Modelling of the Dynamic Response of Laminated Structures on Impulse Loading
Abstract
Parameters of a laminated structure effect considerably on the selection of a theory being used. Layers in the pack, which have significantly differing physical characteristics, make the structure all the more susceptible to transverse strain, viz. shear and reduction. The application of 3D elasticity theory equations for investigating non-stationary deformation in laminated structures is faced with significant mathematical complexities. Therefore, 2D theories have found extensive implementation in the design of real structures. The key feature of the modern stage of development of multilayer structures mechanics consists in the transition from more simple 2D models to more complex ones possessing higher accuracy. Therefore, the development of refined 2D models of multilayered structures for the investigation of non-stationary deformation processes is an important problem. The purpose of this research is to develop a method for calculating the response of layered plates under impulse loading, as well as a comparative analysis of possibilities of different 2D theories.
The layer-wise refined model of elastodynamic of laminated plates for investigation dynamic process is presented. This model is based on expanding displacement vector components of each layer into power series about the transverse coordinate. It takes into account transverse shear and normal strains in each layer. This allows to describe reliably the dynamic behavior of laminated structural elements with different physical and mechanical properties of layers. The motion equations and boundary condition are obtained from a variational principle. The solution method is an analytical-numerical one.
The model possibilities are illustrated on investigations of three-layer structures under impulse loading. The results are compared with data obtained from the classical theory as well as the layer-wise theory based on the broken line hypothesis (the Grigoliuk-Chulkov's model). Special attention is placed on analyzing the stress-strained state of laminated structures subjected to local loads. The proposed approach can be used in design of the laminated glazing.
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References
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