均布荷载下受有预加张力圆薄膜的轴对称变形

Axisymmetrical deformation of prestressed circular membrane under uniformly distributed loads

针对受有预加张力的弹性圆薄膜结构,利用F ppl-von Krmn薄膜理论建立基本方程,推广了Hencky变换,得到了均布荷载作用下受有预加张力弹性圆薄膜轴对称大变形的一般解。给出了圆薄膜中心挠度,径向和环向薄膜内力的幂级数形式计算公式。研究表明:当预加张力相对于荷载很小的情况下,解答趋近于Hencky理论结果;当预加张力相对于荷载很大的情况下,解答趋近于线性理论结果。研究结果可用于薄膜预张力测量技术的理论分析。

With establishing the fundamental equation of prestressed circular membrane under Foppl-von Kdrmdn membrane theory, Hencky transform is extended and the general solution of axisymmetrical deformation of prestressed circular membrane under uniformly distributed loads is obtained. The central deflection, the radial and circumferential stresses of the membrane are given in the form of power series. And it is found that the solution approaches to the results from Hencky theory when the prestressing is far less than the loads; and the solution approaches to the results based on linear theory when the prestressing is far greater than the loads.