Nonlinear Behavior of Beams Having Initially Small Imperfection Subjected to Sinusoidal Load

Atacan, Ayfer Tekin; Yükseler, R. Faruk

doi:10.17798/bitlisfen.592938

Cited by 5 publications

(4 citation statements)

References 17 publications

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“…[145][146][147][148] The details of the numerical procedure carried out by choosing a displacement component instead of the loading parameter as an independent variable are specified in Tekin and Yu¨kseler. 133 It should be noted that the snap-back behavior is not encountered in the present study.…”

Section: Numerical Approachesmentioning

confidence: 60%

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Nonlinear buckling and post-buckling analyses of functionally graded circular shallow arches

Atacan,

Yükseler

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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Snap-through analysis of thin, functionally graded (FG), fixed, circular shallow arches subjected to uniformly distributed vertical load is examined in this paper. The modulus of elasticity varies gradually along with the normal to the axis of the arch in alliance with the power law form. The solution of the geometrically nonlinear problem is carried out by using a numerical scheme accounting for the moderately large deflections theory based on small strain and moderate rotation in the von Kármán sense. The combined effect of the parameters that is, the power law index, the ratio of the modulus of elasticity and the modified slenderness ratio on the support reactions, the snap-buckling and post-buckling behaviors of the fixed circular shallow arches are examined. It is found that the lowest buckling load is considerably affected by the variation of these parameters. In addition, the effects of the material distribution on internal forces, deformed configurations and rotation angle are presented at various stages of the deformation.

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Section: Numerical Approachesmentioning

confidence: 60%

“…The expression in the parentheses of equation (18) is called the effective shear force, 133 and it is the approximate sum of the vertical components of the shear force Q , which is known to be the derivative of the bending moment in elementary theory, 134 and the axial force N :…”

Section: Governing Equationsmentioning

confidence: 99%

Nonlinear buckling and post-buckling analyses of functionally graded circular shallow arches

Atacan,

Yükseler

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Burada, iç kuvvetlerin (N, M) işaret kuralları, Tekin Atacan ve Yükseler [20] çalışmasında belirtilen tarzdadır. İlkel kusur küçük olduğundan, normal kuvvetin kiriş boyunca değişimi ihmal edilecektir.…”

Section: Problemi̇n Matemati̇ksel Modeli̇ (Mathematical Model Of the ...unclassified

“…Burada, V efektif kesme kuvveti olarak adlandırılmakta olup [20], Eş. 13 ile ifade edilmiş olan düşey doğrultudaki denge denklemi Eş.…”

Section: Problemi̇n Matemati̇ksel Modeli̇ (Mathematical Model Of the ...unclassified

Snap-buckling and post-buckling analyses of fixed supported beams having initially small circular imperfection under the effect of uniformly distributed vertical load

Atacan

Yükseler

2022

Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi

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 Effects of a geometric parameter on the buckling values and the post-buckling behavior  Deformed shapes of the initially imperfect beam during various stages of deformation  Distributions of internal forces during various stages of loading Figure A. Equilibrium paths of a fixed beam having initially small circular imperfection and deformed shapes at various stages of deformationPurpose: In this study, snap-buckling and post-buckling behavior of fixed beams having initially small circular imperfection under lateral loading is examined. In addition to the effects of a geometric parameter (which is a function of the thickness, radius and central angle of the circular neutral line of the undeformed beam) on buckling values, its effects on support reactions and internal forces are also investigated. Theory and Methods:The governing differential equations obtained within the framework of the Euler-Bernoulli beam theory are transformed into algebraic equations with the help of the finite difference method. The resulting nonlinear algebraic equations are solved by the displacement-controlled Newton-Raphson method. By drawing loaddeflection graphs, the effects of the concerning geometric parameter on the buckling values and the postbuckling behavior are analyzed. Results:Unlike the previous studies on the subject; the variations of the support reactions, the diagrams of the deformed shapes of the fixed beams having initially small circular imperfection as well as the diagrams of the internal forces at various stages of the loading including the buckling and post-buckling states are investigated for various values of the geometric parameter. Conclusion:For fixed beams having an initially small imperfection under a vertical loading, not only the bending behavior but also the stability behavior should be examined. A geometric parameter which can be defined according to the geometry of an initially imperfect beam can have significant effects on the equilibrium paths, buckling values, support reactions, deformed shapes, and internal forces.

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A finite strain theory for incompressible rubber-like circular arches with an application

Faruk Yükseler

2024

Thin-Walled Structures

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Nonlinear Behavior of Beams Having Initially Small Imperfection Subjected to Sinusoidal Load

Cited by 5 publications

References 17 publications

Nonlinear buckling and post-buckling analyses of functionally graded circular shallow arches

Nonlinear buckling and post-buckling analyses of functionally graded circular shallow arches

Snap-buckling and post-buckling analyses of fixed supported beams having initially small circular imperfection under the effect of uniformly distributed vertical load

A finite strain theory for incompressible rubber-like circular arches with an application

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