Instability of a rectangular CCCC-nanoplate

Abstract

The spectrum of critical loads and equilibrium forms of a CCCC-nanoplate (C — clamped edge) at various values of a non–local nanoparameter has been studied. The symmetric solution is represented by two hyperbolo-trigonometric series in two coordinates which obeyed the basic differential equation of the physical state of Eringen. The boundary conditions for the absence of deflections and angles of rotation of the pinched faces were precisely satisfied. As a result, a homogeneous infinite system of linear algebraic equations with respect to unknown coefficients of these series is obtained containing a relative compressive load as the main parameter. After the conversion, the system began to contain only one sequence of coefficients. An iterative process of searching for a non-trivial solution in combination with the method of iterating over the load value is constructed. For each value of the nonlocal parameter, the first four critical loads for symmetric forms of supercritical equilibrium are found and their 3D images are obtained. It was found that critical loads decreased with an increase in the nonlocal parameter. The influence of the number of members held in rows and the number of iterations on the accuracy of the results is investigated. The results obtained can be used in the design of various nanoscale smart structures.

Keywords

• rectangular cccc-nanoplate
• eringen theory
• critical load spectrum
• fourier series