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

HT Thai, TP Vo, TK Nguyen, SE Kim - Composite Structures, 2017 - Elsevier
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 …

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect …

Z Al Mahmoud, B Safaei, S Sahmani, M Asmael… - … Methods in Engineering, 2024 - Springer
Recently, the mechanical performance of various mechanical, electrical, and civil structures,
including static and dynamic analysis, has been widely studied. Due to the neuroma's …

Vibration analysis of a strain gradient plate model via a mesh-free moving Kriging Interpolation Method

D Hou, L Wang, J Yan, KM Liew - Engineering Analysis with Boundary …, 2022 - Elsevier
The strain gradient elasticity theory is adopted to capture the small-scale effect of
micro/nanostructures to derive the governing equation by using Hamilton's principle. A mesh …

Vibration analysis of non-uniform orthotropic Kirchhoff plates resting on elastic foundation based on nonlocal elasticity theory

SS Ma'en, WG Al-Kouz - International Journal of Mechanical Sciences, 2016 - Elsevier
The free vibration analysis of non-local orthotropic Kirchhoff plates has been investigated.
Kirchhoff plates at the micro/nanoscale are modeled using Eringen's nonlocal elasticity …

Nonlocal strain gradient-based geometrically nonlinear vibration analysis of double curved shallow nanoshell containing functionally graded layers

PH Cong, N Van Huong, TT Thien, ND Duc - Aerospace Science and …, 2024 - Elsevier
It is a fact that while examining the mechanical behavior of nano/microscopic materials, size
effects become apparent. This study aims at presenting a new approach to geometrically …

Size-dependent theories of beams, plates and shells

J Awrejcewicz, AV Krysko, MV Zhigalov… - … modelling and numerical …, 2021 - Springer
This chapter concerns the latest literature review devoted to micro/nanosize-dependent
mathematical models of beams, plates and shells. The review includes nonlocal theory of …

[HTML][HTML] Closed-form solutions for free vibration of rectangular nonlocal Mindlin plates with arbitrary homogeneous boundary conditions

G Li, Y Xing, Z Wang - Composites Part C: Open Access, 2021 - Elsevier
In this paper, an extended separation-of-variable (SOV) method is developed to achieve the
closed-form solutions for free vibration of rectangular nonlocal Mindlin plates with arbitrary …

Free vibration characteristics and wave propagation analysis in nonlocal functionally graded cylindrical nanoshell using wave-based method

D He, D Shi, Q Wang, C Ma - Journal of the Brazilian Society of …, 2021 - Springer
In this article, the free vibration characteristics and wave propagation analysis of functionally
graded materials (FGM) cylindrical nanoshell is investigated by a semi-analytical method …

Superharmonic resonance analysis of nonlocal nano beam subjected to axial thermal and magnetic forces and resting on a nonlinear elastic foundation

MS Sari - Microsystem Technologies, 2017 - Springer
In this article, the second and third order superharmonic resonances of a nonlocal Euler–
Bernoulli beam are investigated. Eringen's nonlocal elasticity theory that takes into account …

Free vibration analysis of non-local annular sector Mindlin plates

SS Ma'en - International Journal of Mechanical Sciences, 2015 - Elsevier
The free vibration analysis of non-local annular sector Mindlin plates has been investigated.
Mindlin plates at the micro/nano-scale are modeled using Eringen׳ s nonlocal elasticity …