Analytical solution for large deflections of a cantilever beam under nonconservative load based on homotopy analysis method

Kimiaeifar, Amin; Domairry, G.; Mohebpour, Saeed Reza; Sohouli, Abdolrasoul; Davodi, A. G.

doi:10.1002/num.20538

Cited by 20 publications

(13 citation statements)

References 23 publications

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“…(24), one can express the boundary conditions of F and M of the beam on its two ends. It is noted that the force and moment balance presented in Eq.…”

Section: Virtual Work Equationmentioning

confidence: 99%

“…Most of the previous works in this context are somehow restricted to special beam configurations, e.g., works by Bisshopp and Drucker [7], Rao and Rao [33], Lee [26], Zakharov et al [47], Shvartsman [38] and Kimiaeifar et al [24] are restricted to straight beams or works by Srpčič and Saje [44], Nallathambi et al [28] and Batista [2] are restricted to the plane problem of beams.…”

mentioning

confidence: 98%

“…Shvartsman [39] has extended the method used by Shvartsman [38] further for the analysis of curved beams, and using an explicit fourth-order Numerov integrating scheme has solved the problem of large deflections of the curved beam. Kimiaeifar et al [24] have presented an analytical solution based on a homotopy analysis method for the static large deflection analysis of a straight beam subjected to a tip-concentrated tip load with a fixed inclination angle with respect to the beam reference line. Chen [12] has used a moment integral approach for the large deflection analysis of straight beams under combined conservative loads.…”

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confidence: 99%

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Large deflection analysis of geometrically exact spatial beams under conservative and nonconservative loads using intrinsic equations

Masjedi

Ovesy

2014

Acta Mech

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Large deflection analysis of geometrically exact beams under conservative and nonconservative loads is considered. A Chebyshev collocation method is used for the discretization of the governing equations of the spatial beam with intrinsic formulation. In the case of nonconservative (follower) loads, since the formulation is expressed in a deformed frame, the formulation is fully free from any displacement or rotational variables, and a direct solution can be achieved. In the case of conservative loads, the applied loads are functions of beam rotations, and in order to retain the intrinsic nature of the formulation, a direct integration of rotations is avoided and an iterative solution of the governing equations in addition to an update on the beam rotations as a post-processing step has been employed. A number of test cases have been considered and are compared to the existing experimental as well as numerical results in the literature. A very good agreement has been observed in the comparison cases, and it is shown that the intrinsic formulation in conjunction with a Chebyshev collocation method while exhibiting advantages in ease of implementation, computational cost and convergence characteristics over other methods can effectively capture the large deflection behavior of spatial beams under various load conditions.

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“…(24), one can express the boundary conditions of F and M of the beam on its two ends. It is noted that the force and moment balance presented in Eq.…”

Section: Virtual Work Equationmentioning

confidence: 99%

mentioning

confidence: 98%

mentioning

confidence: 99%

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Large deflection analysis of geometrically exact spatial beams under conservative and nonconservative loads using intrinsic equations

Masjedi

Ovesy

2014

Acta Mech

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“…Previously, large deflections of a flexible link have been studied extensively when modelled as a nonlinear cantilever beam experiencing an external force (tip concentrated and/or distributed loads) in the steady case, using the arc length coordinate system. Many different methods have been implemented, including the analytical homotopy analysis method [12,13] as well as numerical techniques such as the finite-element method [14]; a smooth curvature model [15]; an ellipticfunction solution combined with the shooting method [16,17]; a fourth-order Runge-Kutta method [18,19]; a beam-constraint model [20]; and a finite-difference method [21]. Although analysis of a cantilever beam undergoing large deflections is extensive, models combining these with rigid bodies, to form pseudo-kinematic chains, are very limited.…”

Section: Introductionmentioning

confidence: 99%

“…Figure13. Experimental linear trajectory control error x for all joint types when feedforward control was derived using an idealized hinge assumption and implemented for (a) DR F , (b) DR L and (c) DR P .…”

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confidence: 99%

Nonlinear flexure coupling elements for precision control of multibody systems

Bailey¹,

Lusty²,

Keogh³

2018

Proc. R. Soc. A.

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Conventional multibody systems used in robotics and automated machinery contain bearing components that exhibit complex and uncertain tribological characteristics. These limit fundamentally the precision of the automated motion and also cause wear. Replacing traditional bearing joints with flexure couplings eliminates these tribological effects, together with wear, reducing necessary system maintenance and offering a potential for increased motion precision. A flexure-coupled multibody system is considered and a novel general solution technique is presented. Derivation of a large deflection flexure coupling model is provided and subsequently validated using an experimental facility. A focused study of a unique double-flexure-coupling rigid body system is given; the formulated nonlinear mathematical model can be used for feedforward control. Equivalent control is also applied to a corresponding system with traditional bearing joints. The feasibility of replacing bearing joints by flexure couplings is demonstrated in terms of accurate large displacement control and reduction of high-frequency disturbances.

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Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method

Doeva

Masjedi

2021

Acta Mech

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New analytical solutions for the static deflection of anisotropic composite beams resting on variable stiffness elastic foundations are obtained by the means of the Homotopy Analysis Method (HAM). The method provides a closed-form series solution for the problem described by a non-homogeneous system of coupled ordinary differential equations with constant coefficients and one variable coefficient reflecting variable stiffness elastic foundation. Analytical solutions are obtained based on two different algorithms, namely conventional HAM and iterative HAM (iHAM). To investigate the computational efficiency and convergence of HAM solutions, the preliminary studies are performed for a composite beam without elastic foundation under the action of transverse uniformly distributed loads considering three different types of stacking sequence which provide different levels and types of anisotropy. It is shown that applying the iterative approach results in better convergence of the solution compared with conventional HAM for the same level of accuracy. Then, analytical solutions are developed for composite beams on elastic foundations. New analytical results based on HAM are presented for the static deflection of composite beams resting on variable stiffness elastic foundations. Results are compared to those reported in the literature and those obtained by the Chebyshev Collocation Method in order to verify the validity and accuracy of the method. Numerical experiments reveal the accuracy and efficiency of the Homotopy Analysis Method in static beam problems.

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Analytical solution for large deflections of a cantilever beam under nonconservative load based on homotopy analysis method

Cited by 20 publications

References 23 publications

Large deflection analysis of geometrically exact spatial beams under conservative and nonconservative loads using intrinsic equations

Large deflection analysis of geometrically exact spatial beams under conservative and nonconservative loads using intrinsic equations

Nonlinear flexure coupling elements for precision control of multibody systems

Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method

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