Keywords: parabolic thickness variation, large deflection, laminated plate, dynamic response, non-linear, blast loading.

Plates with parabolic thickness variation are particularly used to obtain an optimized structure by saving weight. Predicting the dynamic response of plates subjected to time dependent loads is important for the design of aerospace and marine structures. Several studies are reported on both free vibration and dynamic response analysis of isotropic, orthotropic and laminated composite flat and tapered plates subjected to air blast loading [1,2,3]. But, there is not a study reported on the air blast loading of finite rectangular laminated plates with parabolic thickness variation along two sides.

In this study, a closed form solution is presented for the transient analysis of the simply supported laminated composite plates with parabolic thickness variation subjected to air blast loading. In-plane stiffness and inertia effects are considered in the formulation of the problem and transverse shear stresses are ignored. The geometric nonlinearity effects are taken into account by using the von Karman large deflection theory of thin plates. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. The Galerkin method is used to obtain the nonlinear differential equations in the time domain. The finite difference method is applied to solve the system of coupled nonlinear equations.

The displacement-time and strain-time histories are obtained for three different points. The strain-time histories are obtained at the mentioned points on the top, middle and bottom surfaces of the plate. The analyses indicate that there is a good correlation between the results obtained using the present method and the finite element method. Therefore, the method presented here can be used for the dynamic response analysis of laminated plates with parabolically varying thickness in preliminary design. The method can be extended for the optimization of such structures, for the analysis of the tapered and parabolic plates subject to different types of dynamic loads and for accounting the nonlinear material properties. These will be the subject of future research.

1

H.S. Türkmen, Z. Mecitoglu, "Nonlinear structural response of laminated composite plates subjected to blast loading", AIAA Journal, 37(12), 1639-1647, 1999. doi:10.2514/2.646

2

Ö. Civalek, "Fundamental frequency of isotropic and orthotropic rectangular plates with linearly varying thickness by discrete singular convolution method", Applied Mathematical Modelling, 33, 3825-3835, 2009. doi:10.1016/j.apm.2008.12.019

3

S. Susler, Z. Kazanci, H.S. Turkmen, "Dynamic Behaviour of Tapered Plates subjected to Blast Loading", in B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru, M.L. Romero, (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 290, 2010. doi:10.4203/ccp.93.290

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