A Mixed Co-Rotational 3d Beam Element Formulation for Arbitrarily Large Rotations

Li, Z. X.; Vu‐Quoc, L.

doi:10.18057/ijasc.2010.6.2.6

Cited by 9 publications

(16 citation statements)

References 27 publications

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“…In general, the two smallest components of one orientation vector and one smaller component of another orientation vector at a node can be selected as global rotational variables, and these vectors can be oriented to three global coordinate axes in the initial configuration or defined as those of the beam element presented in [83][84][85].…”

Section: Element Kinematics In the Local Co-rotational Systemmentioning

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: Element Kinematics In the Local Co-rotational Systemmentioning

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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“…Different from other existing corotational shell elements, which use rotation axial vectors (pseudovectors) or the related spin tensors as degrees of freedom, leading to nonsymmetric tangent matrix, the present element formulation employs vectorial rotational variables that are components of polar (proper) vectors to develop a corotation framework for large displacement and large rotation problems. Any existing applied moments that correspond to the rotation axial vectors are transformed into equivalent loads for the corresponding vectorial rotation variables …”

Section: Treatment Of Special Load and Boundary Conditionmentioning

confidence: 99%

“…Any existing applied moments that correspond to the rotation axial vectors are transformed into equivalent loads for the corresponding vectorial rotation variables. 70 Assuming that vector e n is rotated through infinitesimal rotations of T = ⟨ x y z ⟩to become vector e n + 1 , then an approximate relationship of e n and e n + 1 can be given as e n+1 = e n + × e n = [I + S ( )] e n ,…”

Section: Treatment Of Special Load and Boundary Conditionmentioning

confidence: 99%

A nine‐node corotational curved quadrilateral shell element for smooth, folded, and multishell structures

Vu‐Quoc

et al. 2018

Numerical Meth Engineering

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Summary A nine‐node corotational curved quadrilateral shell element with novel treatment for rotation at intersection of folded and multishell structures is presented. The element's corotational reference frame is defined by the two bisectors of the diagonal vectors generated using the four corner nodes and their cross product. In reference frame, the element rigid‐body rotations are excluded in calculating the local nodal variables from the global nodal variables. Rotations are not represented by axial (pseudo) vectors but by components of polar (proper) vectors, of which additivity and commutativity lead to symmetry of the tangent stiffness matrix. In the global coordinate system, the two smallest components of the midsurface normal vector at each node of a smooth shell or at nodes away from the intersection of nonsmooth shells are defined as rotational variables. In addition, of the two nodal orientation vectors at intersections of folded and multishell structures, two smallest components of one vector, together with one smaller component of another vector, are employed as rotational variables, leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure. In the local coordinate system, the two smallest components of the midsurface normal vector(s) at any node of a smooth shell or in each smooth patch of nonsmooth shell are defined as rotational variables. Different from other existing corotational finite‐element formulations, the resulting element tangent stiffness matrix is symmetric owing to the commutativity of the local nodal variables in calculating the second derivative of strain energy with respect to these nodal variables. To alleviate membrane and shear locking phenomena, the membrane strains and the out‐of‐plane shear strains are replaced with assumed strains, using the Mixed Interpolation of Tensorial Components approach, for obtaining the element tangent stiffness matrices and the internal force vector. Finally, a series of benchmark, challenging smooth, folded, and multishell structures undergoing large displacements and large rotations are analyzed to demonstrate the reliability and computational accuracy of the proposed formulation.

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“…Now we turn our attention to nonlinear deformation of the bend using the following data [19][20][21][22][23][24][25][26]: R = 100, a = 1,  = 45, E = 10 7 , and  = 0. The values of tip displacements of the bend obtained by different finite-element models are summarized in Table 6.…”

Section: Tablementioning

confidence: 99%

Formulation of a geometrically nonlinear 3D beam finite element based on kinematic-group approach

Levyakov

2015

Applied Mathematical Modelling

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Please cite this article as: S.V. Levyakov, Formulation of a geometrically nonlinear 3D beam finite element based on kinematic-group approach, Appl. Math. Modelling (2015), doi: http://dx. AbstractA relatively simple finite element with 12 degrees of freedom is proposed for geometrically nonlinear analysis of spatial shear deformable beams and rods. The finite-element formulation is based on the concept of kinematic group, which is a geometrical object comprising two nodes on the rod axis and two adjoined vectors (directors) which define orientation of the cross section at each node. Results of some sample problems are given to show the applicability of the element to study nonlinear deformation and stability of three-dimensional elastic rods undergoing finite rotations.

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A Mixed Co-Rotational 3d Beam Element Formulation for Arbitrarily Large Rotations

Cited by 9 publications

References 27 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

A nine‐node corotational curved quadrilateral shell element for smooth, folded, and multishell structures

Formulation of a geometrically nonlinear 3D beam finite element based on kinematic-group approach

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