In the framework of a strict mathematical approach based on classical theory of elasticity we present an idea of the deployment and stretching of the circular solar sail attached to the inflatable toroidal shell. It is predicted that by introducing the gas into the inflatable toroidal shell one can deploy and stretch a large size circular solar sail membrane. The formulas for the toroidal shell and sail membrane stresses and strains caused by the gas pressure in the shell are derived. The analytical expressions can be applied to a wide range of solar sail sizes. Numerical calculations for the sail of radii up to 100 m made of CP1 membrane and attached to the toroidal shell with the varied cross-section radius are presented. The normal transverse vibration modes of the sail membrane under tension caused by gas pressure in the shell are calculated. The feasibility of deployment and stretching of a solar sail with a large size circular membrane attached to the inflatable toroidal shell is demonstrated.

在基于经典弹性理论的严格数学方法的框架内，我们提出了连接到充气环形壳的圆形太阳帆的展开和拉伸的想法。据预测，通过将气体引入可充气的环形外壳，可以展开和拉伸大尺寸的圆形太阳帆膜。推导了由壳内气体压力引起的环形壳和帆膜应力和应变的计算公式。解析表达式可以应用于各种太阳帆尺寸。给出了半径达 100 m 的帆的数值计算，该帆由 CP1 膜制成，并附在具有不同横截面半径的环形壳上。计算了由壳内气压引起的帆膜在张力作用下的法向横向振动模式。