In this paper, the predictions of different beam theories for the behavior of a shape memory polymer (SMP) beam in different steps of a thermomechanical cycle are compared. Employing the equilibrium equations, the governing equations of the deflection of a SMP beam in the different steps of a thermomechanical cycle, for higher order beam theories (Timoshenko Beam Theory and von-Kármán Beam Theory), are developed. For the Timoshenko Beam Theory, a closed form analytical solution for various steps of the thermomechanical cycle is presented. The nonlinear governing equations in von-Kármán Beam theory are numerically solved. Results reveal that in the various beam length to beam thickness ratios, one of the beam theories provides the most accurate results. In other words, employing the Euler–Bernoulli Beam Theory for developing the governing equations, especially in the large and small beam length to beam thickness ratios, leads to erroneous results.

In this paper, mechanical response of a micro/nanorotating disk made of functionally graded materials (FGMs) with variable thickness is investigated. Through utilizing variational method and considering the strain gradient theory, the governing equations and the boundary conditions are derived. In order to verify the developed formulation, in special limiting cases, the results are compared with those available in the literature. These comparisons show an excellent correspondence. Employing numerical techniques, some numerical results are presented to investigate the effect of variations of properties and thickness on the response of the small scale rotating disk. It is found that the non-homogeneity constants have a remarkable effect on the stress distribution in the FG rotating disk. Furthermore, the amount of stress could be reduced in the rotating disk through fabricating it with variable thickness.