轴对称荷载下凯威特单层球面网壳的近似能量法

Approximate energy method for Kiewitt single-layer spherical reticulated shells under axisymmetric load

网壳结构的计算方法包括有限元法、拟壳法和解析法.把凯威特球面网壳结构的杆件分为环杆与斜杆两类.在轴对称荷载作用下,竖向荷载需要由斜杆的竖向刚度承担,斜杆在水平方向的支撑刚度由环杆提供.因此在荷载势能作用下,网壳结构发挥的能量是环杆的应变能与斜杆竖向弹簧势能.根据构件的受力状态确定内力-变形方程,得到能量方程,建立总势能方程,求解极值问题,得到结构变形函数,从而确定构件内力.该方法可实现网壳结构的近似计算,也从另一个角度理解网壳的传力机理.

Calculation methods of reticulated shells include finite element method,shell analogy method,and analytical method.The members of Kiewitt spherical reticulated shell structure is divided into two types：ring bars and diagonal bars.Under the action of axisymmetric load,the vertical load needs to be carried by the vertical stiffness of diagonal bars,and supporting stiffness of diagonal bars in the horizontal direction is provided by ring bars.Therefore,under the action of load potential energy,the energy exerted by the reticulated shell structure involves the strain energy of ring bars and the vertical spring potential energy of diagonal bars.According to the stress state of the components,the internal force-deformation equation is determined,and the energy equation is obtained.The total potential energy equation is then established,and the extreme value problem is solved.The structural deformation function is finally obtained,and the internal force of members is determined.This method provides the approximate calculation of reticualed shell structure and helps to understand the force-transferring mechanism of reticulated shell from another point of view.