Natural frequencies and mode shapes of laminated composite skew hypar shells with complicated boundary conditions using finite element method

In the present investigation, free vibration behaviour is studied for the laminated composite skew hypar shells having twist radius of curvature. A higher-order shear deformation theory (HSDT) is employed using the C-0 finite element formulation. Higher-order terms in the Taylor's series expansion are used to represent the higher-order transverse cross sectional deformation modes. The formulation includes Sanders' approximation for doubly curved shells considering the effect of transverse shear. The structural system is considered to be undamped. The effects of different parameters are studied on the free vibration aspects of laminated composite skew hypar shells. Effect of cross curvature is included in the formulation. The C-0 finite element formulation has been done quite efficiently to overcome the problem of C-1 continuity associated with the HSDT. The isoparametric FE used in the present model consists of nine nodes with seven nodal unknowns per node. Since there is no result available in the literature based on HSDT on the problem of free vibration of laminated composite skew hypar shells, the correctness of the present formulation is established by comparing problems of laminated composite hypar shells without skew angle and with the laminated composite skew plates available in the published literature. New results are presented by varying geometry, boundary conditions, ply orientations and skew angles which will serve as benchmark for future researchers.