A stabilized co‐rotational curved quadrilateral composite shell element

Li, Z. X.; Liu, Y. F.; Izzuddin, B.A.; Vu‐Quoc, L.

doi:10.1002/nme.3084

Cited by 13 publications

(16 citation statements)

References 77 publications

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“…Similar to this simpler co-rotational framework, Izzuddin [19] defined a new local co-rotational system and adopted vectorial rotation for quadrilateral shell elements, through which not only the invariance to node ordering but also a symmetric tangent stiffness matrix can be achieved. Pertaining studies on shell elements with this co-rotational framework were also presented in references (Li and Vu-Quoc [20]; Li et al [21]; Li et al [22]; Li et al [23]; Li et al [24]; Izzuddin and Liang [25]; Li et al [26]). …”

Section: Introductionmentioning

confidence: 84%

“…(22) following standard mathematical flow. However, based on the pure deformational model, a novel and simpler derivation of the EICR algorithm can be proposed, in which the geometrical stiffness matrix is derived by the load perturbation of the linear equilibrium equations in its local coordinates system.…”

Section: Co-rotational Algorithmmentioning

confidence: 99%

“…(22); k is due to the warping and corresponds to the last terms in Eq. (22). The details of each geometrical stiffness matrix will be introduced as follows.…”

Section: Co-rotational Algorithmmentioning

confidence: 99%

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A Co-Rotational Framework for Quadrilateral Shell Elements Based on the Pure Deformational Method

Tang

Liu

Chan

2018

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ABSTRACT:In this paper, a novel co-rotational framework for quadrilateral shell element allowing for the warping effect based on the pure deformational method is proposed for geometrically nonlinear analysis. This new co-rotational framework is essentially an element-independent algorithm which can be combined with any type of quadrilateral shell element. As the pure deformational method is adopted, the quantities of the shell element can be reduced, such that it needs less computer storage and therefore enhances the computational efficiency. In the proposed framework, the geometrical stiffness is derived with a clear physical meaning and regarded as the variations of the nodal internal forces due to the motions and deformations of shell element. Furthermore, the warping effect of quadrilateral shell element is considered, and for this reason, the structures undergoing significant warping can be efficiently solved by the proposed formulation. Finally, several benchmark examples are used to verify the validation and accuracy of the proposed method for geometrically nonlinear analysis.Keywords: element-independence, co-rotational method, flat quadrilateral shell element, pure deformation, geometrically nonlinear analysis, explicit tangent stiffness DOI: 10.18057/IJASC. 2018.14.1.6 INTRODUCTIONShell structures and steel frames made up of thin-wall members are commonly used in civil and structural engineering. Generally, it needs huge computer time to analyze a structure by finite shell elements compared with beam-column elements, especially in nonlinear analyses. Thus, the development of shell elements with high performance as well as the co-rotational framework with improved computational efficiency continuously attracts the attention of many researchers.There are three common methods based on the Lagrangian kinematic description for geometrically nonlinear analyses, i.e. total Lagrangian (TL), updated Lagrangian (UL) and co-rotational approaches. The last method is latest and attracts more attention than the others recently due to its simplicity and efficiency. The basic idea of the co-rotational method is that the total motions of an element can be divided into two parts, including the rigid body motions and the pure deformations.To decompose them, a local frame is attached to and co-rotated with the element. Then, the translations and rotations of the local frame are taken as the rigid body movements, while the deformations of the element produced in the local frame are regarded as the pure deformations. In reality, the classification of the Lagrangian kinematic descriptions for geometrically nonlinear analysis is not absolute. The co-rotational approach can be incorporated with either the total Lagrangian (TL) or the updated Lagrangian (UL) formulations. In the following, some research works related to the co-rotational description are discussed.

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Section: Introductionmentioning

confidence: 84%

Section: Co-rotational Algorithmmentioning

confidence: 99%

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A Co-Rotational Framework for Quadrilateral Shell Elements Based on the Pure Deformational Method

Tang

Liu

Chan

2018

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“…Following the original proposal by Rankin et al [33,34], this framework is still used [35][36][37][38][39][40]. With respect to the fixed frame fe 1 ; e 2 ; e 3 g, a corotational (CR) frame fe 1 ; e 2 ; e 3 g is defined as…”

Section: Geometrically Nonlinear Formulationmentioning

confidence: 99%

Imperfection sensitivity analysis of laminated folded plates

Barbero

Madeo

Zagari

et al. 2015

Thin-Walled Structures

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“…This formulation could allocate a superior recovery of the rotation filed. Li et al (2011) also introduced a corotational quadrilateral composite shell element employing vectorial rotation variables. Recently, Eriksson and Faroughi (2013), developed a triangular space membrane element based on a CR approach for quasi-static inflation simulations.…”

Section: Introductionmentioning

confidence: 99%

Co-rotational formulation for dynamic analysis of space membranes based on triangular elements

Faroughi

Eriksson

2015

Int J Mech Mater Des

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Nonlinear triangular space membrane elements are developed for the analysis of thin structures subjected to dynamic loading. By using a co-rotated framework, displacements are decomposed into rigid body motions and pure deformational displacements. The novelty of the formulation is that it employs the co-rotated framework to derive tangent dynamic matrix and an inertial force vector. Closed forms for the inertia force vector, the tangent dynamic matrix, the mass matrix and the gyroscopic matrix are derived directly from the current coordinate transformation matrix. Three numerical examples are presented to illustrate the robustness and efficiency of the new corotational formulation. The efficiency of the proposed approach is compared to the updated Lagrangian method, and savings in computation of up to 50 %, were achieved.

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A stabilized co‐rotational curved quadrilateral composite shell element

Cited by 13 publications

References 77 publications

A Co-Rotational Framework for Quadrilateral Shell Elements Based on the Pure Deformational Method

A Co-Rotational Framework for Quadrilateral Shell Elements Based on the Pure Deformational Method

Imperfection sensitivity analysis of laminated folded plates

Co-rotational formulation for dynamic analysis of space membranes based on triangular elements

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