Analyses of free vibration and thermal buckling of nanobeams using nonlocal shear deformation beam theories under various boundary conditions are precisely illustrated. The present beam is restricted by vertically distributed identical springs at the top and bottom surfaces of the beam. The equations of motion are derived using the dynamic version of Hamilton's principle. The governing equations are solved analytically when the edges of the beam are simply supported, clamped or free. Thermal buckling solution is formulated for two types of temperature change through the thickness of the beam: Uniform and linear temperature rise. To validate the accuracy of the results of the present analysis, the results are compared, as possible, with solutions found in the literature. Furthermore, the influences of nonlocal coefficient, stiffness of Winkler springs and span-to-thickness ratio on the frequencies and thermal buckling of the embedded nanobeams are examined.

In this research, thermal buckling analysis of circular functionally graded plates with Actuator/Actuator piezoelectric layers (FGPs) is studied based on neutral plane, classical and first order shear deformation plate theories. Mechanical properties of the plate are considered as those of Reddy Model. Plate is assumed to be under thermal loading. Nonlinear temperature rises through the thickness and boundary conditions are considered clamped. Equilibrium and stability equations have been derived using calculus of variations and application of Euler equations. Finally, critical buckling temperature changes are studied based on the mentioned theories for a sample plate. An appropriate agreement is seen among the present results and the results of other researches.

Thermal buckling behaviour of rectangular laminated composite plates with initial geometrical imperfections is investigated in this article. The equilibrium, stability, and compatibility equations of an imperfect composite plate are derived using the first order shear deformation plate theory. The plate is assumed to be under longitudinal temperature rise. Resulting equations are used to obtain the thermal buckling load of the composite plate in closed-form solutions. The effect of initial imperfections on buckling loads are discussed.