Analysis of low order non-standard continualization methods for enhanced prediction of the dispersive behaviour of a beam lattice

Gómez-Silva, F.; Zaera, R.

doi:10.1016/j.ijmecsci.2021.106296

Cited by 20 publications

(6 citation statements)

References 50 publications

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“…It should be noted that when dimensionless variables are considered, the characteristic length takes the unitary value, and its presence is not noticeable in Eqs. ( 9) and ( 10) [41,52]. Therefore, the approximation order is determined by the order of the dimensionless spatial derivative.…”

Section: Standard Modelsmentioning

confidence: 99%

“…Polyzos and Fotiadis [34] employ several standard continualization procedures, leading to nonclassical continuum models with high-order differential equations, whereas Bacigalupo and Gambarotta [35] propose a non-standard continualization technique denominated Regularization, removing these high-order derivatives. Gómez-Silva et al [36] and Gómez-Silva and Zaera [37] [40] and Gómez-Silva and Zaera [41] study a lattice beam system considering bending deformation, Gómez-Silva and Zaera including next-nearest interactions in [42]. A modified semi-continuum Euler beam model with relaxation phenomenon is developed by Shen and Li in [43], where they present the bending deformation of a extreme-thin beam with micro/nano-scale thickness.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Low-order non-classical continuum models for the improved prediction of an anisotropic membrane lattice’s dynamics

Gómez-Silva

Zaera²

2022

Thin-Walled Structures

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Section: Standard Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Low-order non-classical continuum models for the improved prediction of an anisotropic membrane lattice’s dynamics

Gómez-Silva

Zaera²

2022

Thin-Walled Structures

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“…In view of equations (12,(16)(17), the analytical expression of the primary kinematic variables j w, is lastly derived as…”

Section: Analytical Analysis Of Flexurementioning

confidence: 99%

“…Remarkable features of CNTs, however, cannot be precisely realized applying the classical approach of the elasticity theory. A great attention is, accordingly, devoted in the recent literature to the generalized elasticity theories, such as nonlocal elasticity approach [6][7][8][9][10][11][12][13][14][15][16], strain gradient theory [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], and unified elasticity frameworks [32][33][34][35][36][37][38][39][40][41][42][43][44], for nanoscopic study of the field quantities.…”

Section: Introductionmentioning

confidence: 99%

Modified couple stress flexure mechanics of nanobeams

Sedighi¹,

Abouelregal²,

Faghidian³

2021

Phys. Scr.

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In view of numerous contributions accessible in the literature associated with the modified couple stress theory, its deficiency in precise description of the material response of continua with nanostructural features is investigated. The flexure mechanics of nano-scale beams in the framework of the modified couple stress theory is reassessed applying a consistent variational scheme. The physically motivated constitutive laws of the stress resultant fields, flexural moment and shear force, associated with the modified couple stress beam are introduced. The well-established differential conditions of equilibrium equipped with the proper mathematical form of the higher-order boundary conditions are reinstated. The exact analytical solutions of the kinematic fields of the nano-sized beam are derived by direct solving of the governing coupled differential equations. The flexure response of the modified couple stress beam is numerically illustrated wherein the effects of the symmetric rotation gradients along with the transverse shear deformation are examined. Closed-form analytical formulae of the elastic modulus of Carbon Nanotubes are detected and thoroughly discussed. Serious suspicions on the applicability of the modified couple stress beam model in accurately capturing the size-effects in nano-materials are emerged as evinced by rigorous examination of the elastic modulus of CNTs.

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“…To this end, the enhanced continualization technique proposed by Bacigalupo and Gambarotta [5] for onedimensional lattice and by Bacigalupo and Gambarotta [6] for twodimensional lattices undergoing transversal motion is here developed. This technique, which has been also successfully tested in comparative studies by Gómez-Silva et al [17] and Gómez-Silva and Zaera [18], is here applied to a representative case of square beam-lattice to obtain the field equations governing the motion of the equivalent non-local continuum formulated at different orders. Through the presented approach both non-local stiffness and inertia terms are obtained, in agreement with the non-local continuum models proposed by the seminal papers of Mindlin (1964) [34], Eringen (1983) [35], Askes and Aifantis (2011) [36], and more recently by Bacigalupo and Gambarotta (2014) [37], De Domenico and Askes [12], and De Domenico et al [13].…”

Section: Introductionmentioning

confidence: 99%