A quasi-3D theory for functionally graded porous microbeams based on the modified strain gradient theory

2021 ◽  
Vol 257 ◽  
pp. 113066
Author(s):  
Armagan Karamanli ◽  
Thuc P. Vo
Keyword(s):  
Strain Gradient ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory

Structural instability of non-conservative functionally graded micro-beams tunable with piezoelectric layers

2019 ◽  
Vol 30 (4) ◽  
pp. 593-605 ◽  
Author(s):  
Mohammad Hosseini ◽  
Reza Bahaadini ◽  
Zahra Khalili-Parizi
Keyword(s):  
Functionally Graded Material ◽  
Strain Gradient ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Stress Theory ◽  
Graded Material

This investigation aims to explore the non-conservative instability of a functionally graded material micro-beam subjected to a subtangential force. The functionally graded material micro-beam is integrated with piezoelectric layers on the lower and upper surfaces. To take size effect into account, the mathematical derivations are expanded in terms of three length scale parameters using the modified strain gradient theory in conjunction with the Euler–Bernoulli beam model. However, the modified strain gradient theory includes modified couple stress theory and classical theory as special cases. Applying extended Hamilton’s principle and Galerkin method, the governing equation and corresponding boundary conditions are obtained and then solved numerically by the eigenvalue analysis, respectively. The results illustrated effects of non-conservative parameter, length scale parameter, different material gradient index, and various values of piezoelectric voltage on the natural frequencies, flutter and divergence instabilities of a cantilever functionally graded material micro-beam. It is found that both the material gradient index and applied piezoelectric voltage have significant influence on the vibrational behaviors, divergence and flutter instability regions. Furthermore, a comparison between the various micro-beam theories on the basis of modified couple stress theory, modified strain gradient theory, and classical theory are presented.

Multilayer GPLRC composite cylindrical nanoshell using modified strain gradient theory

2019 ◽  
Vol 47 (5) ◽  
pp. 521-545 ◽  
Author(s):  
Zanyar Esmailpoor Hajilak ◽  
Johar Pourghader ◽  
Davoud Hashemabadi ◽  
Farzaneh Sharifi Bagh ◽  
Mostafa Habibi ◽  
...  
Keyword(s):  
Strain Gradient ◽  
Thermal Environment ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Reinforced Composites ◽  
Modified Strain Gradient Theory ◽  
Scale Parameters ◽  
Number Of Layers ◽  
Resonance Frequencies

In this paper, influence of modified strain gradient theory (MSGT) on buckling, free and forced vibration characteristics of the composite cylindrical nanoshell reinforced with graphene nanoplatelet (GPL) in thermal environment is investigated. The material properties of piece-wise functionally graded graphene-reinforced composites GPLRC are assumed to be graded in the thickness direction of a cylindrical nanoshell and are estimated through a nanomechanical model. The results show that GPL distribution pattern, three length scale parameters, number of layers and GPL weight function have important role on resonance frequencies, buckling load, relative frequency and dynamic deflections of the GPLRC cylindrical nanoshell.

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