Abstract: Introduction: With the great advances in technology in recent years, micro and nano structures have found many engineering applications. In these structures, nano/micro plates are widely used in micro- and nano electromechanical systems (MEMS and NEMS) such as sensors. In investigation of micro and nano structures, the classical continuum mechanics or classical elasticity theories which is scale independent theories, are not capable of explanation of the size-dependent behaviors. Nonclassical continuum theories such as higher order gradient theories, strain gradient theories and the couple stress theory are capable of explanation of the size dependent behaviors which occur in nano, micro scale structures. So, in the calculation of the mechanical responses of the nano and micro structures, nonclassical continuum theories must be taken into for obtaining more realistic results. Buckling problems are very important for structural elements because their losing stability and strength. If a structure is supported as immovable, the buckling case can occur under compressive load or temperature rising. After buckling case, structure do not return initial configuration and its stability loses. During the lifetime of the nano structures, it can occur buckling in the structure's material because subjected to higher temperature conditions or higher compressive loads. Also, because the nano structures have a slender geometry properties, the buckling cases are very important these type structures. Understanding the buckling analysis and behaviour of nano structures and calculate the critical buckling temperatures are very important for safety of nano structures. Aim: In this study, the buckling analysis of a nano scale rectangular plate is investigated and analyzed under temperature rising. The mechanical modelling of the nano plate, the modified couple stress theory which a type of nonlocal continuum theory, is considered and used. The critical buckling temperatures are calculated and discussed in the numerical examples. The effect of the material length scale parameter the nano plate and the dimension parameters of the nano plate on the thermal buckling behavior and critcal buckling temperatures of the nano plate are investigated and discussed. Also, the difference between classical theory and the modified couple stress theory is investigated for different values of the material length scale parameters and the dimensions parameters of the nano plate. Content: In accordance with this purpose, a rectangular nano plate is modeled with using the modified couple stress theory and the material of the nano plate is selected as epoxy material. The material properties of the epoxy are taken in the published same papers. The boundary conditions are selected as pinned for all edges. Constraints: At the present time, the experimental investigations of the micro materials are still a challenge because of difficulties confronted in the micro scale. Therefore, mechanical theories and atomistic simulations have been used for micro structural analysis. The process of the atomistic simulations is very difficult and takes much time. Classical continuum mechanics does not contain the size effect, because of its scale-free character. So, continuum theory is the most preferred method for the analysis of the micro and nano structures. Method: The governing equations of the problem are obtained by using virtual work principle. Kirchhoff-Love plate theory is considered in the solution of the problem. In the solution method of the considered problem, the Navier method is used. In obtaining the numerical results and graphs, MATLAB program is used. Findings: The numerical results shows that that an increase in the thickness of the nano plate leads to a decline on effects of size effect and difference between the results of classical theory and the modified couple stress theory. The difference between classical theory and the modified couple stress theory is significant when the ratio of material length scale parameter/thickness increases. It shows that the material parameter has a very important role on the buckling responses of the nano plates. Conclusion: In this paper, the static deflections of rectangular nano plate examined based on MCST by using GDQ method. In numerical study, the effect of the material length scale parameter and the dimension parameters of the nano plate on the static responses of the nano plate is presented in both the CT and MCST. Numerical results show that the geometry properties and the dimensionless material length scale parameter have a very important role on the static behavior of the nano plate. MCST displays important size-dependence in higher values of the l/t ratios. Also, it is found the numerical results that the displacements of the nano plate by the CT are always larger than those by the MCST.
Anahtar Kelimeler: Nano Plates, Couple Stress Theory, Termal Buckling
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