Theoretical and Experimental Analysis of Large Deformation Induced Frequency, Static and Transient Responses of Layered Structure with Cutout under Thermo-Mechanical Loading

Abstract

The geometrically nonlinear behavior of cutout abided laminated plate/shell panels under the thermo-mechanical loading is being analyzed in this research. It has been performed computationally via a higher-order finite element (FE) formulation to predict the responses, i.e., static bending, free vibration, and transient deflection. The laminated shell physical model is formulated mathematically using an equivalent single layer theory based on the third-order expansion of displacement variables. Thus, the model maintains the necessary shear deformation, corresponding stress, and strain variation through the panel thickness direction. Additionally, the induced large-deformation within the panel due to the geometrical nonlinearity has been integrated mathematically through Green's and von- Karman strain, including Lagrangian description. Hamilton's principle uses the nonlinear governing equation of motion for the layered structure with and without cutout. The approximate nonlinear numerical solutions are calculated using the selective integration scheme (Gauss-Quadrature) associated with Picard's direct iterative method and the isoparametric FE steps. The finite element discretization of the shell panel is being done using a nine-noded (with nine nodal degrees of freedom) quadrilateral Lagrangian element. A generic computational algorithm has been prepared in MATLAB utilizing the current nonlinear mathematical formulation considering all of the nonlinear higher-order strains to maintain the necessary generality. In general, the consistency of the numerical FE solution is checked initially with adequate numbers of convergence tests. Similarly, the numerical solution accuracy is verified with the available published results (numerical and analytical). The numerical results are compared with the experimental data for the second stage verification at the parent institute by utilizing the available/fabricated lab-scale test rig. Subsequently, the role of cutout parameters (size, shape, position, and orientation), including the various geometrical parameters, loading conditions, and edge-support conditions on the nonlinear structural responses, are studied for a clear insight into the damaged structural modeling. Moreover, the parametric study has been carried out using the temperature-dependent elastic properties of the laminate. The temperature distribution over the surface and thickness of the structure is assumed to be uniform. In addition, the effect of nonlinear strain terms on the final structural responses is presented. Based on the observation, the applicability of the full geometrical (Green-Lagrange) strain-displacement relation is established.