The Dynamic Response of Multidirectional Functionally Graded Plates Impacted by Blast Loading
ARMY TANK AUTOMOTIVE RESEARCH DEVELOPMENT AND ENGINEERING CENTER WARREN MI
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The theoretical model for the dynamic response of multi-directional functionally graded thin plates under an in-air blast loading from a Friedlander type pressure loading is presented. The theory is presented in the context of the classical linear plate theory CPT which is based on the Kirchoff-Love assumptions. The plate is assumed to be thin, in-plane strains are small compared to unity, and the transverse and normal strains are considered to be negligible. Additionally, the theoretical model assumes that the material properties of the two constituent materials vary in all three coordinate directions. This implies in-plane as well as through the thickness grading according to 3 independent power law distributions. Simply supported boundary conditions are assumed along all four edges. The governing equations of motion are derived through the use of Hamiltons Principle. The dynamic response is determined through the use of numerical integration, using the Gaussian-Quadrature Method, the Galerkin Method, and the Fourth-Order Runge-Kutta Method with zero initial conditions. Results are presented using the technique of spatial tailoring to determine the optimization of the 3D-Grading from a response standpoint. Finally, validations are made with simpler cases found within the literature.
- Theoretical Mathematics