Nonlinear Analyses of Axisymmetric Membranes with Shooting Method

Abstract

For the first time the generalized boundary conditions are formulated and recommended for the large‐deflected and sagging axisymmetric membranes supported by circular linearly elastic rings at the contours. The similitude theory is used to define the optimal structure for nondimensional variables and parameters of membranes. As a result, the new nondimensional differential equations and boundary conditions are derived and recommended for nonlinear analyses of flat and sagging membranes. These equations allow the reduction of numerical analyses to just a single load case for the spectrum of possible loadings. The “shooting” method is successfully used for analyses of flat and sagging axisymmetric membranes. The new interpolation procedure recommended for the shooting procedure is the square parabola method of interpolation, which much more effective than existing methods. The “shooting” method is compared to exact solutions for flat and sagging membranes. For practical purposes, flat axisymmetric membranes with rigid central circular plates of different radii