A New Shell Finite Element With Drilling Degrees of Freedom and Its Relation to Existing Formulations

Winkler, Robert; Plakomytis, Dimitrios

doi:10.7712/100016.1998.11192

Cited by 6 publications

(6 citation statements)

References 32 publications

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“…Recently, some advances have been reported that reduced or eliminated the dependence of the solution on the drilling stiffness parameters. 12,22 The second, global approach attempts to treat the drilling degrees of freedom in the assembled system of equations. 24 One possibility is to introduce constraints applied to singular degrees of freedom upon detection of zero pivots.…”

Section: Handling Of the Drilling Rotationsmentioning

confidence: 99%

“…On the other hand, too small of a drilling stiffness would destroy the condition number of the stiffness matrix. Recently, some advances have been reported that reduced or eliminated the dependence of the solution on the drilling stiffness parameters 12,22 …”

Section: Handling Of the Drilling Rotationsmentioning

confidence: 99%

“…9 Another issue that faces developers of simple facet elements is how to handle drilling rotations: rotations about the "normal" to the shell surface. Some formulations opt for adding drilling rotation degrees of freedom at various levels 3,[10][11][12] (theory, discrete model), others prefer to get rid of rotations altogether. 13,14 We elect to transform the drilling rotations out at the element level, while keeping them in the assembled global system of balance equations.…”

Section: Introductionmentioning

confidence: 99%

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Robust flat‐facet triangular shell finite element

Krysl

2022

Numerical Meth Engineering

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A flat facet finite element with three nodes and six degrees of freedom per node for linear static and dynamic analysis of thick and thin shells is presented. The membrane response is modeled with constant strain triangles. The bending response treats the transverse shear with an improved version of the discrete-shear-gap technique. The main novelty of the present approach is the robust treatment of the drilling rotations: the element internally responds to five degrees of freedom per node, but externally it naturally possesses six degrees of freedom per node. The drilling degree of freedom is decoupled from the bending and twisting, and the undesirable user-selectable arbitrary stabilization is avoided. The element is shown to be robust for extremely thin shells, and passes tests such as the Raasch hook problem. Performance is illustrated with static and dynamic examples including branched and folded shells.

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Section: Handling Of the Drilling Rotationsmentioning

confidence: 99%

Section: Handling Of the Drilling Rotationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust flat‐facet triangular shell finite element

Krysl

2022

Numerical Meth Engineering

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“…In this example, the acting load gives rise to in-plane bending and extensive shear deformation. The solutions for the vertical displacement at the point A (u A ) are normalized with the reference solution u ref ¼ 23:91 provided by Winkler and Plakomytis [43] and listed in Table 5. Obviously, the present element performs better than the Abaqus S3 element in this test case.…”

Section: Cooks Membranementioning

confidence: 99%

A three-node shell element based on the discrete shear gap and assumed natural deviatoric strain approaches

Rama¹,

Marinković²,

Zehn³

2018

J Braz. Soc. Mech. Sci. Eng.

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Thin-walled structures are of enormous importance in the structural engineering world. Their successful design calls for numerically efficient, accurate and reliable numerical tools. A new three-node shell element with six degrees of freedom per node-three translations and three rotations-is presented in this paper. The discrete shear gap approach together with the cell smoothing technique is implemented for treatment of shear locking. The membrane behavior is resolved by means of the assumed natural deviatoric strains formulation with certain adjustments implemented to accommodate for shell behavior. Examples are given to demonstrate the applicability of the proposed element for modeling shell structures. The accuracy and convergence rate are tested on a chosen set of well-known challenging benchmark problems, and the results are compared with those yielded by the Abaqus S3 element. Keywords Triangular shell element Á Discrete shear gap Á Strain cell smoothing Á Assumed natural deviatoric strains Á Drilling degree of freedom

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“…Four-node hybrid shell element based on the modified complementary energy functional almost insensitive to mesh distortions was described in [19]. Different methods of incorporating the drilling degree of freedom (DOF) in formulation of the EAS shell elements were compared in [20]. Mixed shell elements with the drilling DOF using the co-rotational kinematics concept were presented in [21][22][23].…”

mentioning

confidence: 99%

Robust four-node elements based on Hu–Washizu principle for nonlinear analysis of Cosserat shells

Daszkiewicz

Witkowski

Burzyński

et al. 2019

Continuum Mech. Thermodyn.

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Mixed 4-node shell elements with the drilling rotation and Cosserat-type strain measures based on the three-field Hu-Washizu principle are proposed. In the formulation, apart from displacement and rotation fields, both strain and stress resultant fields are treated as independent. The elements are derived in the framework of a general nonlinear 6-parameter shell theory dedicated to the analysis of multifold irregular shells. The novelty of the developed elements stems from the fact that the measures of assumed strains and stress resultants are asymmetric. The original interpolation of drilling and bending components of strains and stress resultants is proposed. In the formulation of new mixed elements, two variants of the interpolation of membrane components are used and interpolation of the independent fields is defined in the natural or skew coordinates. Accuracy and efficiency of the developed elements are tested in several linear and nonlinear numerical examples. It is shown that smaller number of independent parameters in the interpolation of membrane components gives more accurate results. The proposed mixed 4-node elements enable the use of large load steps in nonlinear computations. Moreover, they require significantly less equilibrium iterations than other shell elements formulated in the 6-parameter shell theory. Keywords Shell • Finite element • Mixed element • Cosserat • Asymmetric strains • Drilling rotation 1 Introduction Thin-walled shell structures are widely used in different branches of industry, e.g. aircraft, automotive, civil engineering. However, these structures are very sensitive to loss of stability and local damage, like delamination, cracking, etc. The detailed and comprehensive nonlinear analysis (postbuckling, damage, plasticity) requires an appropriately refined finite element discretization. Hence, accuracy and efficiency of the shell element formulation play both essential roles in fast and correct design process of thin-walled shell structures. Moreover, Communicated by Andreas Öchsner.

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A New Shell Finite Element With Drilling Degrees of Freedom and Its Relation to Existing Formulations

Cited by 6 publications

References 32 publications

Robust flat‐facet triangular shell finite element

Robust flat‐facet triangular shell finite element

A three-node shell element based on the discrete shear gap and assumed natural deviatoric strain approaches

Robust four-node elements based on Hu–Washizu principle for nonlinear analysis of Cosserat shells

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