Thermal buckling of thin spherical shells under uniform external pressure and non-linear temperature

Abstract

The thermal buckling of the shells is among the popular topics in solid mechanics. To date, most studies adopt the linear constitutive equation method. However, the non-linear temperature is important when studying thermal buckling. In this study, the non-linear constitutive equation of isotropic materials is derived using the tensor method to obtain the stability equation of axisymmetric spherical shells. Moreover, quadratic non-linear constitutive equations are applied to study the thermal buckling of spherical shells, and the heat stability equations of spherical shells expressed by displacements are obtained. Considering the common function of external pressure and temperature, the potential energy function of the spherical shell expressed in displacement is obtained using the principle of least potential energy. Moreover, the Ritz method is used to study the thermal buckling of simple, supported shells. The changing trend of the critical pressure caused by the temperature change of the thin spherical shells is analyzed, as well as the influence of the temperature nonlinearity on the critical pressure.