Analysis of buckling of circular plate with delamination by using third order shear deformation theory

Document Type : Dynamics, Vibrations, and Control

Authors

-

Abstract

Delamination is one of the common flaws in the composite plates, which may be created during manufacturing, boring or loading in the composite plate. This flaw has an impact on the flexibility, strength and performance of composite plates and structures and reduces them, which may even result in a layer fracture or complete fracture in the composite plate. In this study, a circular composite plate with the circular delamination under buckling load is considered. Given that the delamination grows and the delamination boundary is movable, the equilibrium equations governing the circular plate with circular delamination is produced by using Calculus of Variations method with moving boundary. The theory used in this paper for finding equilibrium equations governing the mentioned plate is the third order shear deformation theory. Ultimately, for isotropic and orthotropic materials, the critical buckling load is determined by using spectral homotopy analysis method and the results of the present paper is compared with the results of other studies. The results produced shows a good conformity with the other reference results.

Keywords

References

Afrouzian, A., Pol, M. H., Liaghat, G. H. and Aleni, H. M. “An Experimental Investigation on Mode-II Interlaminar Fracture Toughness of Nanosilica Modified Glass/Epoxy Fiber-Reinforced Laminates”, Modares Mechanical Engineering, Vol. 15, No. 3, pp. 283-290, 2015. (In Persian)##
2. Shokrieh, M. M. and Abdolvand, H. R. “Three-Dimensional Thermodynamical Modeling of Fire Effect on Polymer Matrix Composites, Considering Variation Of Thermal Properties”, Aerospace Mechanics Journal, Vol. 5, No. 4, pp. 15-32, 2010. (In Persian)##
3. Malekzadeh Fard, K., Nazari, A., Mozaffari, A. and Ebrahimi, M. “The Effect of Appling Functionally Graded Core to Decrease Delamination of Composite Sandwich Panel Under Transverse Load”, Aerospace Mechanics Journal, Vol. 8, No. 1, pp. 71-84, 2012. (In Persian)##
4.   Hajko, P., Tejchman, J. and Wójcik, M. “Investigations of Local/Global Buckling of Cylindrical Metal Silos with Corrugated Sheets and Open-Sectional Column Profiles”, Int. J. Thin-Walled Structures, Vol. 123, pp. 341-350, 2018.##
5.   Ma, Y., Cheng, X., Wang, Z., Guo, X., Zhang, J. and Xu, Y. “Buckling and Post-Buckling Behaviors of 1/3 Composite Cylindrical Shell With an Opening”, Int. J. STEEL AND COMPOSITE STRUCTURES, Vol. 27, No. 5, pp. 555-566, 2018.##
6. Fratamico, D. C., Torabian, S., Zhao, X., Rasmussen, K. J. and Schafer, B. W. “Experiments on the Global Buckling and Collapse of Built-Up Cold-Formed Steel Columns”, Int. J. CONSTRUCTIONAL STEEL RESEARCH, Vol. 144, No. 1, pp. 65-80, 2018.##
7.   Watkins, R. T., Reedlunn, B., Daly, S. and Shaw, J. A. “Uniaxial, Pure Bending, and Column Buckling Experiments on Superelastic Niti Rods and Tubes”, Int. J. Solids and Structures, Vol. 146, No. 1, pp. 1-28, 2018.##
8.   Park, M. and Choi, D-H. “A Two-Variable First-Order Shear Deformation Theory Considering In-Plane Rotation for Bending, Buckling and Free Vibration Analyses of Isotropic Plates”, Int. J. Applied Mathematical Modelling, Vol. 61, No. 1, pp. 49-71, 2018.##
9.   Amabili, M. “Nonlinear Vibrations and Stability of Laminated Shells Using a Modified First-Order Shear Deformation Theory”, European Journal of Mechanics-A/Solids, Vol. 68, No. 1, pp. 75-87, 2018.##
10. Reddy, J. N. “Mechanics of Laminated Composite Plates and Shells: Theory And Analysis”, CRC press, 2004.##
11. Haghani, A., Mondali, M. and Faghidian, S. “Linear and Nonlinear Flexural Analysis of Higher-Order Shear Deformation Laminated Plates with Circular Delamination”, Int. J. Acta Mechanica, Vol. 229, No. 4, pp. 1631-1648, 2018.##
12. Shiri, M. G. and Jaamialahmadi, A. “Buckling Analysis of Intelligent Nanoplate under Inplane Loading Based on Nonlocal Elasticity and Shear and Normal Deformation Theories”, Modares Mechanical Engineering, Vol. 17, No. 2, pp. 427-438, 2017. (In Persian)##
13.Bolza, O. “Lectures on The Calculus of Variations”, Courier Dover Publications, 2018.##
14. Haghani, A. “The Solution of The Nonlinear Equations of Delamination in Composite Plates Using Modified Third Order Shear Deformation Theory”, Ph.D. Thesis, Islamic azad university science and research branch, pp.93-105, 2017. (In Persian)##
15. Simitses, G., Sallam, S. and Yin, W. “Effect of Delamination of Axially Loaded Homogeneous Laminated Plates”, AIAA journal, Vol. 23, No. 9, pp. 1437-1444, 1985.##
16. Motsa, S., Sibanda, P., Awad, F. and Shateyi, S. “A New Spectral-Homotopy Analysis Method for the MHD Jeffery–Hamel Problem”, Int. J. Computers & Fluids, Vol. 39, No. 7, pp. 1219-1225, 2010.##
17. Liao, S. “Beyond Perturbation: Introduction to the Homotopy Analysis Method”, CRC press, 2003.##
18. Chen, D. and Dai, L. “Delamination Growth of Laminated Circular Plates Under In-Plane Loads and Movable Boundary Conditions”, Int. J. Communications in Nonlinear Science and Numerical Simulation, Vol. 18, No. 11, pp. 3238-3249, 2013.##

Files

History

  • Receive Date: 11 September 2018
  • Revise Date: 01 October 2019
  • Accept Date: 14 June 2020
  • Publish Date: 21 June 2020

Share

How to cite

Statistics