The effect of different boundary conditions on the stability behavior of heterogeneous orthotropic truncated conical shells

This study provides analytical formulations and solutions for stability analysis of heterogeneous orthotropic truncated conical shells subjected to mixed boundary conditions and external (lateral and hydrostatic) pressures using the Donnell shell theory. The mixed boundary conditions are as follows: Functionally Graded Materials (FGM) truncated conical shells have a sleeve at one end that prevents their elongation, displacement and rotation. The other end of these shells are freely supported. Thus, the fundamental equations of heterogeneous orthotropic truncated conical shells are derived and solved by applying the Galerkin method for two mixed boundary condition cases using new approximation functions. Then, expressions for dimensionless critical external pressures are obtained. Finally, a detailed study is carried out to examine the effect of heterogeneity, material orthotropy, and mixed boundary conditions on critical external pressures.