"Вестник МГСУ"

The article describes the problem of stability of elastic orthotropic rectangular plates for the case when two opposite sides are simply supported, and two other sides have boundary with either simple supports or fixed supports, which are arbitrarily combined. The plate that is simply supported all over the contour is not considered in the article since the authors described it in the earlier publication. The external load is uniformly distributed along the side and is applied to the shorter side of the plate. To solve the stability problem, the authors use an approximate analytical method - the form factor interpolation method, which is based on the functional relationship between an integral geometric parameter of the mid-plane surface (the form factor) and an integral mechanical parameter (the critical force of buckling). Subject: stability of elastic orthotropic rectangular plates for the case when two opposite sides are simply supported and two other sides have combination of simple supports and fixed supports arbitrarily combined. Materials and methods: the form factor interpolation method (FFIM) is used to solve the stability problem of elastic orthotropic rectangular plates. The solutions which were obtained by the FFIM method were compared with the results of calculations by FEM (the program SCAD Office 11.5). Results: for orthotropic rectangular plates with combined boundary conditions, we obtained analytical expressions for critical force surfaces and they depend on an integral geometric parameter - form factor and flexural stiffness ratio. To the authors’ knowledge, these expressions are obtained for the first time. The critical force surface for orthotropic rectangular plates constitutes one of the boundaries of this integral physicomechanical parameter for the entire set of orthotropic plates with arbitrary convex contour. Therefore, this surface can be used for obtaining reference solutions by the form factor interpolation method. We demonstrated how to obtain the solution of the stability problem for orthotropic rectangular plates by the form factor interpolation method using the results obtained from the aforementioned analytical expressions as the reference solutions. The solutions obtained by the form factor interpolation method are compared with the results of calculations by the finite element method and show a good accuracy. Conclusions: the analytical expressions for critical loads presented in this work can be used directly for the stability analysis of orthotropic rectangular plates loaded in one direction as well as to obtain one of the reference solutions by the form factor interpolation method for plates with arbitrary convex contour and combined boundary conditions. The proposed approach can be extended to other forms of plates, boundary conditions and loading types.

To the present moment there are a lot of ways to define heat conductivity and thermal diffusivity of solid bodies. The schemes of determining heat conductivity, which use transient methods, usually include a heater and a cooler. The sample is placed in between them. The temperature and temperature differential is determined using several thermocouples.The authors present a method of determining the thermal characteristics of a sample in the form of a rectangular plate, allowing to apply only one thermocouple, which leads to a simple analytical expression for thermal diffusivity. The described method provides high-precision determination of thermal diffusivity of the body of small size and with the accuracy sufficient for practice — conductivity coefficient. The method uses a simple mathematical model and minimal hardware resources compared to other methods. The exception is the heat-insulating materials. The determination of their thermal conductivity using this method can lead to poor accuracy.