1992 年 40 巻 463 号 p. 453-463
The reflecting surface of an inflatable reflector for space use consists of one or several inflatable elements (membrane elements), which are pressurized to generate an accurate reflecting surface. The surface of an inflatable element deforms as the pressure is applied. If the element is pressurized on the ground, gravity force also changes the deflection of the element. This means that the internal pressure and the gravity force influence the surface error of the element. This paper presents an analysis of the deflection and the surface accuracy of an inflatable element subjected to pressure and gravity loadings based on a flexible membrane strip model, the initial configuration of which is straight or a circle arc, with both ends immovably supported. The gravity is assumed to act in any direction in the plane which includes the membrane strip. The perturbation method is used to solve the membrane deflection due to the gravity force, assuming the ratio of gravity to pressure and the center height of the membrane to be small. The analytical expressions for the deflection and the surface error of the membrane strip subjected to pressure and gravity are obtained. It is found that the effect of gravity on the surface error increases as the ratio of gravity to pressure and the center height of the strip increases, and as the rigidity (Young Modulus) of the membrane decreases. It is also found that if the membrane strip is not so rigid (Young Modulus is not so high), the effect of gravity on the deflection is smallest with the membrane vertically placed. On the other hand if the membrane strip is rigid enough, the effect of gravity is smallest with the membrane horizontally placed.