A total Lagrangian Timoshenko beam formulation for geometrically nonlinear isogeometric analysis of planar curved beams

Vo, Duy; Nanakorn, Pruettha

doi:10.1007/s00707-020-02675-x

Cited by 21 publications

(15 citation statements)

References 39 publications

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“…( 22) is consistent with the stress field derived in Ref. [4,5,15,16,19,21,22,27,28] for finite strains.…”

Section: Materials Constitutive Modelsupporting

confidence: 89%

“…𝐸(𝐶 11 − 1) 𝑆 12 = 𝜇𝐶 12 𝑆 13 = 𝜇𝐶 13 ; 𝐸 = 𝜇(3𝜆 + 2𝜇)/(𝜆 + 𝜇) (22) in which 𝐸 represents Young modulus of the material. Eq.…”

Section: Materials Constitutive Modelmentioning

confidence: 99%

“…They also studied the effect of cross-section geometries in the large deformation regime. Vo and•Nanakorn [22] presented a new total Lagrangian Timoshenko beam formulation with the isogeometric analysis approach for a geometrically nonlinear analysis of planar curved beams.…”

Section: Introductionmentioning

confidence: 99%

“…He also studied some examples in the large deformation and post-buckling regime. Liao et al [22] also presented a differential quadrature formulation for post-buckling analysis of beams and 2D frames. Small displacements and rotations for an elastic domain were considered to derive equilibrium equations and stiffness matrix.…”

Section: Introductionmentioning

confidence: 99%

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Large-deformation instability behaviors of 3D beams supported with 3D hinge joints subjected to axial and torsional loadings

Damanpack

Bodaghi

2021

Acta Mech

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In this paper, an instability analysis of three-dimensional (3D) beams supported with 3D hinges under axial and torsional loadings is presented in large displacement and rotation regime. An exact displacement field is proposed based on the central line and orientation of the crosssection consisting of nine parameters corresponded to 3D centroid movements and rotations. Cauchy-Green deformation tensor is derived in the local coordinate system according to the proposed displacement field. Deformation tensor and a normal-shear constitutive model with highly polynomial non-linearity are developed based on the continuum mechanics. A finite element formulation is then established based on the higher order shape functions to avoid shear and membrane locking issues. The elemental governing equations of equilibrium as well as 3D nodal forces and moments are obtained using the Hamiltonian principle. To solve the final nonlinear equilibrium equations, Newton-Raphson and Riks techniques through an incrementaliterative scheme are implemented. The numerical results are presented to assess instability behaviors of beams with different cross sections and various 3D boundary conditions. The effects of 3D hinge joints on the stability of beams under axial and torsional loadings are studied for the first time. The numerical results reveal instability in bending and lateral-torsional buckling for beams supported by 3D hinge joints. This phenomenon is proved by both finite strain model and its linearization for small deformations. The numerical results show that the present finite element formulation is robust, reliable as well as simple and easy to model instability of 3D beams in the large displacement regime.

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“…( 22) is consistent with the stress field derived in Ref. [4,5,15,16,19,21,22,27,28] for finite strains.…”

Section: Materials Constitutive Modelsupporting

confidence: 89%

“…𝐸(𝐶 11 − 1) 𝑆 12 = 𝜇𝐶 12 𝑆 13 = 𝜇𝐶 13 ; 𝐸 = 𝜇(3𝜆 + 2𝜇)/(𝜆 + 𝜇) (22) in which 𝐸 represents Young modulus of the material. Eq.…”

Section: Materials Constitutive Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Large-deformation instability behaviors of 3D beams supported with 3D hinge joints subjected to axial and torsional loadings

Damanpack

Bodaghi

2021

Acta Mech

View full text Add to dashboard Cite

show abstract

“…The major goal is to achieve a smooth transition from geometric design to analysis using computer-aided design (CAD) basis functions, e.g., non-uniform rational B-spline (NURBS) basis functions, for both processes. In the last decades, IGA has experienced a rapid evolution with many engineering applications, for example, vibration analysis [1,2], structural analysis [3][4][5][6][7][8], damage and fracture problems [9,10], optimization [11,12]. In particular, dynamic analysis of beam structures using the IGA approach has been studied in recent years.…”

Section: Introductionmentioning

confidence: 99%

Dynamic multi-patch isogeometric analysis of planar Euler–Bernoulli beams

Borković

Nanakorn

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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This study presents a novel isogeometric Euler-Bernoulli beam formulation for in-plane dynamic analysis of multi-patch beam structures. The kinematic descriptions involve only displacements of the beam axis, which are approximated by non-uniform rational B-spline (NURBS) curves. Translational displacements of the control points are here considered as control variables. The motivation of this work is to propose a penalty-free method to handle in-plane dynamic analysis of multi-patch beam structures. A simple relation between cross-sectional rotations at the ends of the beams and control variables is derived, allowing the incorporation of the end rotations as degrees of freedom. This improved setting can straightforwardly tackle beam structures with many rigid multi-patch connections, a major challenging issue when using existing isogeometric Euler-Bernoulli beam formulations. Additionally, rotational boundary conditions are conveniently prescribed. Numerical examples with complicated beam structures such as circular arches and frames with kinks are considered to show the accuracy and performance of the developed formulation. The computed results are verified with those derived from the conventional finite element method, and the superior convergence properties of the proposed formulation are illustrated. We additionally discuss about the possible extension of the present approach to spatial beam structures.

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Self‐Sustained and Coordinated Rhythmic Deformations with SMA for Controller‐Free Locomotion

Zhou,

2024

Advanced Intelligent Systems

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This study presents a modular, electronics‐free, and fully onboard control and actuation approach for shape memory alloy (SMA)‐based soft robots to achieve locomotion tasks. This approach exploits the nonlinear mechanics of compliant curved beams and carefully designed mechanical control circuits to create and synchronize rhythmic deformation cycles, mimicking the central pattern generators prevalent in animal locomotions. More specifically, the study elucidates a new strategy to amplify the actuation performance of the shape memory coil actuator by coupling it to a carefully designed, monostable curve beam with a snap‐through buckling behavior. Such SMA‐curved beam assembly is integrated with an entirely mechanical circuit featuring a slider mechanism. This circuit can automatically cut off and supply current to the SMA according to its deformation status, generating a self‐sustained rhythmic deformation cycle using a simple DC power supply. Finally, this study presents a new strategy to coordinate (synchronize) two rhythmic deformation cycles from two robotic modules to achieve efficient crawling locomotion but still use a single DC power. This work represents a significant step toward fully autonomous, electronics‐free SMA‐based locomotion robots with fully onboard actuation and control.

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A total Lagrangian Timoshenko beam formulation for geometrically nonlinear isogeometric analysis of planar curved beams

Cited by 21 publications

References 39 publications

Large-deformation instability behaviors of 3D beams supported with 3D hinge joints subjected to axial and torsional loadings

Large-deformation instability behaviors of 3D beams supported with 3D hinge joints subjected to axial and torsional loadings

Dynamic multi-patch isogeometric analysis of planar Euler–Bernoulli beams

Self‐Sustained and Coordinated Rhythmic Deformations with SMA for Controller‐Free Locomotion

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