A new approach for elasto-plastic finite strain analysis of cantilever beams subjected to uniform bending moment

Tayyar, Gökhan Tansel

doi:10.1007/s12046-016-0475-x

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…By substituting equation (7) into equation (6), the bending moment of the plasticised cross-section for the incremental analysis of deflection of the prismatic fixed-end beam can be defined as follows 19 :…”

Section: Solution For the Elastoplastic Bending Of The Prismatic Fixe...mentioning

confidence: 99%

“…4,5 Further research covered proposing of a new model for elastoplastic finite strain analysis of prismatic and non-prismatic rectangular cantilever beams under bending moment. 6 A theoretical solution has also been proposed for the large deflection analysis of prismatic rectangular cantilever beams made of elastoplastic materials with non-linear strain hardening. 7 Research has covered the influence of the inclined load on the large deflection of elastoplastic cantilever rectangular beams.…”

Section: Introductionmentioning

confidence: 99%

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Semi-analytical solution for elastoplastic deflection of prismatic fixed-end beams with circular cross-section

Zorić

Trajković-Milenković

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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Prismatic fixed-end beams with circular cross-section are often used in engineering. Therefore, there is a need for a solution of an elastoplastic deflection of prismatic fixed-end beams with circular cross-section loaded by lateral displacement at one end of the beam, which is suitable for practical use. The elastoplastic deflection beam theory does not provide a solution in a closed form for such a problem. Hence, a semi-analytical solution is proposed in this paper. Homogenous and isotropic beams with the bilinear elastoplastic strain hardening behaviour are covered in the proposed solution. The elastic deflection of a beam is determined by the Bernoulli–Euler formula. However, differential equation of beam bending in the plastic domain of material behaviour does not have a solution in a closed form. Therefore, an incremental procedure for determining the curvature of the plasticised region of the beam is suggested. The proposed semi-analytical solution is validated by comparing to the finite element analysis results of 16 different fixed-end beam models with varying geometric and material characteristics. Also, validation is done with experimental results of the bar damper device, available in the literature, which has been selected as a sample of a real engineering system where the proposed solution can be applied. A satisfying agreement between the proposed semi-analytical results and the subsequent numerical and experimental results is herein achieved, confirming the solution’s reliability. Finally, a parametric study is conducted using the proposed semi-analytical solution in order to determine the influence of geometrical parameters and material characteristics on the mechanical properties of prismatic fixed-end beams with circular cross-section loaded by lateral displacement at one end of the beam.

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Section: Solution For the Elastoplastic Bending Of The Prismatic Fixe...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Semi-analytical solution for elastoplastic deflection of prismatic fixed-end beams with circular cross-section

Zorić

Trajković-Milenković

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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Newton vs. Euler–Lagrange approach, or how and when beam equations are variational

Babilio,

Lenci

2024

Meccanica

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There is a clear and compelling need to correctly write the equations of motion of structures in order to adequately describe their dynamics. Two routes, indeed very different from a philosophical standpoint, can be used in classical mechanics to derive such equations, namely the Newton vectorial approach (i.e., roughly, sum of forces equal to mass times acceleration) or the Euler–Lagrange variational formulation (i.e., roughly, stationarity of a certain functional). However, it is desirable that whichever derivation strategy is chosen, the equations are the same. Since many structures of interest often consist of slender and highly flexible beams operating in regimes of large displacement and large rotation, we restrict our attention to the Euler-Bernoulli assumptions with a generic initial configuration. In this setting, the question that arises is: What conditions must the constitutive assumptions satisfy in order for the equations of motion obtained by Newton’s approach to be identical to the Euler–Lagrange equations derived from an appropriate Lagrangian, natural or virtual, for any arbitrary initial configuration? The aim of this paper is to try to answer this basic question, which indeed does not have an immediate and simple answer, in particular as a consequence of the fact that bending moment could be related to two different notions of flexural curvature.

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A new approach for elasto-plastic finite strain analysis of cantilever beams subjected to uniform bending moment

Cited by 2 publications

References 15 publications

Semi-analytical solution for elastoplastic deflection of prismatic fixed-end beams with circular cross-section

Semi-analytical solution for elastoplastic deflection of prismatic fixed-end beams with circular cross-section

Newton vs. Euler–Lagrange approach, or how and when beam equations are variational

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