期刊
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
卷 180, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijengsci.2022.103747
关键词
Nanobeams; Foundations; Size effects; Nonlocal continua; Analytical solutions; NEMS
资金
- Italian Ministry of Education, University and Research, Italy [PRIN-code 2017J4EAYB, 2020-2021]
- research program ReLUIS, Italy 2020-2021
- Croatian Science Foundation, Croatia [IP-2019-04-4703]
This study solves the problem of nanobeams on nano-foundations by improving the Eringen-Wieghardt integral elasticity theory. The effectiveness of the proposed nonlocal approach is demonstrated through analytical solutions of beam-soil systems simulating nanocomposites and biological cells.
A plethora of current applicative problems of Nano-Engineering involve nanostructures in-teracting with elastic media which exhibit significant size effects. Internal elasticity of the nanostructure and external elasticity of the surrounding foundation can be conveniently modelled by two nonlocal continua, provided that the relevant structure-soil problem results to be well-posed. This issue is still an open problem of Engineering Science and is solved in the present study by improving the Eringen-Wieghardt integral elasticity theory for nanobeams on nano-foundations, without having to resort to local/nonlocal mixtures, governed by a higher number of scale parameters, or physically questionable artifices to get mathematical consistency. Nanobeams resting on nano-foundations are modelled by stress-driven and displacement-driven laws providing nonlocal curvatures and reactions by convolution integrals of bending mo-ments and displacements with bi-exponential averaging kernels. Advantageously, the relevant integro-differential problem is reverted to a simpler differential formulation equipped with non-classical boundary conditions. Effectiveness of the proposed nonlocal approach is illustrated by analytically solving beam-soil systems simulating nanocomposites and biological cells.
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