A comparison of primal- and dual-mixed finite element formulations for Timoshenko beams

Bertóti, E.

doi:10.1007/s00366-013-0333-y

Cited by 4 publications

(3 citation statements)

References 6 publications

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“…The main goal of the present work is to perform analytical and numerical comparisons of different finite element formulations for cylindrical shells in the framework of the dimensionally reduced Naghdi shell model. The formulations investigated in this paper have much similarity and analogy to those presented for the Timoshenko beam in [17]. The strong and the (Galerkin-type) weak formulations of the governing equations for axisymmetric deformations are summarized in Section 2.…”

Section: Introductionmentioning

confidence: 93%

“…The difference in the membrane stiffness matrices has no significant effect on the performance of the elements, which is due to the coefficient h 2 /R 2 and to the fact, that in practical finite element computations the relation h R applies. The rather small difference in the shear parts results, however, in a dramatic change in the approximation properties of the elements for thin shell problems and, as is well known, the primal-mixed formulation leads to shear locking-free displacement computations, just like in the case of the Timoshenko beam element (see, e.g., [2,18] and [17]). Note that the primal-mixed element of Section 3.2 can also be obtained by the reduced integration technique applied in the standard displacement formulation.…”

Section: 51mentioning

confidence: 99%

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Comparative study of primal- and dual-mixed finite element models for cylindrical shells

Bertóti¹

2015

JCAM

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Dedicated to Professor Barna Szabó on the occasion of his eightieth birthdayand to Professor Imre Kozák on the occasion of his eighty-fifth birthdayAbstract. Analytical and numerical comparisons of a primal-mixed, a dual-mixed and a consistent primal-dual mixed finite element formulation are presented for cylindrical shells using the lowest possible order, constant and linear, polynomial approximations within the framework of the Naghdi shell model. The stiffness matrices and the load vectors of the mixed elements are explicitly derived and compared to each other and to that of the standard displacement-based shell element for axisymmetric deformations. It is pointed out that the stiffness matrices of the dual-mixed and the primal-dual mixed elements can be related to that of the standard shell element through two geometry-, material-and mesh-dependent coefficients. One of these coefficients turns out to be a reliable shear locking indicator which can be used to transform the standard displacement-based shell element into a shear locking-free dual-mixed one, independently of the thickness and the loading of the shell. The numerical comparisons indicate that the dual-mixed element is the only element that gives second-order rates of asymptotic convergence for all the variables, including the bending moment and shear force computations.Mathematical Subject Classification: 05C38, 15A15

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Section: Introductionmentioning

confidence: 93%

Section: 51mentioning

confidence: 99%

Comparative study of primal- and dual-mixed finite element models for cylindrical shells

Bertóti¹

2015

JCAM

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“…Finite element formulations in elasticity provides wide strategies to tackle many kinds of problems, usually based on multi-field variational principles in the form of weightedresidual integrals as well as their weaken forms in which the mixing between these two strong and weak forms nowadays is often known as primal-mixed and Dual-mixed formulation. A valuable study of such topic is given in [23], in what follows the weak formulation will be followed.…”

Section: Mixed Finite Beam Element Modelsmentioning

confidence: 99%

Euler-Bernoulli and Timoshenko Beam Theories Analytical and Numerical Comprehensive Revision

Ahmed

Rifai

2021

EJENG

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Obtaining reliable and efficient results of a specified problem solution depends upon understanding the strategy of the method of analysis, which is emanated from all related physical basics of the problem, formulated with master mathematical tools to give its governing mathematical model. These two categories require deep study in a wide range of references and literature in order not only to apply the method professionally, but also to look for improvements, developments, and contributions in the field of the method. Consequently, although Euler-Bernoulli and Timoshenko beam theories are the oldest ones, but surely, they represent a cornerstone for most modern methods in structural analysis; In what follows, a detailed revision of these theories and their applications analytically and in numerical style is presented in a proper and simplified entrance to be able to understand more advanced topics such as thin and thick plate theories. Illustrative examples will be used to show and discuss the methods.

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The simplest node-based equilibrium finite element for 2D Poisson equation with exploration of the equivalence among hybrid, flux-based and stress-function-based equilibrium elements

Lin

Liu

et al. 2023

Engineering with Computers

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A comparison of primal- and dual-mixed finite element formulations for Timoshenko beams

Cited by 4 publications

References 6 publications

Comparative study of primal- and dual-mixed finite element models for cylindrical shells

Comparative study of primal- and dual-mixed finite element models for cylindrical shells

Euler-Bernoulli and Timoshenko Beam Theories Analytical and Numerical Comprehensive Revision

The simplest node-based equilibrium finite element for 2D Poisson equation with exploration of the equivalence among hybrid, flux-based and stress-function-based equilibrium elements

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