A robust quadrilateral membrane finite element with drilling degrees of freedom

This paper presents buckling and free vibration analysis of composite plate/shell structures of various shapes, modulus ratios, span-to-thickness ratios, boundary conditions and lay-up sequences via a novel smoothed quadrilateral flat element. The element is developed by incorporating a strain smoothing technique into a flat shell approach. As a result, the evaluation of membrane, bending and geometric stiffness matrices are based on integration along the boundary of smoothing elements, which leads to accurate numerical solutions even with badly-shaped elements. Numerical examples and comparison with other existing solutions show that the present element is efficient, accurate and free of locking.

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“…Details of the formulation can be found in the original reference [20] and only a brief review is presented here.…”

Section: Membrane Partmentioning

confidence: 99%

Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations

Nguyen‐Van

Mai‐Duy

Karunasena

et al. 2011

Computers & Structures

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“…Ibrahimbegovi c et al [29] amended the displacement interpolation of a four-node quadrilateral element by the Allman-type [2] quadratic modes in order to improve the coarse mesh accuracy of the element. This considerably improves the bending behavior of the element.…”

Section: On the Value Of The Regularizing Parameter In The Hughes±brementioning

confidence: 99%

Stabilized and block approximate inverse preconditioners for problems in solid and structural mechanics

Benzi

Kouhia²,

Tůma

2001

Computer Methods in Applied Mechanics and Engineering

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“…In this study, a quadrilateral shell element formed by the membrane element with drilling rotations proposed by Ibrahimbegovic et al [40] and the DKQ plate element proposed by Batoz and Tahar [41] is adopted for demonstration. The shell element was also extended into the geometrically nonlinear analysis by authors (Tang et al [32]; Tang et al [42]) and obtained success.…”

Section: Geometrical Stiffness Due To Warping Effectmentioning

confidence: 99%

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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A robust quadrilateral membrane finite element with drilling degrees of freedom

Cited by 216 publications

References 15 publications

Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations

Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations

Stabilized and block approximate inverse preconditioners for problems in solid and structural mechanics

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

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