Numerical nonlinear frequency analysis of pre-damaged curved layered composite structure using higher-order finite element method

The influence of the internal debonding on the structural stiffness and the nonlinear modal characteristics of the layered structure are examined extensively in the current research article. For the investigation purpose, the shell frequency responses are obtained numerically for both the linear and the nonlinear cases via a generic type of mathematical formulation using the Equivalent Single Layer (ESL) theory in the framework of two kinematic models. The current formulation not only includes the influence of the transverse shear deformations but also satisfies the parabolic variation of transverse shear stress through the thickness. Additionally, the geometrical nonlinear distortion modeled via Green-Lagrange strain-displacement relations. Further, the internal debonding between the adjacent layers are modeled using sub-laminate approach and the displacement continuity between segments (laminate and delaminate) have been established through the intermittent continuity conditions. The nonlinear system governing equation of the vibrated structure is obtained via Hamilton's principle and converted to set of nonlinear algebraic equations through the isoparametric finite element (FE) steps. The desired responses are solved numerically with the help of robust (direct iterative method) technique and compared with available results to demonstrate the solution accuracy. Subsequently, an adequate number of examples are solved for the delaminated structure using the current higher-order nonlinear models and the influential parameters discussed in detail.