Thermoelastic buckling of thin spherical shells

Thermoelastic stability of thin perfect spherical shells based on deep and shallow shell theories is presented. To derive the equilibrium and stability equations according to deep shell theory, Sanders's nonlinear kinematic relations are substituted into the total potential energy function of the shell and the results are extremized by the Euler equations in the calculus of variation. The same equations are also derived based on quasi-shallow shell theory. An improvement is obtained for equilibrium and stability equations related to the deep shell theory in comparison with the same equations related to shallow shell theory. Approximate one-term solutions that satisfy the boundary conditions are assumed for the displacement components. The Galerkin- Bubnov method is used to minimize the errors due to this approximation. The eigenvalue solution of the stability equations is obtained using computer programs. For several thermal loads it is found that the deep shell theory results are slightly more stable as compared to the shallow shell theory results under the same thermal loads. The results are compared with the Algor finite element program and other known data in the literature.