A COMPUTATIONAL MODEL FOR PARTIALLY-PLASTIC STRESS ANALYSIS OF ORTHOTROPIC VARIABLE THICKNESS DISKS SUBJECTED TO EXTERNAL PRESSURE

Year 2014, Volume: 2 Issue: 1, 1 - 13, 01.06.2014

AHMET N. Eraslan YASEMİNKAYA BÜŞRAÇİFTÇİ

Abstract

A computational model is developed to predict the states of stressand deformation in partially plastic, orthotropic, variable thickness, nonisothermal, stationary annular disks under external pressure. Assuming a state ofplane stress and using basic equations of mechanics of a disk, Maxwell relation,Hill’s quadratic yield condition, and a Swift type nonlinear hardening law, asingle governing differential equation describing the elastic and partially plasticresponse of an orthotropic, variable thickness, nonisothermal disk is obtained.The solution of this nonlinear second order differential equation subject to freeand pressurized boundary conditions is achieved by a shooting method. In thisarticle, we move towards the governing equation by going through basic equations that lead to it and present its solution procedure and some interestingresults

Keywords

Orthotropic disk , Variable thickness , Elastoplasticity , Hill’s quadraticyield criterion , Shooting method

References

• Argeso, H., Analytical solutions to variable thickness and variable material property rotating disks for a new three-parameter variation function. Mechanics Based Design of Structures and Machines 40 (2012), 133-152.
• Bayat, M., Sahari, B. B., Saleem, M., Hamouda, A. M. S., and Reddy, J. N., Thermo elastic analysis of functionally graded rotating disks with temperature-dependent material proper- ties: Uniform and variable thickness. International Journal of Mechanics and Materials in Design 5 (2009),263-279.
• Boresi, A. P., Schmidt, R. J., and Sidebottom, O. M., Advanced mechanics of materials, 5th Ed., Wiley, New York, (1993).
• Callıoglu, H., Stress analysis of an orthotropic rotating disc under thermal loading. Journal of Reinforced Plastics and Composites 23 (2004),1859-1867.
• Eraslan A. N., Stress distributions in elastic-plastic rotating disks with elliptical thickness profiles using Tresca and vonMises criteria. ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik 85 (2005), 252-266.
• Eraslan, A. N., and Akis, T., On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems. Acta Mechanica 181 (2006), 43-63.
• Eraslan, A. N., and Argeso, H., Limit angular velocities of variable thickness rotating disks. International Journal of Solids and Structures 39 (2002), 3109-3130.
• Eraslan, A. N., and Orcan, Y., Elastic-plastic deformation of a rotating solid disk of expo- nentially varying thickness. Mechanics of Materials 34 (2002), 423-432.
• Eraslan, A. N., and Orcan, Y., A parametric analysis of rotating variable thickness elasto- plastic annular disks subjected to pressurized and radially constrained boundary conditions. Turkish Journal of Engineering and Environmental Sciences 28 (2004), 381-395.
• Gupta, V., and Singh, S. B., Creep analysis in anisotropic composite rotating disc with hyperbolically varying thickness. Applied Mechanics and Materials 116 (2012), 4171-4178.
• Hill. R., User-friendly theory of orthotropic plasticity in sheet metals. International Journal of Mechanical Sciences 35 (1993), 19-25.
• Rees, D. W. A., The mechanics of solids and structures. McGraw-Hill, New York, (1990).
• Timoshenko, S., and Goodier, J. N., Theory of elasticity, 3rd Ed., McGraw-Hill, New York, (1970).
• Tutuncu, N., and Temel, B., An efficient unified method for thermoelastic analysis of func- tionally graded rotating disks of variable thickness. Mechanics of Advanced Materials and Structures 20 (2013), 38-46.
• Ugural, A. C., and Fenster, S. K., Advanced strength and applied elasticity, 3rd Ed., Prentice- Hall, London, (1995). [16] Vullo, V., and Vivio, F., Elastic stress analysis of non-linear variable thickness rotating disks subjected to thermal load and having variable density along the radius. International Journal of Solids and Structures 45 (2008), 5337-5355.
• You, L. H., Wang, J. X., and Tang, B. P., Deformations and stresses in annular disks made of functionally graded materials subjected to internal and/or external pressure. Meccanica 44 (2009), 283-292.
• Zenkour, A. M., Stress distribution in rotating composite structures of functionally graded solid disks. Journal of Materials Processing Technology 209 (2009), 3511-3517.
• Department of Engineering Sciences, Middle East Technical University, 06800, Ankara- TURKEY
• E-mail address: [e-mail] , [e-mail] , [e-mail]