STABILITY OF A ELASTIC ORTHOTROPIC CANTILEVER PLATE

Abstract

The paper studies the stability of a elastic orthotropic rectangular cantilever plate under compressive forces applied to the face opposite to the seal. The aim of the study is to obtain the range of critical forces and the relevant shapes of the supercritical equilibrium. The deflection function is chosen as a sum of two hyperbolic-trigonometric series with the addition of special compensating terms for the free terms of the Fourier cosine series to the symmetric solution. Meeting all conditions of the boundary value problem leads to the infinite homogeneous system of linear algebraic equations with respect to the unknown coefficients of the series. The task of the research is to create a numerical algorithm allowing to find eigenvalues of the solving system with high accuracy. The search for critical loads (eigenvalues), which give a non-trivial solution to this system, is carried out by a brute-force search of the compressive load value in combination with the method of successive approximations. The initial values of the basic coefficients in the first functional series are set arbitrarily in the form of a decreasing sequence. For the square ribbed plate, the first three critical loads of the symmetric solution and the first critical load of the antisymmetric solution are obtained. The authors present 3D images of the respective equilibrium forms. The research results can be used to study the stability of cantilever sensor elements of nanoscale transistors and smart structures.

Keywords

• orthotropic cantilever plate
• stability
• fourier series
• critical load
• equilibrium form