Free vibration and nonlinear transient analysis of imperfect laminated structures

The free vibration and nonlinear transient analysis of imperfect laminated structures with emphasis on computational methods for accurate and efficient analysis are studied. The evaluation of interlaminar stresses is also studied by approximating global displacements of laminated plates. Free vibration response of imperfect laminated structures is studied in the presence of geometric and stress imperfections. The stress imperfections are the initial stresses as caused by preloads. Using a 48 degrees of freedom thin shell element, the effect of complex, arbitrary in-plane and out-of-plane loads on the transverse vibrations of thin arbitrarily laminated plates, cylindrical panels, and hyperbolic shells without and with geometric imperfections is analyzed. The, effects of geometric parameters (aspect ratio and panel curvature) and material properties (varying the number of layers but keeping the same laminate thickness) of imperfect plates are examined.

The nonlinear transient response of imperfect structures is next obtained using the direct time integration schemes as applied to the full set of equations and also using reduction methods. Two time integration schemes, the Newmark method and the Wilson () method, are first tested on a series of linear and nonlinear examples without and with geometric imperfections. Reduction methods using the normal modes and Ritz vectors as the base vectors are employed to reduce the size of the nonlinear problem and thus save computational resources. The resulting reduced (but still coupled) set of equations is integrated in a step-by-step fashion using the aforementioned time integration schemes along with an iterative scheme for dynamic equilibrium. Also, the nonlinear dynamic response of imperfect plates subjected to impact loads is studied. The evaluation of the loads (due to a projectile) depends on a contact law which relates contact forces with indentation. The well-known Hertzian law and its previously proposed modification are incorporated. The transient response of an example problem is obtained using both full and reduced equations of motion.

Finally, for accurate determination of interlaminar shear and normal stresses of laminated structures, a postprocessor for displacement-based finite element solutions of laminated plates under transverse loads is developed. The postprocessor can be used for the finite element solutions that have been obtained using either the classical laminated plate theory or the first order shear deformation theory. The equilibrium equations of elasticity are integrated directly. These equations include the influence of the products of in-plane stresses for geometrically nonlinear problems. To obtain accurately the derivatives of in-plane stresses the finite element nodal displacement data is first interpolated using polynomials with global support (Le., the interpolating polynomials are defined over the whole domain). Two types of polynomials, Chebyshev and a class of orthogonal polynomials that can be generated for a given location of known data points are used.