Analysis of a gradient-elastic beam on Winkler foundation and applications to nano-structure modelling

D. M. Manias; T. K. Papathanasiou; S. I. Markolefas; E. E. Theotokoglou

doi:10.1016/j.euromechsol.2015.10.004

Analysis of a gradient-elastic beam on Winkler foundation and applications to nano-structure modelling

D. M. Manias, T. K. Papathanasiou, S. I. Markolefas, E. E. Theotokoglou

Electrical Engineering

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

An equation of motion governing the response of a first strain gradient beam, including the effect of a Winkler elastic foundation, is derived from the Hamilton-Lagrange principle. The model is based on Mindlin's gradient elasticity theory, while the Euler-Bernoulli assumption for slender beams is adopted. Higher-continuity Hermite Finite Elements are presented for the numerical solution of related Initial-Boundary Value (IBV) problems. In the static case an analytical solution is derived and the convergence characteristics of the proposed Finite Element formulation are validated against the exact response of the configuration. Several examples are presented using "equivalent beam" data for Carbon Nanotubes (CNT's) and the effect on the Winkler foundation is studied. Finally, applicability of the derived model for the simulation of micro-structures, as for example CNT's or Microtubules, is discussed.

Original language	British English
Pages (from-to)	45-58
Number of pages	14
Journal	European Journal of Mechanics, A/Solids
Volume	56
DOIs	https://doi.org/10.1016/j.euromechsol.2015.10.004
State	Published - Mar 2016

Keywords

Euler-Bernoulli beams
Gradient elasticity
Winkler foundation

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10.1016/j.euromechsol.2015.10.004

Cite this

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title = "Analysis of a gradient-elastic beam on Winkler foundation and applications to nano-structure modelling",

abstract = "An equation of motion governing the response of a first strain gradient beam, including the effect of a Winkler elastic foundation, is derived from the Hamilton-Lagrange principle. The model is based on Mindlin's gradient elasticity theory, while the Euler-Bernoulli assumption for slender beams is adopted. Higher-continuity Hermite Finite Elements are presented for the numerical solution of related Initial-Boundary Value (IBV) problems. In the static case an analytical solution is derived and the convergence characteristics of the proposed Finite Element formulation are validated against the exact response of the configuration. Several examples are presented using {"}equivalent beam{"} data for Carbon Nanotubes (CNT's) and the effect on the Winkler foundation is studied. Finally, applicability of the derived model for the simulation of micro-structures, as for example CNT's or Microtubules, is discussed.",

keywords = "Euler-Bernoulli beams, Gradient elasticity, Winkler foundation",

author = "Manias, {D. M.} and Papathanasiou, {T. K.} and Markolefas, {S. I.} and Theotokoglou, {E. E.}",

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year = "2016",

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doi = "10.1016/j.euromechsol.2015.10.004",

language = "British English",

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T1 - Analysis of a gradient-elastic beam on Winkler foundation and applications to nano-structure modelling

AU - Manias, D. M.

AU - Papathanasiou, T. K.

AU - Markolefas, S. I.

AU - Theotokoglou, E. E.

PY - 2016/3

Y1 - 2016/3

N2 - An equation of motion governing the response of a first strain gradient beam, including the effect of a Winkler elastic foundation, is derived from the Hamilton-Lagrange principle. The model is based on Mindlin's gradient elasticity theory, while the Euler-Bernoulli assumption for slender beams is adopted. Higher-continuity Hermite Finite Elements are presented for the numerical solution of related Initial-Boundary Value (IBV) problems. In the static case an analytical solution is derived and the convergence characteristics of the proposed Finite Element formulation are validated against the exact response of the configuration. Several examples are presented using "equivalent beam" data for Carbon Nanotubes (CNT's) and the effect on the Winkler foundation is studied. Finally, applicability of the derived model for the simulation of micro-structures, as for example CNT's or Microtubules, is discussed.

AB - An equation of motion governing the response of a first strain gradient beam, including the effect of a Winkler elastic foundation, is derived from the Hamilton-Lagrange principle. The model is based on Mindlin's gradient elasticity theory, while the Euler-Bernoulli assumption for slender beams is adopted. Higher-continuity Hermite Finite Elements are presented for the numerical solution of related Initial-Boundary Value (IBV) problems. In the static case an analytical solution is derived and the convergence characteristics of the proposed Finite Element formulation are validated against the exact response of the configuration. Several examples are presented using "equivalent beam" data for Carbon Nanotubes (CNT's) and the effect on the Winkler foundation is studied. Finally, applicability of the derived model for the simulation of micro-structures, as for example CNT's or Microtubules, is discussed.

KW - Euler-Bernoulli beams

KW - Gradient elasticity

KW - Winkler foundation

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SN - 0997-7538

VL - 56

SP - 45

EP - 58

JO - European Journal of Mechanics, A/Solids

JF - European Journal of Mechanics, A/Solids

ER -

Analysis of a gradient-elastic beam on Winkler foundation and applications to nano-structure modelling

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Keywords

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