Journal
APPLIED MATHEMATICAL MODELLING
Volume 74, Issue -, Pages 1-20Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2019.04.019
Keywords
Buckling analyses; Analytical modelling; Nanobeam; Modified nonlocal model; High-order boundary conditions; Weighted residual approach
Funding
- National Key R&D Problem of China [2017YFB1102801]
- National Natural Science Foundation of China [11802242]
- Natural Science Basic Research Plan in Shaanxi Province of China [2018JQ1019]
- Fundamental Research Funds for the Central Universities [31020170QD072]
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In this work, a three characteristic-lengths featured size-dependent gradient-beam is constructed by adopting the modified nonlocal model, resulting in much more general constitutive equation with stress gradient up to four-order and strain gradient to two-order. The six-order differential governing equation for transverse displacement is formulated. All boundary conditions especially variational consistent higher order boundary conditions of the present model are derived with the aid of weighted residual approach. The closed-form solutions to critical buckling loads under different sets of boundary conditions are systematically formulated with higher order boundary conditions incorporated. The numerical results show that both nonlocal parameters have significant effect on the buckling behaviors. Meanwhile, if two nonlocal parameters are taken as same, the present results cannot always reduce to that from Eringen's nonlocal model. Due to its clear physical meaning, the present model is expected to be widely adopted in mechanical analyses of nano-structures. (C) 2019 Elsevier Inc. All rights reserved.
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