Stability and optimal shape of Pflüger micro/nano beam

Glavardanov, V.B.; Spasic, D. T.; Atanacković, Teodor M.

doi:10.1016/j.ijsolstr.2012.05.016

Cited by 14 publications

(7 citation statements)

References 24 publications

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“…Examples include buckling/post-buckling, vibration and rotation analysis as in [8,12,30,31,33], [1,21,22,32] and [26], respectively. Optimization of such rods have also been studied in [3,4,16]. The constitutive equation…”

Section: Problem Formulationmentioning

confidence: 99%

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Nano- and viscoelastic Beck’s column on elastic foundation

2015

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Beck's type column on Winkler type foundation is the subject of the present analysis. Instead of the Bernoulli-Euler model describing the rod, two generalized models will be adopted: Eringen non-local model corresponding to nano-rods and viscoelastic model of fractional Kelvin-Voigt type. The analysis shows that for nano-rod, the Herrmann-Smith paradox holds while for viscoelastic rod it does not.

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Section: Problem Formulationmentioning

confidence: 99%

“…The non-local constitutive moment-curvature equation will now be adopted in order to analyse dynamic stability of Beck's column on Winkler foundation and to determine if the Herrmann-Smith paradox is removed. Adjoining (14), (15), (16) it is derived that…”

Section: Problem Formulationmentioning

confidence: 99%

Nano- and viscoelastic Beck’s column on elastic foundation

2015

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“…Glavardanov et al [37] presented optimal shapes against buckling of elastic nonlocal small-scale Pflüger beams with Eringen's model. Eltaher et al [38,39] presented static, buckling, and free vibration analysis of functionally graded (FG) nonlocal size-dependent nanobeams using the finite element method.…”

Section: Introductionmentioning

confidence: 99%

Postbuckling and Free Vibration of Multilayer Imperfect Nanobeams under a Pre-Stress Load

et al. 2018

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This paper investigates the postbuckling and free vibration response of geometrically imperfect multilayer nanobeams. The beam is assumed to be subjected to a pre-stress compressive load due to the manufacturing and its ends are kept at a fixed distance in space. The small-size effect is modeled according to the nonlocal elasticity differential model of Eringen within the nonlinear Bernoulli-Euler beam theory. The constitutive equations relating the stress resultants to the cross-section stiffness constants for a nonlocal multilayer beam are developed. The governing nonlinear equation of motion is derived and then manipulated to be given in terms of only the lateral displacement. The static problem is solved for the buckling load and the postbuckling deflection in terms of three parameters: Imperfection amplitude, size, and lamination. A closed-form solution for the buckling load in terms of all of the beam parameters is developed. With the presence of imperfection and size effects, it has been shown that the buckling load can be either less or greater than the Euler buckling load. Moreover, the free vibration in the pre and postbuckling domains are investigated for the first five modes. Numerical results show that the effects of imperfection, the nonlocal parameter, and layup on buckling loads and natural frequencies of the nanobeams are significant.

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“…In order to solve more complex problems of plane elastica i.e. problems with different constitutive axioms and different load, engineering communities are still interested in efficient methods for solving both linear and nonlinear differential equations, see [2][3][4][5][6][7][8]. Recently, due to an enormous and wide-spread availability of computational power one more efficient method was added to the list, see [9] where the Laplace transform and the method of successive approximations (LT&MSA for short), was used in finding the analytical approximative solutions describing Toda oscillators …”

Section: Introductionmentioning

confidence: 99%