Dynamic Response of FGM Plates Under Blast Load

Subject Areas : composite materials

reza  azarafza ¹ (Faculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran)
puya  pirali ² (Faculty of Materials and Manufacturing Technologies,Malek Ashtar University of Technology, Tehran, Iran)
Ali  Davar ³ (Faculty of Materials and Manufacturing Technologies,Malek Ashtar University of Technology, Tehran, Iran)
majid  ghadimi ⁴ (Faculty of Materials and Manufacturing Technologies,Malek Ashtar University of Technology, Tehran, Iran)

Received: 2021-01-09 Accepted : 2021-04-09 Published : 2024-02-24

Keywords: Dynamic Response, Explosive Loading, Functional Graded Materials, Rectangular FGM Plates ,

Abstract :

The present study investigates the deformation of FGM plates under blast load. Hamilton's principle is used to obtain the dynamic Equations. The two constituent phases, ceramic and metal, vary across the wall thickness according to a prescribed power law. Boundary conditions are assumed to be Simply Supported (SS). The type of explosive loading considered is a free in-air spherical air burst and creates a spherical shock wave that travels radially outward in all directions. For the pressure time of the explosion loading, Friedlander’s exponential relation has been used. In order to determine the response analytically, the stress potential field function is considered. Using the Galerkin method, the final Equations are obtained as nonlinear and nonhomogeneous second-order differential Equations. The effect of temperature including thermal stress resultants and different parameters on the dynamic response have been investigated. Results have been compared with references and validated. Results showed that the amplitude of the center point deflection of the FGM plate is less than the pure metal plates when exposed to blast load, by increasing the volumetric index percentage of FGM, center point deflection is increased and in the FGM plates, deformation of symmetrical plates is smaller than the asymmetric plates. Also by applying the damping coefficient of the FGM plates, the amplitude of center point deflection is reduced, and by increasing the aspect ratio of the FGM plate, its center point deflection against explosion waves is reduced and by considering the effects of thermal resultant forces and moments, center point deflection is increased.

References:

[1] Shen, H. S., Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, CRC Press, Tylor & Francis Group, London, New York, Published January 15, 2011, ISBN 9780367386016.
[2] Turkmen, H. S., Mecitoglu, Z., Dynamic Response of a Stiffened Laminated Composite Plate Subjected to Blast Load, Journal of Sound and Vibration, Vol. 221, No 3, 1999, pp. 371-389, DOI.org/10.1006/jsvi.1998.1976.
[3] Chi, S., Chung, U., Mechanical Behavior of Functionally Graded Material Plates Under Transverse Load, Int. J. Solids and Structures, Vol. 43, N0. 13, 2006, pp. 3657-3674, DOI.org/10.1016/j.ijsolstr.2005.04.011.
[4] Alibeigloo, A., Exact solution for Thermoelastic Response of Functionally Graded Rectangular Plates, Composite Structures, Vol. 92, No. 1, 2010, pp. 113-121, DOI.org/10.1016/j.compstruct.2009.07.003.
[5] Tung, H. V., Duc, N. D., Nonlinear Analysis of Stability for Functionally Graded Plates Under Mechanical and Thermal Loads, Composite Structures, Vol. 92, No. 5, 2010, pp. 1184-1191, DOI.org/10.1016/j.compstruct.2009.10.015.
[6] Hause, T., Advanced Functionally Graded Plate-Type Structures Impacted by Blast Loading, International Journal of Impact Engineering, Vol. 38, No. 5, 2011, pp. 314-321, DOI.org/10.1016/j.ijimpeng.2010.11.006.
[7] Aksoylar, C., Ömercikog˘lu, A., Mecitog˘lu, Z., and Omurtag, M. H., Nonlinear Transient Analysis of Fgm and FML Plates Under Blast Loads, Composite Structures, Vol. 94, No. 2, 2012, pp. 731-744, DOI.org/10.1016/j.compstruct.2011.09.008.
[8] Sreenivas, P., Siva Kumar, A., Pavuluri, S., and Kumari, A. A., Investigation on Transient Dynamic Response of Functionally Graded Materials, International Journal of Application or Innovation in Engineering & Management, Vol. 2, No. 9, 2013, pp. 214-218.
[9] Goudarzi, M., Zamani, J., Experimental and Numerical Investigation of the Maximum Deflection of Circular Aluminum Plate Subjected to Free Air Explosion, (In Persian) Modares Mechanical Engineering, Vol. 15, No. 1, 2015, pp. 219-226.
[10] Duong, N. T., Duc, N. D., Evaluation of Elastic Properties and Thermal Expansion Coefficient of Composites Reinforced by Randomly Distributed Spherical Particles with Negative Poissons Ratio, Composite Structures, Vol. 153, 2016, pp. 569–577, DOI:10.1016/j.compstruct.2016.06.069.
[11] Duc, N. D., Duc, N., Tuan, N. D., Tran, P., and Quan, T. Q., Nonlinear Dynamic Response and Vibration of Imperfect Shear Deformable Functionally Graded Plates Subjected to Blast And Thermal Load, Journal of Mechanics of Advanced Materials and Structure, Vol. 24, No. 4, 2016, pp. 318-329, DOI:10.1080/15376494.2016.1142024.
[12] Duc, N. D., Quang, V. D., and Anh, V. T. T., The Nonlinear Dynamic and Vibration of the S-FGM Shallow Spherical Shells Resting On an Elastic Foundations Including Temperature Effects, International Journal of Mechanical Sciences, Vol. 123, 2017, pp. 54–63, DOI.org/10.1016/j.ijmecsci.2017.01.043.
[13] Cong, P. H., Anh, V. M., and Duc, N. D., Nonlinear Dynamic Response of Eccentrically Stiffened FGM Plate using Reddys TSDT in Thermal Environment, Journal of Thermal Stresses, Vol. 40, No. 6, 2017, pp. 704–732, DOI.org/10.1080/01495739.2016.1261614.
[14] Hajlaoui, A., Triki, E., Frikha, A., Wali, M., and Dammak, F., Nonlinear Dynamics Analysis of FGM Shell Structures with a Higher Order Shear Strain Enhanced Solid-Shell Element, Latin American Journal of Solids and Structure, Vol. 14, 2017, pp. 72-91, DOI.org/10.1590/1679-78253323.
[15] Thang, P. T., Duc, N. D., and Nguyen-Thoi, T., Thermomechanical Buckling And Post-Buckling of Cylindrical Shell with Functionally Graded Coatings and Reinforced by Stringers, Aerospace Science and Technology, Vol. 66, 2017, pp. 392-401, DOI.org/10.1016/j.ast.2017.03.023.
[16] Duc, N. D., Quang, V. D., Nguyen, P. D., and Chien, T. M., Nonlinear Dynamic Response of Functionally Graded Porous Plates on Elastic Foundation Subjected to Thermal and Mechanical Loads, J. Appl. Comput. Mech., Vol. 4. No. 4, 2018, pp. 245-259, DoI:10.22055/JACM.2018.23219.1151.
[17] Hong kong, P., Dinh Duc, N., Studied Analytical Solutions for The Nonlinear Dynamic Response of ES-FGM Plate Under Blast Load, Vietnam Journal of Mechanics, VAST, Vol. 40, No. 1, 2018, pp. 33 – 45, DOI:10.15625/0866-7136/9840.
[18] Kim, S. E., Duc, N. D., Nam, V. H. and Sy, N. V., Nonlinear Vibration and Dynamic Buckling of Eccentrically Oblique Stiffened FGM Plates Resting On Elastic Foundations in Thermal Environment, Thin-Walled Structures, Vol. 142, 2019, pp. 287-296, DOI.org/10.1016/j.tws.2019.05.013.
[19] Duc, N. D., Hadavinia, H., Quan, T. Q., and Khoa, N. D., Free Vibration and Nonlinear Dynamic Response of Imperfect Nanocomposite FG-CNTRC Double Curved Shallow Shells in Thermal Environment, European Journal of Mechanics - A/Solids, Vol. 75, 2019, pp. 355-366, DOI.org/10.1016/j.euromechsol.2019.01.024.
[20] Upadhyay, A., Shukla, K., Geometrically Nonlinear Static and Dynamic Analysis of Functionally Graded Skew Plates, Communication in Nonlinear Science and Numerical Simulation, Vol. 18, No. 8, 2013, pp. 2252-2279, DOI.org/10.1016/j.cnsns.2012.12.034.
[21] Soltani, M., Hatami, S., and Azhari, M., Free Vibration of Thin Functionally Graded Plates by Exact Finite Strip Method, Journal of computational Methods in Engineering, Vol. 32, No. 2, 2014, pp. 33-54.
[22] Thang, P. T., Nguyen-Thoi, T., and Lee, J., Closed-form Expression for Nonlinear Analysis of Imperfect Sigmoid-FGM Plates with Variable Thickness Resting On Elastic Medium, Composite Structures, Vol. 143, 2016, pp. 143-150, DOI.org/10.1016/j.compstruct.2016.02.002.
[23] Smith, P., Hetherington, J., Blast and Ballistic Loading of Structures, 1st Edition, CRC Press. Tylor & Francis GrouPublished August 15, 1994, ISBN 9780367866877.