横观各向同性矩形板的非经典稳定问题

针对四边简支的横观各向同性矩形板单向受非均匀对称压力作用的稳定问题给出了三维分析方法.首先通过引入位移函数和应力函数,从三维基本方程出发构造了两类相互独立的状态空间方程.其次结合层合近似理论,求解了对应非经典稳定问题的状态空间方程.进而利用子层间的连续条件和矩形板上下表面的自由条件,导出了两类独立的特征方程.

Non-classical stability of a transversely isotropic rectangular plate

A three|dimensional method is proposed to analyze the stability problem of a transversely isotropic rectangular plate with simply supported edges, subjected to uniaxial non|uniform pressure. First of all, by introducing two displacement functions and two stress functions, two independent state equations are derived from the three|dimensional elasticity equations. Then the state equations are solved for the non|classical stability problem, by employing the laminated approximation theory. Making use of the continuity conditions between layers and the free boundary conditions at the upper and lower surfaces, two independent eigenequations are obtained. ;