Thermomechanically coupled deformation of pressurized spherical shells with initial stress

Abstract

The coupled deformation of spherical shells is a fundamental issue in diverse fields. This study derives an analytical solution that captures the coupled thermomechanical behavior of initially stressed spherical shells, incorporating the effects of internal/external pressures. Crucially, the analysis assumes a spatially uniform temperature field throughout the shell. The internal pressure is explicitly modeled as a configuration-dependent load governed by the ideal gas law, thereby intrinsically coupling the pressure to the evolving configuration and temperature. The analytical solution is applied to systematically investigate three different scenarios—thermal inflation under constant external pressure, pressure-induced deformation at constant temperature, and coupled thermo-pressure inflation. The results reveal that these factors markedly influence the deformation and stress distributions. Validation is achieved by comparing the theoretical solution with experimental results and finite-element simulations, including specific verifications against the theoretical ideal gas law curves. This work presents a comprehensive theoretical framework for predicting the responses of initially stressed spherical shells subjected to coupled thermomechanical loading under realistic service conditions.