Elastica of a variable-arc-length circular curved beam subjected to an end follower force

Pulngern, Tawich; Sudsanguan, Tanin; Athisakul, Chainarong; Chucheepsakul, Somchai

doi:10.1016/j.ijnonlinmec.2012.10.002

Cited by 13 publications

(7 citation statements)

References 25 publications

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“…We have 14 equations for the proposed element, Eqs. (23) up to (36) for the straight beam-, and Eqs. (19) up to (22) together with Eqs.…”

Section: Kinematic Equationsmentioning

confidence: 98%

“…Beside the two most popular methods of GEF and ANCF, new researches with new ideas are also performed for different problems of beam large deflection; see [33][34][35][36][37][38][39]. Analytical methods such as assumed modes method [40][41][42][43][44] can also be developed or combined with the finite element method for use in the large deflection of the beam structures.…”

Section: And Mahdi Sharifniamentioning

confidence: 99%

“…(19) up to (22) together with Eqs. (27) up to (36) for the curved beam. There are 20 unknowns for the element, parameters a 1 and a 2 together with six nodal unknowns for each of the three nodes.…”

Section: Kinematic Equationsmentioning

confidence: 99%

See 2 more Smart Citations

A new beam element for analysis of planar large deflection

Sharifnia

2018

J Braz. Soc. Mech. Sci. Eng.

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In the present study, a simple and efficient finite element approach is presented for large deflection analysis of both the straight and curved Euler-Bernoulli beams in the planar static problems. The linear stress-strain relationship is assumed for the Euler-Bernoulli beam. In some of finite element methods, displacements together with rotations, and in some others, positions are considered as the main fields of interpolation. However, in the present study, the main idea for the interpolation is using the dimensions of the deformed element instead of the displacements. Therefore, the slope angle (like the previous works) and the length of beam centroidal axis (unlike the previous works) are used as the main field parameters. This treatment creates simplicity in the constitutive equations. Next, using the weighted residual method, the constitutive equations are applied to the element. Using the equilibrium equations and kinematic equations, the position coordinates of the nodes are related to the internal forces and the main field parameters. In the present study, three-node element and, consequently, Simpson's 1/3 rule is used for integration. For solving nonlinear equations of the beam, the Newton-Raphson method is used. Finally, several numerical examples are presented and compared with the previous works to illustrate the validity and efficiency of the new element.

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“…We have 14 equations for the proposed element, Eqs. (23) up to (36) for the straight beam-, and Eqs. (19) up to (22) together with Eqs.…”

Section: Kinematic Equationsmentioning

confidence: 98%

Section: And Mahdi Sharifniamentioning

confidence: 99%

See 1 more Smart Citation

A new beam element for analysis of planar large deflection

Sharifnia

2018

J Braz. Soc. Mech. Sci. Eng.

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“…Based on a new variational principle expressed in terms of stress components, Cannarozzi and Molari [7] proposed a nonlinear formulation for curved, extensible, shear flexible, elastic planar beams. e research of curved beams considering the extension of axis length was also conducted by Pulngern et al [8]. In their work, the postbuckling behaviors of a variable-arc-length circular curved beam subjected to an end follower force were examined by using the elliptic integrals method and shooting method.…”

Section: Introductionmentioning

confidence: 99%

Geometrically Nonlinear Analysis of Functionally Graded Timoshenko Curved Beams with Variable Curvatures

Wan

Liu

2019

Advances in Materials Science and Engineering

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In this paper, geometrically nonlinear analysis of functionally graded curved beams with variable curvatures based on Timoshenko beam theory is presented. Considering the axial extension and the transversal shear deformation, geometrically nonlinear governing equations for the FGM curved beams with variable curvatures subjected to thermal and mechanical loads are formulated. Material properties of the curved beams are assumed to vary arbitrarily in the thickness direction and be independent on the temperature change. By using the numerical shooting method to solve the coupled ordinary differential equations, the nonlinear response of static thermal bending of a FGM semielliptic beams subjected to transversely nonuniform temperature rise is obtained numerically. e effects of material gradient, shear deformation, and temperature rise on the response of the curved beam are discussed in detail. Nonlinear bending of a closed FGM elliptic structure subjected to two pinching concentrated loads is also analyzed. is paper presents some equilibrium paths and configurations of the elliptic curved beam for different pinching concentrated loads.

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“…Baghani et al, 2014;Bickford, 1982;Carrera et al, 2012;Dong et al, 2013;Ghosh et al, 2013;Kang, 2014;Li, 2014;Miranda et al, 2013;Pradhan and Chakraverty, 2014;Reddy, 1984;Salamat-talab et al, 2012;Sarkar and Ganguli, 2013;Thai and Vo, 2012;Timoshenko, 1921;Vlasov, 1961;Wang et al, 2000), (ii) large displacements but infinitesimally small strains (e.g. Chen, 2010;Chen and Hung, 2014;Freno and Cizmas, 2012;Jang, 2013;Karlson and Leamy, 2013;Lin and Lin, 2011;Monsalve et al, 2007;Nallathambi et al, 2010;Neukirch et al, 2012;Posada et al, 2011;Pulngern et al, 2013;Reddy, 2010;Reddy and Borgi, 2014;Sapountzakis and Mokos, 2008;Tari, 2013); there have been only very few studies on the rods undergoing finite strains (e.g., Dias and Audoly, 2014;Hori and Sasagawa, 2000), considering both of the geometrical and physical nonlinearities, and specially rubber-like rods (e.g. Attard and Hunt, 2008;Dai and Li, 2009;Lacarbonara, 2008;Libai and Simmonds, 1998;Makowski and Stumpf, 1988).…”

Section: Introductionmentioning

confidence: 99%

A theory for rubber-like rods

Yükseler

2015

International Journal of Solids and Structures

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A theory for incompressible rubber-like straight rods undergoing finite strains and finite rotations is presented. Strains are expanded asymptotically for transverse coordinate of undeformed rod. The equations of equilibrium and corresponding boundary conditions are derived by implementing minimum total potential energy principle. Necessary conditions for the satisfaction of the stress-free boundary conditions on the top and bottom free surfaces of the rubber-like rods are derived. For the illustration and test of the proposed theory, the flexural buckling problem of Mooney-Rivlin rods under axial compressive loads is considered. Exact solutions corresponding to (i) various alternatives about the perturbation terms of the strain components, (ii) a very rigorous rod theory developed previously, and (iii) the three dimensional elasticity are obtained and compared.Degree of accuracy of the aforementioned approaches is discussed basing on the three dimensional elasticity solution. It is observed that considering all of the second order permutation terms yields very appealing results, almost coinciding with the results corresponding to the three dimensional elasticity for thin and quite thick rods.

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Elastica of a variable-arc-length circular curved beam subjected to an end follower force

Cited by 13 publications

References 25 publications

A new beam element for analysis of planar large deflection

A new beam element for analysis of planar large deflection

Geometrically Nonlinear Analysis of Functionally Graded Timoshenko Curved Beams with Variable Curvatures

A theory for rubber-like rods

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