General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels

The main aim of this paper is to provide a general framework for the formulation and the dynamic analysis computations of moderately thick laminated doubly-curved shells and panels. A 2D higher-order shear deformation theory is also proposed and the differential geometry is used to define the arbitrary shape of the middle surface of shells and panels with different curvatures. A generalized nine-parameter displacement field suitable to represent in a unified form most of the kinematical hypothesis presented in literature has been introduced. Formal comparison among various theories have been performed in order to show the differences between the well-known First-order Shear Deformation Theory (FSDT) and several Higher-order Shear Deformation Theories (HSDTs). The 2D free vibration shell problems have been solved numerically using the Generalized Differential Quadrature (GDQ) technique. The GDQ rule has been also used to perform the numerical evaluation of the derivatives of the quantities involved by the differential geometry to completely describe the reference surfaces of doubly-curved shell structures. Numerical investigations concerning four types of shell structures have been carried out. GDQ results are compared with those presented in literature and the ones obtained using commercial programs such as Abaqus. Very good agreement is observed