Thermal buckling of functionally graded triangular microplates

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.