1993 年 41 巻 471 号 p. 196-204
Large deformation of pressurized shallow spherical membranes including flat membranes, is analyzed via the Ritz method based on potential energy minimization. The material of the membrane is assumed to obey Hooke's law and the deformation is assumed not to be very large. A function which expresses the change of the deflection profile of the membrane effectively with a few unknown parameters is used as a trial function for the potential energy functional. The deflections and stresses calculated by this method agreed fairly well with other analytical solutions. This energy method is applied also to the case of one-dimensional membranes. The energy method presented in this paper is shown to give a symplified and rather accurate solution for a pressurized shallow spherical membrane and a one-dimensional membrane.