The present study focuses on recent research on thermoelasticity theories as well as their associated reformed models related to the micro-/nano-beams/nano-bars. Our goal is to present an overview of the use and limitations of existing relevant theories. The properties of these theories were analyzed by many researchers in a variety of fields as well as different problems, providing insight into their characteristics. In this review, we discuss theory, techniques, formulation, as well as limitations for solving equations for micro-/nano-beams/nano-bars. In light of the fact that this review may be a useful tool for researchers who work in sensitive industries such as MEMS/NEMS/Resonators/Sensors.

In this study, the resultant forces and moments acting on infinite symmetric FGPs with a triangular hole subject to uniaxial tensile load were examined via an analytical method using the complex variable approach. The mechanical properties of graded plates are hypothesized to vary throughout the thickness exponentially. The impact of various factors, namely hole orientation, hole aspect ratio as well as the hole corner curve on stress distribution and moment resultants is considered. In order to approve the credibility of the analytical approach, its outcomes are compared to numerical results acquired from ABAQUS finite element modeling. This comparison showed a favorable agreement level among the acquired analytical and numerical outcomes. Based on these results, the mentioned factors entail a considerable effect on the distribution of resultant forces and moments at the proximity of the hole and the load bearing tolerance of functional grated plates with holes may be enhanced by suitable selection of the aforementioned parameters.

The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive.