Analytical Solutions for Circular Elastic Membranes Under Pressure

Abstract

This study investigates the problem of a circular elastic membrane clamped or adhered at its boundary and subjected to uniform transverse pressure. Many analytical solutions for this classical problem have been developed previously, using either a series-based approach (notably accurate but lengthy and implicit) or approximate kinematics (relatively simple yet lacking accuracy). Here, we seek new analytical solutions using a perturbed spherical cap to represent the shape of the pressurized membrane. Our approach yields simple, explicit solutions of remarkable accuracy for the deformed profile, pressure–deflection relation, strain distributions, and energy release rate, which are directly applicable to emerging ultrathin membrane systems.