

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“…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%

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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“…For the nonlinear equilibrium equations of the shell theory considered in [18], however, "every attempt to find SA (statically admissible) stresses would be illusory", as stated on page 75 of [18]. Dual-mixed hp finite element models for cylindrical shells using first-order stress functions and rotations have been developed in [19] and [20].…”

Section: Introductionmentioning

confidence: 99%

Equilibrated stress space for nonlinear dimensionally reduced shell models in terms of first-order stress functions

Bertóti¹

2020

JCAM

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Considering the power series expansion of the three-dimensional variables with respect to the shell thickness coordinate, an equilibrated stress space for the first Piola-Kirchhoff stress vectors is derived in convective curvilinear coordinate system. The infinite series of the two-dimensional translational equilibrium equations are satisfied by introducing two first-order stress function vectors expanded into power series. For the important case of thin shells, the infinite number of two-dimensional equilibrium equations is truncated to obtain a ‘first-order’ model, where the equilibrated stress-space requires three vectorial stress function coefficients only. The formulation presented for thin shells is compared to the nonlinear equilibrium equations of the classical shell theories, written in terms of the first Piola-Kirchhoff stress resultants and stress couples and satisfied by the introduction of three first-order stress function vectors.

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Derivation of a dual-mixed hp-finite element model for axisymmetrically loaded cylindrical shells

Cited by 6 publications

References 31 publications

Multi-field Dual-Mixed Variational Principles Using Non-symmetric Stress Field in Linear Elastodynamics

Multi-field Dual-Mixed Variational Principles Using Non-symmetric Stress Field in Linear Elastodynamics

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

Equilibrated stress space for nonlinear dimensionally reduced shell models in terms of first-order stress functions

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