A high-precision co-rotational formulation of 3D beam elements for dynamic analysis of flexible multibody systems

Wang, Gang; Zai-kang, QI; Xu, Jinshuai

doi:10.1016/j.cma.2019.112701

Cited by 22 publications

(7 citation statements)

References 44 publications

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“…where . By the principle of field consistency, it can be obtained that: (7) where is the transformation matrix between the co-rotational coordinate system and the structural coordinate system, and its specific form is given in [8].…”

Section: Co-rotational Normal Expressionmentioning

confidence: 99%

See 1 more Smart Citation

A Novel Geometric Nonlinear Analysis Method for Planar Beam Structures Based on Co- Rotation and Substructure Method

Liang,

Deng

2023

J. Phys.: Conf. Ser.

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Nonlinear behavior analysis of structures using finite element methods requires multiple iterative solutions. Therefore, improving computational efficiency while ensuring the accuracy of nonlinear calculations is crucial. In this paper, a new geometric nonlinear analysis method for planar beam structures is proposed, based on the co-spinning method and the substructure method, using a substructure containing two planar beam elements as an example. The co-spinning method accurately calculates small deformations by subtracting rigid body displacement from the large displacement of the structure. The substructure method condenses the degrees of freedom of internal nodes into boundary nodes, greatly reducing the order of the nonlinear equilibrium equation group of the structure. The two methods are combined, and a calculation program is developed using the arc length method, which has good performance in solving nonlinear equation groups. Two classic examples are used to verify the correctness of the proposed method by comparing the results with existing literature.

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Section: Co-rotational Normal Expressionmentioning

confidence: 99%

“…Recent studies have shown that the C.R. Method has several advantages, including a simple formulation, applicability to various element types [4][5] , and ease of incorporating material nonlinearity [6][7] . Therefore, it has become a hot research topic for scholars both domestically and abroad.…”

Section: Introductionmentioning

confidence: 99%

A Novel Geometric Nonlinear Analysis Method for Planar Beam Structures Based on Co- Rotation and Substructure Method

Liang,

Deng

2023

J. Phys.: Conf. Ser.

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“…The Gibbs-Appell equation represents an alternative to Lagrange's equations. To use these, it is necessary to know the energy of acceleration, obtained in Equation (33). The Gibbs-Appell equations are [62]:…”

Section: Gibbs-appell Formalismmentioning

confidence: 99%

“…The evaluation of inertial forces is a central and complicated task for the dynamic analysis of flexible multibody systems (FMS). A high-precision formulation for a 3D problem of flexible multibody systems is presented in [33]. The novelty is that the equations of motion were obtained with the principles of virtual power, without having to use the differentiation of the rotation matrix.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Method-Based Elastic Analysis of Multibody Systems: A Review

2022

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This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write the equations of motion, the most used methods are presented, namely the Lagrange equations method, the Gibbs–Appell equations, Maggi’s formalism and Hamilton’s equations. While the method of Lagrange’s equations is well documented, other methods have only begun to show their potential in recent times, when complex technical applications have revealed some of their advantages. This paper aims to present, in parallel, all these methods, which are more often used together with some of their engineering applications. The main advantages and disadvantages are comparatively presented. For a mechanical system that has certain peculiarities, it is possible that the alternative methods offered by analytical mechanics such as Lagrange’s equations have some advantages. These advantages can lead to computer time savings for concrete engineering applications. All these methods are alternative ways to obtain the equations of motion and response time of the studied systems. The difference between them consists only in the way of describing the systems and the application of the fundamental theorems of mechanics. However, this difference can be used to save time in modeling and analyzing systems, which is important in designing current engineering complex systems. The specifics of the analyzed mechanical system can guide us to use one of the methods presented in order to benefit from the advantages offered.

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“…Furthermore, Le et al 18,32 developed an efficient formulation that can ensure the consistency of the elements and establish an element‐independent framework that is consistent with the idea of Nour‐Omid and Rankin's method 17,30 . In recent years, Wang et al 33 developed a high‐precision corotational formulation with a lumped mass matrix based on the principle of virtual power. Deng et al developed different forms of variable‐domain corotational beam elements for the nonlinear dynamic analysis of sliding beams, 9,34 viscoelastic beams, 35 and arresting gears 36 .…”

Section: Introductionmentioning

confidence: 99%

A two‐dimensional corotational curved beam element for dynamic analysis of curved viscoelastic beams with large deformations and rotations

Deng

Niu

Xue

et al. 2022

Numerical Meth Engineering

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This paper presents a two‐dimensional corotational curved beam element for the dynamic analysis of curved viscoelastic beams with large deformations and rotations. In contrast with traditional straight beam elements, the novelty of the presented formulation lies in introducing a curved reference configuration, which follows the rotation and translation of a corotational frame, to measure the pure elastic deformation of the beam and describe the spatial position of an arbitrary material point. A curvilinear coordinate system is fixed on this reference configuration to measure the local deformation of the element. Based on Hamilton's principle, the global elastic force vector, the global internal damping force vector, the global inertia force vector, and the global external damping force vector are derived using the same shape functions to ensure the consistency and independence of the element. An accurate two‐node curved element and the Kelvin–Voigt model are introduced to consider the axial deformation, bending deformation, shear deformation, rotary inertia, and viscoelasticity of the beam. Three examples are given to verify the validity, computational accuracy, and computational efficiency of the presented formulation. Moreover, the effects of the internal damping and external damping on the dynamic response of a rotating curved beam are investigated.

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A high-precision co-rotational formulation of 3D beam elements for dynamic analysis of flexible multibody systems

Cited by 22 publications

References 44 publications

A Novel Geometric Nonlinear Analysis Method for Planar Beam Structures Based on Co- Rotation and Substructure Method

A Novel Geometric Nonlinear Analysis Method for Planar Beam Structures Based on Co- Rotation and Substructure Method

Finite Element Method-Based Elastic Analysis of Multibody Systems: A Review

A two‐dimensional corotational curved beam element for dynamic analysis of curved viscoelastic beams with large deformations and rotations

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