Geometric nonlinear formulation for curved beams with varying curvature

Pan, Keqi; Liu, Jinyang

doi:10.1063/2.1206306

Cited by 8 publications

(7 citation statements)

References 7 publications

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“…N xx , N yy , and N xy are the units in plane force on the element cross section; M xx , M yy , and Mxy are the bending and torque on the element cross section; and Q x and Q y are the transverse shear force on the element cross section. According to the laminate theory, the internal force and bending torque are defined as the integral of shell stress in the thickness direction [ 29 ]:

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Section: Study On Statics Of Thermoplastic Fiber Variable-angle Lamentioning

confidence: 99%

Mechanical Simulation of Thermoplastic Composite Fiber Variable-Angle Laminates

Cao

Guo

et al. 2020

Materials

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By changing the placement angle of the placement path, the fiber direction can be controlled and adjusted to change the load distribution in the laminate, and the stress and natural frequency performances of the laminate can then be altered to finally obtain laminates with desired mechanical properties. In this paper, the finite element analysis model of variable-stiffness laminates is established based on the fiber placement reference path defined by the Bezier curve method. Based on the analysis of the mechanical properties of the thermoplastic fiber variable-angle laminates obtained by variable-angle trajectory planning, the changes in the stress and deformation of the thermoplastic fiber variable-angle laminate with the connection point parameter β under a compressive load are analyzed. The influence of the parameter β on the static performances of the variable-angle laminates is studied. The simulation results indicate that the maximum stress of the laminate increases first and then decreases as the parameter β increases and reaches the maximum value when the parameter β is 0.5. The minimum stress also shows the same trend as that of the maximum stress and reaches the minimum value when the connection point parameter β is 0.3. The deformation of the variable-angle laminates varies with the change of the connection point parameter β. The maximum deformation increases at first and then decreases for the laminate with the parameter β increasing and reaches the maximum value when the parameter β is 0.8. The minimum deformation of the laminate decreases initially and then increases as the connection point parameter β increases and reaches the minimum value when the parameter β is 0.6. The deformation gradually decreases from the upper and lower ends to the middle, and the deformation area has a symmetrical form. The initial regular rectangular area gradually changes to an elliptical distribution and the area of maximum deformation gradually decreases.

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…”

Section: Study On Statics Of Thermoplastic Fiber Variable-angle Lamentioning

confidence: 99%

Mechanical Simulation of Thermoplastic Composite Fiber Variable-Angle Laminates

Cao

Guo

et al. 2020

Materials

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“…Reissner beam theory is being extensively used for stress and deformation characteristics of arbitrarily curved beam undergoing large deformation and small strain. Center line of such arbitrarily curved beam in its undeformed configuration is modeled by a space curve in parametric form as 3 0 ) ( R s r  [23][24][25][26]. Among three base vectors, two are directed along principal axes of beam cross section and the other one is along beam center line of the undeformed beam.…”

Section: Geometrically Exact Beam Theoriesmentioning

confidence: 99%

“…Due to high nonlinearity present in such initially curved beam structures, system governing equation is generally derived in weak form rather than in strong form, based on geometrically exact theory. Several numerical schemes are then implemented for solution purpose either considering whole domain or through domain discretization [24][25][26][27][28][29][30].…”

Section: Geometrically Exact Beam Theoriesmentioning

confidence: 99%

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Ghuku

Saha

2017

IJET

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The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

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“…Since the elements established by Shabana may produce coupled deformation and shear locking, Sugiyama et al [7,8] adopted the Hellinger-Reissner variational principle to correct the shear stress and established a fully parametric curved beam element and gradient defect curved beam element for analyzing large deformations in flexible multibody systems. Pan et al [9,10] derived nonlinear strain-displacement relations for planar curved beams based on the exact calculation of Green-Lagrangian strains in spatially curved beams and verified the effectiveness of curved beam elements by comparing them with physical experiments. Besides, Zhang et al [11] and Wu et al [12] used ANCF to derive a one-dimensional two-node curved beam element based on the exact expression of curvature and studied the large deformation problem.…”

Section: Introductionmentioning

confidence: 99%

Large deformations of hyperelastic curved beams based on the absolute nodal coordinate formulation

Wang

Guo

et al. 2022

Nonlinear Dyn

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Compared with traditional linear elastic materials, the soft structure composed of incompressible hyperelastic materials has not only geometrical nonlinearity but also material nonlinearity during deformation. In this paper, the absolute nodal coordinate formulation (ANCF) is used to study the large deformations and large overall motions of incompressible hyperelastic curved beams. A novel large deformation dynamic modeling method for curved beams made of hyperelastic materials is proposed, in which a simplified Neo-Hookean model is combined with the onedimensional ANCF beam element. The elastic force vector is calculated according to the exact expression of curvature. The dynamic equations are derived by using the virtual work principle. The dynamic responses of a cantilever silica gel beam under gravity are calculated based on the present method and compared with those of the improved low-order beam element (ILOBE), high-order beam element (HOBE), and commercial finite element analysis software (ANSYS). Simulation results show that the proposed method can accurately describe the large deformation and large overall motion of the beam, and has better computational efficiency. Research in this paper provides an efficient dynamic model for the dynamics analysis of soft robot arms.

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Geometric nonlinear formulation for curved beams with varying curvature

Cited by 8 publications

References 7 publications

Mechanical Simulation of Thermoplastic Composite Fiber Variable-Angle Laminates

Mechanical Simulation of Thermoplastic Composite Fiber Variable-Angle Laminates

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Large deformations of hyperelastic curved beams based on the absolute nodal coordinate formulation

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