扁壳的平衡、振动与稳定

Equilibrium, Vibration and Stability of Shallow Shells

扁壳的微分方程组可以分解成两个相对独立的方程,平板方程和薄膜方程,其力学意义是视扁壳为在全平面中板与薄膜的组合。将荷载进行分解,使一部分属于平板,另部分属于薄膜,平板与薄膜之间满足形变连缓性条件。方程组经分解后,建立了解决平衡、振动与稳定诸问题的简便计算方法。

Treating a shallow shell as a combination of a plate and a membrane,then the governing differential equation of shallow shells may be represented by:D▽~2▽~2W=f(x, y)q(x, y) ▽_k^2φ=(1-f(x,y))q(x,y) which are the differential equation of a plate and the differential equation of a membrane in succession. Then the load is divided into two parts: on the plate and on the membrane. Between the pate and the membrane the equation of conformation of shape exists. Thus we get a simple method for the calculation of the eguilibrium, vibration and stability of a shallow shell.