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Stress Analysis of Rotating Annular Uniform-Thickness and Thickness-Tapered Discs made of Orthotropic and Laminated Composite Materials

Title:

Stress Analysis of Rotating Annular Uniform-Thickness and Thickness-Tapered Discs made of Orthotropic and Laminated Composite Materials

Arora, Parteek (2021) Stress Analysis of Rotating Annular Uniform-Thickness and Thickness-Tapered Discs made of Orthotropic and Laminated Composite Materials. Masters thesis, Concordia University.

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Abstract

Favorable mechanical properties such as high strength-to-weight ratio, high stiffness-to-weight ratio, low specific weight and high fatigue strength, and stiffness tailoring capabilities have enabled the use of composite materials in turbomachinery, automotive and aviation industries. Recent developments on the applications to rotating tapered structures such as thickness-tapered flywheels and rotors in gas turbines and airplane engines have shown increasing use of continuous fiber-reinforced composite materials. Rotating annular thickness-tapered discs made of orthotropic and fiber-reinforced composite materials have preferential stress state as compared to the uniform-thickness discs made of isotropic materials rotating at the same speed. Therefore, due to their distinct characteristics from uniform-thickness discs and wide range of applications, the design of thickness-tapered rotating discs requires comprehensive research to understand their elastic behavior under different loading and boundary conditions.
In the present work, the in-plane stress and displacement analyses of rotating annular uniform-thickness and thickness-tapered discs made of orthotropic and fiber-reinforced composite materials are conducted considering different boundary conditions. A computational solution based on the Rayleigh-Ritz method with finite-element-like modification is developed to evaluate the elastic response of rotating annular thickness-tapered discs made of orthotropic materials. Linear taper and Stodola taper profiles are considered in the elastic analysis of thickness-tapered orthotropic discs with the free-free and the clamped-free boundary conditions. The accuracy of the developed formulation for the elastic response of thickness-tapered orthotropic discs is established based on the convergence of the results obtained for the elastic response using the sub-domain-wise application of Rayleigh-Ritz method in terms of the number of divisions of the thickness-tapered disc, to the results obtained using closed-form analytical solutions available in the literature. For rotating annular uniform-thickness and thickness-tapered fiber-reinforced composite discs with the clamped-free boundary condition, the Rayleigh-Ritz method in conjunction with the Classical Laminate Theory in cylindrical coordinate system is used to evaluate the elastic response. The finite element analysis tool ANSYS is used to model the various three-dimensional internal taper configurations of rotating annular thickness-tapered fiber-reinforced composite discs. The results obtained for the elastic response of uniform-thickness and thickness-tapered fiber-reinforced composite discs using the SOLID185 and SHELL181 elements in ANSYS® are used to verify the results obtained for the same using the Rayleigh-Ritz method based on the Classical Laminate Theory in cylindrical coordinate system. Numerical and symbolic calculations to solve the boundary value problem using the Rayleigh-Ritz method are performed using the technical computing language MATLAB®. The effects of degree of orthotropy, taper profile and taper parameter values on the in-plane stress distributions and radial displacement distribution in the rotating annular thickness-tapered discs made of orthotropic materials are observed for the free-free and clamped-free boundary conditions through extensive parametric studies. The influences of fiber orientation, radius ratio, rotational velocity, laminate configuration, ply reduction and internal taper configuration on the elastic response of rotating annular thickness-tapered fiber-reinforced composite discs are thoroughly examined considering the clamped-free boundary condition. For the parametric studies, a wide range of orthotropic materials are chosen and also, the NCT-301 graphite-epoxy prepreg is chosen as a fiber-reinforced composite material. Important design aspects are systematically brought out.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Mechanical, Industrial and Aerospace Engineering
Item Type:Thesis (Masters)
Authors:Arora, Parteek
Institution:Concordia University
Degree Name:M.A. Sc.
Program:Mechanical Engineering
Date:1 April 2021
Thesis Supervisor(s):Ganesan, Rajamohan
Keywords:Stress Analysis, Rotating Discs, Orthotropic Materials, Laminated Composite Materials, Rayleigh-Ritz Method, ANSYS
ID Code:988376
Deposited By: PARTEEK ARORA
Deposited On:29 Jun 2021 23:17
Last Modified:29 Jun 2021 23:17

References:

[1] A.M. Piramoon, Composite Material Centrifuge Rotor, U.S. Patent and Trademark Office, 1988.
[2] D.D. Tremelling, D. Wu, S.C. Englebretson et al., Rotors for Rotating Machines with Hollow Fiber-Reinforced Composite Shaft, U.S. Patent and Trademark Office, 2018.
[3] S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill, New York, 1970.
[4] A.C. Ugural and S.K. Fenster, Advanced Mechanics of Materials and Applied Elasticity, 5th Edition, Boston: Pearson Education, Inc., 2011.
[5] S. Tang, “Elastic Stresses in Rotating Anisotropic Disks”, Int. J. Mech. Sci., Vol. 11, pp. 509-517, 1969.
[6] T.Y. Reddy and H. Srinath, “Elastic Stresses in a Rotating Anisotropic Annular Disk of Variable Thickness and Variable Density”, Int. J. Mech. Sci., Vol. 16, No. 1, pp. 85-89, 1974.
[7] C.I. Chang, “The Anisotropic Rotating Disks”, Int. J. Mech. Sci., Vol. 17, pp. 397-402, 1975.
[8] J. Kirkhope and G.J. Wilson, “Vibration and Stress Analysis of Thin Rotating Discs using Annular Finite Elements”, Journal of Sound and Vibration, Vol. 44, No. 4, pp. 461-474, 1976.
[9] G. Genta, G. Belingardi and M. Gola, “A Study of the Stress Distribution in Rotating Orthotropic Discs”, Composites, Vol. 10, No. 2, pp. 77-80, 1979.
[10] G. Genta and M. Gola, “The Stress Distribution in Orthotropic Rotating Disks”, Journal of Applied Mechanics, Vol. 48, No. 3, pp. 559-562, 1981.
[11] B. De St. Venant, “Memoire sur la Distribution d’elasticite”, Journal des Math. Pures et Appl., Vol. 2, No. 8, 1863.
[12] K. Wolf, “Zeitschrift fur Angewaudte Mathematik und Mechanik”, Vol. 15, pp. 249, 1935.
[13] G.L. Nigh and M.D. Olson, “Finite Element Analysis of Rotating Disks”, Journal of Sound and Vibration, Vol. 77, No. 1, pp. 61 – 78, 1981.
[14] R.A. Cookson and S.K. Sathianathan, “Analysis of Steady Stresses in Rotating Anisotropic Discs”, First A.M.E. Conference, pp. 29 – 31, 1984.
[15] S. Amada, “Dynamic Shear Stress Analysis of Discs Subjected to Variable Rotations”, Journal of Mechanical Engineering, Vol. 28, No. 240, pp. 1029 – 1035, 1985.
[16] U. Guven, “Elastic-Plastic Stresses in a Rotating Annular Disk of Variable Thickness and Variable Density”, Int. J. Mech. Sci., Vol. 34, No. 2, pp. 133-138, 1992.
[17] G.S. Ray and B.K. Sinha, “Profile Optimization of Variable Thickness Rotating Disc”, Computers and Structures, Vol. 42, No. 5, pp. 809 – 813, 1992.
[18] M.M. Megahed and M.S.A. Kader, “Elastoplastic Analysis of Rotating Shrink-Fitted Discs with Nonlinear Hardening Characteristics”, Int. J. Solid Structures, Vol. 30, No. 6, pp. 751 – 765, 1993.
[19] R. Jain, K. Ramachandra and K.R.Y. Simha, “Rotating Anisotropic Disc of Uniform Strength”, International Journal of Mechanical Sciences, Vol. 41, pp. 639 – 648, 1999.
[20] R. Jain, K. Ramachandra and K.R.Y. Simha, “Singularity in Rotating Orthotropic Discs and Shells”, International Journal of Solids and Structures, Vol. 37, pp. 2035 – 2058, 2000.
[21] N. Tutuncu, “Effect of Anisotropy on Inertio-Elastic Instability of Rotating Disks”, International Journal of Solids and Structures, Vol. 37, pp. 7609 – 7616, 2000.
[22] F. Zhou and A. Ogawa, “Elastic Solutions for a Solid Rotating Disk with Cubic Anisotropy”, Journal of Applied Mechanics, Vol. 69, pp. 81-83, 2002.
[23] A.N. Eraslan, “Elastic-Plastic Deformations of Rotating Variable Thickness Annular Disks with Free, Pressurized and Radially Constrained Boundary Conditions”, International Journal of Mechanical Sciences, Vol. 45, No. 3, pp. 643-667, 2003.
[24] Y. Kaya, “Analytical and Numerical Solutions to Rotating Orthotropic Disk Problems”, M.S. Thesis, Middle East Technical University, 2007.
[25] A.M. Zenkour and D.S. Mashat, “Stress Function of a Rotating Variable-Thickness Annular Disk using Exact and Numerical Methods”, Engineering, Vol. 3, No. 2, pp. 422-430, 2011.
[26] X.L. Peng and X.F. Li, “Elastic Analysis of Rotating Functionally Graded Polar Orthotropic Disks”, International Journal of Mechanical Sciences, Vol. 60, No. 4, pp. 84-91, 2012.
[27] L. Sondhi, S. Sanyal, K.N. Saha et al., “An Approximate Solution to the Stress and Deformation States of Functionally Graded Rotating Disks”, International Conference on Mechanical Engineering, 2016.
(Source - http://dx.doi.org/10.1063/1.4958351)
[28] A.N. Eraslan, Y. Kaya and E. Varli, “Analytical Solutions to Orthotropic Variable Thickness Disk Problems”, Pamukkale University Journal of Engineering Sciences, Vol. 22, No. 1, pp. 24-30, 2016.
[29] V. Yildirim, “Unified Exact Solutions to the Hyperbolically Tapered Pressurized/Rotating Disks Made of Nonhomogeneous Isotropic/Orthotropic Materials”, International Journal of Advanced Materials Research, Vol. 4, No. 1, pp. 1-23, 2018.
[30] V. Yildirim, “The Complementary Functions Method (CFM) Solution to the Elastic Analysis of Polar Orthotropic Rotating Discs”, J. Appl. Comp. Mech., Vol. 4, No. 3, pp. 216-230, 2018.
[31] C.W. Bert, “Centrifugal Stresses in Arbitrarily Laminated, Rectangular-Anisotropic Circular Discs”, Journal of Strain Analysis, Vol. 10, No. 2, pp. 84-92, 1975.
[32] S. Tsuda, E. Shiratori and K. Ikegami, “Rotating Strength of Laminated Composite Discs”, Journal of Mechanical Engineering, Vol. 23, No. 180, pp. 822 – 830, 1980.
[33] E. Shiratori, K. Ikegami and T. Ishii, “Study on the High-Speed Rotating Disc Reinforced by Laminating and Hoop Winding Method”, Journal of Mechanical Engineering, Vol. 24, No. 189, pp. 501 – 506, 1981.
[34] J.A. Gur and Y. Stavsky “On Rotating Polar Orthotropic Circular Disks”, Int. J. Solids Structures, Vol. 17, pp. 57 – 67, 1981.
[35] G. Genta, M. Gola and A. Gugliotta, “Axisymmetric Computation of the Stress Distribution in Orthotropic Rotating Discs”, Int. J. Mech. Sci., Vol. 24, No. 1, pp. 21 – 26, 1982.
[36] M.R. Sitzer, “Stress Distribution in Rotating Aeolotropic Laminated Heterogenous Disc under Action of a Time-Dependent Loading”, Journal of Applied Mathematics and Physics, Vol. 36, pp. 134-145, 1985.
[37] H.V. Lakshminarayana, “Finite Element Analysis of Rotating Laminated Composite Annular Discs”, Composites, Vol. 17, No. 1, pp. 42-48, 1986.
[38] M. Carpino, “Analysis of a Laminate Disk Rotating near a Flat Plate”, Journal of Tribology, Vol. 115, pp. 578 – 583, 1993.
[39] N. Tutuncu, “Effect of Anisotropy on Stresses in Rotating Discs”, Int. J. Mech. Sci., Vol. 37, No. 8, pp. 873-881, 1995.
[40] F. Hild and F.A. Leckie, “Fiber Distribution in Reinforced Ceramic Rotating Discs”, International Gas Turbine and Aeroengine Congress and Exposition, 1995.
[41] N. Tutuncu and A. Durdu, “Determination of Buckling Speed for Rotating Orthotropic Disk Restrained at Outer Edge”, AIAA Journal, Vol. 36, No. 1, pp. 89 – 93, 1998.
[42] J.F. Durodola and O. Attia, “Property Gradation for Modification of Response of Rotating MMC Discs”, Material Science and Technology, Vol. 16, pp. 919 – 924, 2000.
[43] S.M. Arnold, A.F. Saleeb and N.R. Al-Zoubi, “Deformation and Life Analysis of Composite Flywheel Disk Systems”, Composites, Vol. 33, pp. 433 – 459, 2002.
[44] M. Tahani, A. Nosier and S.M. Zebarjad, “Deformation and Stress Analysis of Circumferentially Fiber-Reinforced Composite Disks”, International Journal of Solids and Structures, Vol. 42, pp. 2741 – 2754, 2005.
[45] K.N. Koo, “In-plane Stress Analysis of Rotating Composite Disks”, Journal of the Korean Society of Composite Materials, Vol. 18, No. 4, pp. 8 – 13, 2005.
[46] A.M. Zenkour and M.N.M Allam, “On the Rotating Fiber-Reinforced Viscoelastic Composite Solid and Annular Disks of Variable Thickness”, International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 7, No. 1, pp. 21-31, 2006.
[47] H. Callioglu, M. Topcu and A.R. Tarakcilar, “Elastic-Plastic Stress Analysis of an Orthotropic Rotating Disc”, International Journal of Mechanical Sciences, Vol. 48, pp. 985-990, 2006.
[48] B. C. Fabien, “The Influence of Failure Criteria on the Design Optimization of Stacked-Ply Composite Flywheels”, Struct Multidisc Optim, Vol. 33, pp. 507-517, 2007.
[49] K.N. Koo, “Elastic Stresses and Failure of Rotating Cross-Ply Laminated Disks”, Journal of Mechanical Science and Technology, Vol. 23, pp. 1508-1514, 2009.
[50] K.N. Koo and G.A. Lesieutre, “Vibration and Critical Speeds of Composite-Ring Disks for Data Storage”, Journal of Sound and Vibration, Vol. 329, pp. 833-847, 2010.
[51] A. Almasi, “Application and Stress Analysis of Laminated Composites for High-Speed Impellers of Process Centrifugal Compressors”, J. Process Mechanical Engineering, Vol. 226, No. 5, pp. 256-260, 2011.
[52] F. Zhou, A. Ogawa and R. Hashimoto, “Strain and Stress Distribution in a Rotating Disk made by 2D C/C Laminated Composites”, Proceedings of the 2001 International Conference on Composite Materials, Beijing, 2001
[53] V. Yildirim, “The Complementary Functions Method Solution to the Functionally Graded Polar Orthotropic Rotating Hyperbolic Disks with Both Radially and Circumferentially Aligned Fibers”, International Journal of Engineering & Applied Sciences, Vol. 10, No. 4, pp. 276-290, 2018.
[54] C. Delvadiya, “Dynamic Analysis of Tapered Circular Discs made of Isotropic and Orthotropic Materials using Rayleigh-Ritz Method and ANSYS”, M.A.Sc. Thesis, Concordia University, 2016.
[55] N. Baddour, “A Modelling and Vibration Analysis of Spinning Disks”, Ph.D. Thesis, University of Toronto, 2001.
[56] P.J.G. Schreurs, “Linear Plate Bending and Laminate Theory”, M020, Eindhoven University of Technology, Eindhoven, NB, 2008.
[57] J.M. Berthelot, Composite Materials: Mechanical Behavior and Structural Analysis, New York: Springer, 1999.
[58] A. Zabihollah, “Vibration and Buckling Analysis of Tapered Composite Beams using Conventional and Advanced Finite Element Formulations”, M.A.Sc. Thesis, Concordia University, 2003.
[59] S. Akhlaque, “Buckling Analysis of Tapered Composite Plates using Ritz Method based on Classical and Higher Order Theories”, M.A.Sc. Thesis, Concordia University, 2005.
[60] K.W. Gan, G. Allegri and S.R. Hallett, “A Simplified Layered Beam Approach for Predicting Ply Drop Delamination in Thick Composite Laminates”, Materials & Design, Vol. 108, pp. 570 – 580, 2016.
[61] ANSYS Inc., “ANSYS Mechanical APDL Element Reference”, 2013.
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