Thermal buckling of functionally graded triangular microplates

Abstract

The thermal buckling behavior of thin to moderately thick functionally graded isosceles triangular microplates with temperature-dependent material properties is investigated. The governing equations are derived based on the modified strain gradient theory (MSGT) in conjunction with the first-order shear deformation theory. The adjacent equilibrium criterion and Chebyshev-Ritz method are employed to derive the nonlinear thermal buckling eigenvalue equations, which are solved by a direct iterative method. The fast rate of convergence and accuracy of the method are demonstrated numerically. Then, the effects of length scale parameters, material gradient index, different boundary conditions, apex angle and ratio of width to thickness on the critical temperature rises of the triangular microplates are studied. In addition, comparisons between the results of MSGT and modified couple stress theory and classical theory (CT) are performed. The results show that by increasing the apex angle, the critical temperature rise increases, but increase in the material gradient index and the dimensionless length scale parameter decreases the critical temperature rise. In addition, it is observed that by considering the temperature dependence of material properties, the critical temperature rises decrease significantly. Also, the MSGT and CT yield the highest and the lowest critical temperature rise, respectively.

On the tuning of static pull-in instability and nonlinear vibrations of functionally graded micro-resonators with three different configurations

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Analytical solutions of bending and free vibration of moderately thick micro-plate via two-variable strain gradient theory

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Application of nanotubes in conveying nanofluid: a bifurcation analysis with consideration of internal energy loss and geometrical imperfection

“…An appropriate continuum-based model for a fluid-conveying nanostructure should be size-dependent since the static and dynamic behaviours of nanostructures are considerably influenced by size effects [2][3][4][5][6][7][8][9][10]. Several size-dependent models such as nonlocal [11][12][13][14][15][16], couple stress [17][18][19][20][21][22][23], and strain gradient [24,25] theories have been introduced for nanoscale structures. In the present analysis, a refined combination of the strain gradient and nonlocal models [26][27][28] is utilised since it has been reported that this continuum model is capable of better capturing size influences compared to the pure nonlocal model [29].…”