An efficient mixed interpolated curved beam element for geometrically nonlinear analysis

In this paper, an improved flat triangular shell element is proposed. This element has three nodes, and in each node, six degrees of freedom are considered. Since there are three rotational degrees of freedom at each node, the drilling effect can be incorporated in authors' formulation. A new procedure is also suggested for updating the director vectors about which the rotational degrees of freedom are defined. In order to study large displacements and rotations, Total Lagrangian principles are employed. In addition, updating the rotational degrees of freedom is implemented using enriched updated director vectors, which are formulated based on the finite rotation method. On the other hand, small strains are considered in this formulation. By utilizing MITC method, shear and membrane locking is mitigated from new element. To examine the performance, the element passes three basic tests, including isotropy, and patch test. Moreover, a convergence study is also implemented to show the elemental behavior. Several popular benchmarks are considered to illustrate the accuracy and capability of the suggested element in geometrically nonlinear analyses.

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“…The load-displacement curve of point (A) is provided in Figure 16. Figure 16 The equilibrium path of deep arch under the central point load P.…”

Section: Simply Supported Deep Archmentioning

confidence: 99%

“…They used Mixed Interpolation of Tensorial Components (MITC) to avoid shear and membrane locking in their proposed element [8]. Moreover, some more studies were developed to use this technique [2,[9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

A 6-parameter triangular flat shell element for nonlinear analysis

Rezaiee‐Pajand

Masoodi

Arabi

2019

TECM

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“…Then, the application range of their methods is limited. In addition, these elements [19][20][21][22][23][24][25] were all developed in an inertia coordinate system. The shape functions of these elements are used to ensure the continuity of the global displacement field and cannot take the constitutive relationship of the materials into account.…”

Section: Introductionmentioning

confidence: 99%

“…An element-independent framework is established by using the same shape functions to derive the nonlinear equations of motion of the element based on Hamilton's principle. In contrast with the curved beam elements [19][20][21][22][23][24][25][26][27][28] developed in the inertia coordinate system, the shape functions of the presented element are used to describe the local displacement field. Then, many standard elements, [5][6][7][8] developed based on exact solutions in a curvilinear coordinate system, can be embedded into the framework.…”

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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“…Straight beam elements were previously used extensively for approximating curved beam geometry in finite element analysis. Use of straight elements in large number for approximating curved geometry not only results high computational cost but also arises question on accuracy as well [25]. Development of economically efficient and rigorous curved beam elements has been one of the major focus of engineers for the last few decades [26].…”

Section: Introductionmentioning

confidence: 99%

Large Deflection of Clamped Curved Beam Under Finite Clamping and Different Combinations of Bending-Stretching

Ghuku

Saha

2020

EST

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The paper experimentally and theoretically analyses large deflection behaviour of clamped curved beam subjected to finite clamping and combined bending-stretching loads. The experimental specimen is clamped around central location under vertically concave and convex orientations. For each specimen settings, clamping is done by two different torque values. Application of vertical end loads on the clamped concave and convex systems produces two different combinations of bending and in-plane loadings. Large deflection behaviour of the experimental system is modelled theoretically considering geometric nonlinearities coming from combined bending-stretching, non-uniform curvature and asymmetric geometry. Effect of finite clamping is incorporated in the theoretical model through equivalent additional end loads. Due to the involved geometric nonlinearities, analysis is carried out through variational energy principle based incremental Lagrangian approach in curvilinear system and transformed into global frame. The semi-analytical model is successfully validated by comparing with the experimental results. The combined theoretical-experimental study addresses practical complication associated with local deformation at boundaries. In addition, the physically plausible theoretical model may be of interest for simulation of many real world structures with complicating system parameters. Moreover, observations on combined effects of curvature, loading combinations and finite clamping may provide reference for design optimization of equivalent engineering structures.

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An efficient mixed interpolated curved beam element for geometrically nonlinear analysis

Cited by 20 publications

References 62 publications

A 6-parameter triangular flat shell element for nonlinear analysis

A 6-parameter triangular flat shell element for nonlinear analysis

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

Large Deflection of Clamped Curved Beam Under Finite Clamping and Different Combinations of Bending-Stretching

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