Theoretical study on the axisymmetric deformation problem of prestressed circular membranes under non-uniformly distribution loads

In existing studies, the axisymmetric deformation problem of circular membranes is usually only considered the case under uniformly distributed loads, which makes the corresponding research results of those problems have significant limitations. In fact, in practical engineering, the case of uniformly distributed loads is a relatively ideal state, while the case of non-uniformly distributed loads should be the common phenomenon. In this paper, we analytically studied the axisymmetric deformation problem of prestressed circular membranes under nonuniformly distributed loads, that is, the effects of non-uniformly distributed loads and initial stress were considered simultaneously. Through static equilibrium analysis and deformation coordination conditions, the governing equations of the problem studied here was derived, and the boundary conditions with initial stress was established based on an axisymmetric problems of planar radial stretching. And then, the solution of governing equations was obtained by the power series method. Finally, the effectiveness of the obtained solution was verified based on the existing studies, the extent of application of the obtained solutions is discussed, and the influence of the load change coefficient and initial stress on the deformation of circular membranes were analyzed. The results indicate that the solution presented here have a larger extent of application than those in existing studies since it can be regressed into the prestressd circular membrane solution when the load change coefficient is equal to zero and can also be regressed into the classic Hencky solution when both of the load change coefficient and initial stress are equal to zero.