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Dergiler / Turkish Journal of Engineering and Environmental Sciences / 2005 / Cilt: 29 - Sayı: 4

A Class of Nonisothermal Variable Thickness Rotating Disk Problems Solved by Hypergeometric Functions

Ahmet N. ERASLAN
Sayfa
241–269
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

A displacement formulation is used and the resulting differential equations for the elastic and plastic regions are solved in terms of hypergeometric functions by the introduction of appropriate transformations.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Exact solutions for nonisothermal variable thickness rotating disks represented by different thickness profiles are obtained under plane stress assumption.
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Temel Bulgular & Veri:The solutions are based on Tresca's yield criterion, its associated flow rule and linear strain hardening material behavior.
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Sonuç & Katkı:A displacement formulation is used and the resulting differential equations for the elastic and plastic regions are solved in terms of hypergeometric functions by the introduction of appropriate transformations.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Thermoelastoplasticity · Tresca's criterion · Variable thickness

Özet

Exact solutions for nonisothermal variable thickness rotating disks represented by different thickness profiles are obtained under plane stress assumption. The solutions are based on Tresca's yield criterion, its associated flow rule and linear strain hardening material behavior. Five different plastic regimes governed by different mathematical forms of the yield criterion are considered for each thickness profile. A displacement formulation is used and the resulting differential equations for the elastic and plastic regions are solved in terms of hypergeometric functions by the introduction of appropriate transformations.

Abstract

Exact solutions for nonisothermal variable thickness rotating disks represented by different thickness profiles are obtained under plane stress assumption. The solutions are based on Tresca's yield criterion, its associated flow rule and linear strain hardening material behavior. Five different plastic regimes governed by different mathematical forms of the yield criterion are considered for each thickness profile. A displacement formulation is used and the resulting differential equations for the elastic and plastic regions are solved in terms of hypergeometric functions by the introduction of appropriate transformations.

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Bu Makaleye Atıf Yap

ERASLAN, A. N. (2005). A Class of Nonisothermal Variable Thickness Rotating Disk Problems Solved by Hypergeometric Functions. Turkish Journal of Engineering and Environmental Sciences, Cilt: 29 - Sayı: 4, 241–269. https://ajindex.com/articles/369167

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Kaynakça (10)

  1. Abramowitz, M. and Stegun, A.I. (Eds.), Handbook of Mathematical Functions, US Government Print- ing Office, Fifth Printing, Washington, 1966. Eraslan, plastic Rotating Disks with Elliptical Thickness Profiles Using Tresca and von Mises Criteria”, The Journal of Applied Mathematics and Mechanics (ZAMM) 85, 252-266, 2005.
  2. Eraslan, A.N.,“Tresca’s Yield Criterion and Lin- early Hardening Rotating Solid Disks Having Hy- perbolic Profiles”, Forschung im Ingenieurwesen 69, 28, 2004.
  3. Eraslan, A.N.,“Elastoplastic Deformations of Rotat- ing Parabolic Solid Disks Using Tresca’s Yield Crite- rion”, European Journal of Mechanics A/Solids 22, 874, 2003.
  4. Eraslan, A.N.,“Inelastic Deformations of Rotating Variable Thickness Solid Disks by Tresca and von Mises Criteria”, International Journal of Computa- tional Engineering Science 3, 89-101, 2002a.
  5. Eraslan, A.N.,“Von Mises Yield Criterion and Non- linearly Hardening Variable Thickness Rotating An- nular Disks with Rigid Inclusion”, Mechanics Re- search Communications 29, 339-350, 2002b.
  6. Eraslan, A.N. and Akis, T.,“On the Elastic-plastic Deformation of a Rotating Disk Subjected to a Ra- dial Temperature Gradient”, Mechanics Based De- sign of Structures and Machines 31, 529-561, 2003.
  7. Eraslan, A.N. and Argeso, H.,“Limit Angular Veloc- ities of Variable Thickness Rotating Disks”, Inter- national Journal of Solids and Structures 39, 3109-, 2002.
  8. Eraslan, A.N. and Orcan, Y.,“Elastic-plastic Defor- mation of a Rotating Solid Disk of Exponentially Varying Thickness”, Mechanics of Materials 34, 423-, 2002a.
  9. Eraslan, A.N. and Orcan, Y.,“On the Rotating Elastic-plastic Solid Disks of Variable Thickness Having Concave Profiles”, International Journal of Mechanical Sciences 44, 1445-1466, 2002b. G¨uven, U.,“Elastic-plastic Stress Distribution in a Rotating Hyperbolic Disk with Rigid Inclusion”, In- ternational Journal of Mechanical Sciences 40, 97-, 1998a. G¨uven, U.,“Stress Distribution in a Linear Harden- ing Annular Disk of Variable Thickness Subjected to External Pressure”, International Journal of Me- chanical Sciences 40, 589-601, 1998b. G¨uven, U.,“On the Applicability of Tresca’s Yield Condition to the Linear Hardening Rotating Solid Disk of Variable Thickness”, The Journal of Applied Mathematics and Mechanics (ZAMM) 75, 397-398, a. G¨uven, U.,“Tresca’s Yield Condition and the Linear Hardening Rotating Solid Disk of Variable Thick- ness”, The Journal of Applied Mathematics and Me- chanics (ZAMM) 75, 805-807, 1995b.
  10. Orcan, Y