scholarly journals Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory

2017 ◽  
Vol 153 ◽  
pp. 598-612 ◽  
Author(s):  
Son Thai ◽  
Huu-Tai Thai ◽  
Thuc P. Vo ◽  
H. Nguyen-Xuan
Keyword(s):  
Strain Gradient ◽  
Isogeometric Analysis ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Nonlinear Static

scholarly journals Vibration of cracked functionally graded microplates by the strain gradient theory and extended isogeometric analysis

2019 ◽  
Vol 187 ◽  
pp. 251-266 ◽  
Author(s):  
Hoang X. Nguyen ◽  
Elena Atroshchenko ◽  
Tuan Ngo ◽  
H. Nguyen-Xuan ◽  
Thuc P. Vo
Keyword(s):  
Strain Gradient ◽  
Isogeometric Analysis ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
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.

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