Weak form quadrature element analysis of geometrically exact shells

Zhang, Run; Zhong, Hongzhi

doi:10.1016/j.ijnonlinmec.2015.01.010

Cited by 19 publications

(4 citation statements)

References 38 publications

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“…The weak form quadrature element method (QEM) [18] is an efficient numerical tool that has enjoyed successful applications in analysis of various nonlinear structural problems [19][20][21][22]. It usually proceeds with partitioning the problem domain in the reference coordinate system into integrable elements and performing numerical integration followed by numerical differentiation.…”

Section: Shabana and Eldeebmentioning

confidence: 99%

Weak form quadrature shell elements based on absolute nodal coordinate formulation

He,

Li,

Zhong

2024

Preprint

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Weak form quadrature elements for moderately thick shells with arbitrary initial configurations are developed under the framework of continuum mechanics and the absolute nodal coordinate formulation (ANCF). Nodal variables of the element consist of the position vector, the transverse gradient vector and the transverse derivatives thereof at the shell mid-surface. In-plane gradient vectors which are not taken as nodal variables are obtained with the aid of the differential quadrature analog. Using the transverse gradient vector and one in-plane gradient vector, joint constraint equations for shells with discontinuous slopes are established. Simplified equations of motion with constant mass matrix result. The elements are applicable to analysis of shell structures undergoing large displacements and rotations. Five examples encompassing static and dynamic shell analysis, post-buckling analysis of shells, as well as analysis of shells with discontinuous mid-surface slopes are examined to assess the performance of the proposed elements. Satisfactory results are obtained, validating the efficacy of the proposed elements.

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Section: Shabana and Eldeebmentioning

confidence: 99%

Weak form quadrature shell elements based on absolute nodal coordinate formulation

He,

Li,

Zhong

2024

Preprint

Self Cite

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“…In addition to the research under the frame work of small deformation, the QEM has also been applied to investigate the geometric nonlinear problems. Zhong and his colleagues studied the static large deformation and rotation of slender beams and shell . Liao and Zhong studied the free vibration of geometric nonlinear thin rectangular plates .…”

Section: Introductionmentioning

confidence: 99%

“…Zhou et al performed the geometric nonlinearity beam analysis of composite wind turbine blades . In these studies, the geometric nonlinearities are considered via either the geometrically exact theory or the Green‐Lagrange strain, and none of the research has been reported on the CR formulation of the QEM thus far.…”

Section: Introductionmentioning

confidence: 99%

A co‐rotational weak‐form quadrature planar beam element for geometric nonlinear static and dynamic analysis

Yuan

Wang

Kardomateas

2019

Numerical Meth Engineering

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Summary The co‐rotational formulation of quadrature planar beam element undergoing large displacement and large rotation is presented. A local frame co‐rotates with the differential element and decomposes the motion into a rigid body movement and a strain‐producing deformation. General explicit formulations of elemental vectors and matrices, including internal force vector, external force vector, tangent stiffness matrix, and mass matrix, are derived via the numerical integration together with the differential quadrature law. Thus, the element nodes and numerical integration method can be chosen arbitrarily based on the accuracy requirement and problem type. A number of case studies on the static, postbuckling, and dynamic response of beams and frame structures are conducted. The convergence study shows that the co‐rotational quadrature element has an exponential rate of convergence and the reduced Gauss integration yield the highest accuracy. It is seen that the proposed co‐rotational quadrature beam element is simple in formulations, computationally efficient, and capable of capturing the complex nonlinear behavior of beam and frame structures with high precision.

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“…In this paper, the weak form quadrature element method (QEM), a more general approach proposed by Zhong and his colleagues [10] [11], is used, which has shown great adaptability and efficiency when dealing with problems with complex geometric shapes, loading conditions or non-homogeneous materials [12] [13]. The annular plate is mapped to standard plane domain by geometric transformation, and the formulations are established in plane Cartesian coordinate system.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Multi-Directional Functionally Graded Annular Plates Using the Weak Form Quadrature Element Method

You¹,

Zhong²

2017

Proceedings of the 2017 2nd International Symposium on Advances in Electrical, Electronics and Computer Engineering (ISAEECE 20

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Abstract. Free vibration analysis of multi-directional functionally graded annular plates is achieved in this paper. Uni-directional and bi-directional exponentially varying material properties through the thickness and along the radial direction of the plate are assumed. A four variable refined plate theory and the weak form quadrature element method are employed to establish the formulation. Numerical examples are given and results are compared with other available solutions. Good agreement is achieved, demonstrating the accuracy and high convergence rate of the present method in free vibration analysis of multi-directional functionally graded annular plates.

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Weak form quadrature element analysis of geometrically exact shells

Cited by 19 publications

References 38 publications

Weak form quadrature shell elements based on absolute nodal coordinate formulation

Weak form quadrature shell elements based on absolute nodal coordinate formulation

A co‐rotational weak‐form quadrature planar beam element for geometric nonlinear static and dynamic analysis

Free Vibration Analysis of Multi-Directional Functionally Graded Annular Plates Using the Weak Form Quadrature Element Method

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