A new approach to solution of stability problem of heterogeneous orthotropic truncated cones with clamped edges within shear deformation theory

Abstract

In this study, the stability problem of heterogeneous orthotropic (HTO) truncated conical shells with clamped edges subjected to external pressures (lateral and hydrostatic) within shear deformation theory (ST) is solved using a new approach. After the mathematical and visual design of HTO-truncated conical shells, modified Donnell-type governing equations including transverse shear stresses are derived for them. Stability equations are solved analytically for the first time in this study by constructing new approximation functions depending on an unknown parameter for stress, deflection and two angles of rotation functions under clamped boundary conditions. In addition, the unknown parameter contained in the analytical formulas for the clamped HTO- truncated conical shells within ST is found from the minimum conditions of the critical external pressures. After confirming the accuracy of the results, the influences of shear stresses, orthotropy, heterogeneity and conical shell characteristics on critical lateral and hydrostatic pressures are examined in detail in the presence of clamped boundary conditions.