La Trobe
147084_Huu-Tai,T_2017.pdf (4.81 MB)

A review of continuum mechanics models for size-dependent analysis of beams and plates

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Version 2 2021-06-03, 00:25
Version 1 2021-01-15, 05:12
journal contribution
posted on 2021-06-03, 00:25 authored by Huu Tai Thai, Thuc VoThuc Vo, Trung-Kien Nguyen, Seung-Eock Kim
This paper presents a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures. The review mainly focus on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory due to their common use in predicting the global behaviour of small-scale structures. In each higher-order continuum theory, various size-dependent models based on the classical theory, first-order shear deformation theory and higher-order shear deformation theory were reviewed and discussed. In addition, the development of finite element solutions for size-dependent analysis of beams and plates was also highlighted. Finally a summary and recommendations for future research are presented. It is hoped that this review paper will provide current knowledge on the development of higher-order continuum models and inspire further applications of these models in predicting the behaviour of micro- and nano-structures.


This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2011-0030040) and the School of Engineering and Mathematical Sciences at La Trobe University.


Publication Date



Composite Structures




24p. (p. 196-219)





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