Correlation between beam on Winkler-Pasternak foundation and beam on elastic substrate medium with inclusion of microstructure and surface effects

Limkatanyu, Suchart; Ponbunyanon, Paitoon; Prachasaree, Woraphot; Kuntiyawichai, Kittisak; Kwon, Min Ji

doi:10.1007/s12206-014-0827-6

Cited by 8 publications

(8 citation statements)

References 43 publications

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“…To include the surface-energy effect, this theory has been integrated with the classical continuum-mechanics model. Several structural models (bar, beam, and plate) have employed the Gurtin-Murdoch surface elasticity model [29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

A Thermodynamics-Based Nonlocal Bar-Elastic Substrate Model with Inclusion of Surface-Energy Effect

Sae-Long

Limkatanyu

Prachasaree

et al. 2020

Journal of Nanomaterials

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This paper presents a bar-elastic substrate model to investigate the axial responses of nanowire-elastic substrate systems considering the effects of nonlocality and surface energy. The thermodynamics-based strain gradient model is adopted to capture the nonlocality of the bar-bulk material while the Gurtin-Murdoch surface theory is utilized to consider the surface energy. To characterize the bar-surrounding substrate interaction, the Winkler foundation model is employed. In a direct manner, system compatibility conditions are obtained while within the framework of the virtual displacement principle, the system equilibrium condition and the corresponding natural boundary conditions are consistently obtained. Three numerical simulations are conducted to investigate the characteristics and behaviors of the nanowire-elastic substrate system: the first is conducted to reveal the capability of the proposed model to eliminate the paradoxical behavior inherent to the Eringen nonlocal differential model; the second is employed to characterize responses of the nanowire-elastic substrate system; and the third is aimed at demonstrating the dependence of the system effective Young’s modulus on several system parameters.

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Section: Introductionmentioning

confidence: 99%

A Thermodynamics-Based Nonlocal Bar-Elastic Substrate Model with Inclusion of Surface-Energy Effect

Sae-Long

Limkatanyu

Prachasaree

et al. 2020

Journal of Nanomaterials

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“…The modified strain gradient theory of Lam et al [1] can be reduced from Form I or III of Mindlin's strain gradient elasticity theory (e.g., [7]) and can be further simplified to a modified couple stress theory (MCST; e.g., [12,13]), which contains only one material length scale parameter. By using this MCST, non-classical models have been proposed for Bernoulli-Euler beams [14][15][16], Timoshenko beams [17,18] and Reddy-Levinson beams [19,20]. Liang et al [21] developed a nonclassical Bernoulli-Euler beam model based on a simplified strain gradient elasticity theory (e.g., [22][23][24]), which is also known as the dipolar gradient elasticity theory (e.g., [25,26]).…”

Section: Introductionmentioning

confidence: 99%

A new Bernoulli–Euler beam model based on a reformulated strain gradient elasticity theory

Zhang

Gao

2019

Mathematics and Mechanics of Solids

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A new non-classical Bernoulli–Euler beam model is developed using a reformulated strain gradient elasticity theory that incorporates both couple stress and strain gradient effects. This reformulated theory is first derived from Form I of Mindlin’s general strain gradient elasticity theory. It is then applied to develop the model for Bernoulli–Euler beams through a variational formulation based on Hamilton’s principle, which leads to the simultaneous determination of the equation of motion and the complete boundary conditions and provides a unified treatment of the strain gradient, couple stress and velocity gradient effects. The new beam model contains one material constant to account for the strain gradient effect, one material length scale parameter to describe the couple stress effect and one coefficient to represent the velocity gradient effect. The current non-classical beam model reduces to its classical elasticity-based counterpart when the strain gradient, couple stress and velocity gradient effects are all suppressed. In addition, the newly developed beam model includes the models considering the strain gradient effect only or the couple stress effect alone as special cases. To illustrate the new model, the static bending and free vibration problems of a simply supported beam are analytically solved by directly applying the general formulas derived. The numerical results reveal that the beam deﬂection predicted by the current model is always smaller than that by the classical model, with the difference being large for very thin beams but diminishing with the increase of the beam thickness. Also, the natural frequency based on the new beam model is found to be always higher than that based on the classical model.

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“…Finally, as stated, representing the filling material by a Winkler foundation is a simplification aimed at obtaining a mathematically tractable problem. This obviously implies approximations that could be improved by modeling the filling material by a more complex model, as the Winkler-Pasternak foundation, (Limkatanyu et al, 2014), (Civalek, 2007), (Kerr, 1964).…”

Section: Remembering That and That Givesmentioning

confidence: 99%

Mechanics of filled cellular materials

Ongaro

Falco

Barbieri

et al. 2016

Mechanics of Materials

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Correlation between beam on Winkler-Pasternak foundation and beam on elastic substrate medium with inclusion of microstructure and surface effects

Cited by 8 publications

References 43 publications

A Thermodynamics-Based Nonlocal Bar-Elastic Substrate Model with Inclusion of Surface-Energy Effect

A Thermodynamics-Based Nonlocal Bar-Elastic Substrate Model with Inclusion of Surface-Energy Effect

A new Bernoulli–Euler beam model based on a reformulated strain gradient elasticity theory

Mechanics of filled cellular materials

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