A \([1,2]\)-order theory for elastodynamic analysis of thick orthotropic shells (Q675638)

A higher-order shell theory is developed for elastodynamic analysis of orthotropic shells. The theory accounts for all basic deformations including transverse shear and transverse normal strains and stresses. The theory is developed in orthogonal curvilinear coordinates in which the reference surface components of the displacement vector vary linearly through the thickness while the transverse displacement is parabolic. Transverse shear and transverse normal strains are formulated to satisfy physical traction conditions at the top and bottom shell surfaces. Analytical solutions for the free vibration of isotropic and orthotropic cylindrical shells are obtained for a wide range of thickness/radius and thickness/wavelength rations and found to be in close agreement with the exact elasticity solutions.