A DKT shell element for dynamic large deformation analysis

Wu, S. David; Li, Guangyao; Belytschko, Ted

doi:10.1002/cnm.783

Cited by 14 publications

(8 citation statements)

References 32 publications

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“…Existing 3-node triangular shell elements can be categorized into 4 types: Type 1 with only 3 displacement degrees-of-freedom (dofs) per node [14][15][16][17][18][19][20][21][22]; Type 2 with 3 displacement dofs and 2 rotational dofs per node [23][24][25]; Type 3 with 3 displacement dofs at the vertices and the rotational dofs at side nodes [26][27]; Type 4 with 3 displacement dofs and 3 rotational dofs per node [28][29][30][31][32][33]. Most existing 3-node rotation-free triangular shell elements are based on the Kirchhoff assumption, ignoring shear deformation, can therefore only be employed in modeling thin plate and shell problems [21].…”

Section: Introductionmentioning

confidence: 99%

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

Li¹,

Izzuddin²,

Vu‐Quoc³

et al. 2017

Volume 13 Number 3

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A 3-node co-rotational triangular elasto-plastic shell element is developed. The local coordinate system of the element employs a zero-'macro spin' framework at the macro element level, thus reducing the material spin over the element domain, and resulting in an invariance of the element tangent stiffness matrix to the order of the node numbering. The two smallest components of each nodal orientation vector are defined as rotational variables, achieving the desired additive property for all nodal variables in a nonlinear incremental solution procedure. Different from other existing co-rotational finite-element formulations, both element tangent stiffness matrices in the local and global coordinate systems are symmetric owing to the commutativity of the nodal variables in calculating the second derivatives of strain energy with respect to the local nodal variables and, through chain differentiation with respect to the global nodal variables. For elasto-plastic analysis, the Maxwell-Huber-Hencky-von Mises yield criterion is employed together with the backward-Euler return-mapping method for the evaluation of the elasto-plastic stress state, where a consistent tangent modulus matrix is used. Assumed membrane strains and assumed shear strains---calculated respectively from the edge-member membrane strains and the edge-member transverse shear strains---are employed to overcome locking problems, and the residual bending flexibility is added to the transverse shear flexibility to improve further the accuracy of the element. The reliability and convergence of the proposed 3-node triangular shell element formulation are verified through two elastic plate patch tests as well as three elastic and three elasto-plastic plate/shell problems undergoing large displacements and large rotations.

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Section: Introductionmentioning

confidence: 99%

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

Li¹,

Izzuddin²,

Vu‐Quoc³

et al. 2017

Volume 13 Number 3

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“…Furthermore, many of the approaches are applied to simple geometries such as plates, or spherical and cylindrical geometries [18,19,12,20]. Towards a general, flexible and robust methodology to deal with fracture in Kirchhoff-Love shells, we propose here treating fracture with a phasefield model and discretizing the coupled thin-shell/phase-field equations with a recently proposed meshfree method for partial differential equations on manifolds of complex geometry and topology [21,22].…”

Section: Introductionmentioning

confidence: 99%

Phase-field modeling of fracture in linear thin shells

Amiri

Millán

Shen

et al. 2014

Theoretical and Applied Fracture Mechanics

285

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We present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximumentropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantage over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected pipes.

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“…In contrast to other ANS elements, there is no need to choose an interpolation for the shear strains or to specify any sampling points, but its accuracy is not good enough. Among various triangular elements, Discrete Kirchhoff triangular (DKT) elements developed by Stricklin et al [10], Dhatt [11,12] and Batoz et al [13] appear attractive, and have been used for dynamic analysis [14]. For the DKT elements, the shear locking effect can be eliminated by removing the shear deformation from element kinematics.…”

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confidence: 99%

An edge-based smoothed triangle element for non-linear explicit dynamic analysis of shells

Zheng

Cui

et al. 2011

Comput Mech

Self Cite

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The paper presents an edge-based smoothed triangular element (EST) for nonlinear analysis of shell structures using an explicit dynamic formulation. In order to improve the accuracy and the convergence of the shell element without additional parameters, the gradient smoothing operation is performed to the strain rates in the smoothing domains associated with the edges of triangular elements. An edge coordinate system is defined local on the edges of the triangular element for the strain smoothing operation. The material nonlinearities for the dynamic solution are treated by using the updated Lagrangian description and an elastic-plastic constitutive law. The shear strains in the element formulation are approximated using the discrete shear gap method to mitigate the shear locking, and this element can be applicable for both thin shells and thick shells. Numerical results for elastic and elastic-plastic problems show the effectiveness and efficiency of the proposed shell element.Keywords Shell · Edge-based smoothed triangular element · Gradient smoothing technique · Non-linear finite element · Explicit finite element

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A DKT shell element for dynamic large deformation analysis

Cited by 14 publications

References 32 publications

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

Phase-field modeling of fracture in linear thin shells

An edge-based smoothed triangle element for non-linear explicit dynamic analysis of shells

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