Abstract
Thin annular discs subject to various loading conditions are a class of commonly used structures in mechanical engineering. Particular examples are aircraft structures and reciprocating machinery. The mechanical analysis and design of such discs may be based either on elastic or elastic/plastic solutions. This monograph deals with the latter approach.
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References
Reid L (1997) Incorporating hole cold expansion to meet durability and damage tolerance airworthiness objectives. SAE International, SAE Paper No 972624
Ghorashi M, Daneshpazhooh M (2001) Limit analysis of variable thickness circular plates. Comput Struct 70:461–468
Durban D (1987) An exact solution for the internally pressurized, elastoplastic, strain-hardening, annular plate. Acta Mech 66:111–128
Guven U (1998) Elastic-plastic stress distribution in a rotating hyperbolic disk with rigid inclusion. Int J Mech Sci 40:97–109
Guven U (1998) Stress distribution in a linear hardening annular disk of variable thickness subjected to external pressure. Int J Mech Sci 40:589–601
Guven U, Altay O (2000) Elastic-plastic solid disk with nonuniform heat source subjected to external pressure. Int J Mech Sci 42:831–842
Eraslan AN (2002) Inelastic deformations of rotating variable thickness solid disks by Tresca and von Mises criteria. Int J Comput Eng Sci 3:89–101
Eraslan AN (2003) Elastoplastic deformations of rotating parabolic solid disks using Tresca’s yield criterion. Eur J Mech A Solids 22:861–874
Eraslan AN (2003) Elastic-plastic deformations of rotating variable thickness annular disks with free, pressurized and radially constrained boundary conditions. Int J Mech Sci 45:643–667
Eraslan AN, Orcan Y (2002) On the rotating elastic-plastic solid disks of variable thickness having concave profiles. Int J Mech Sci 44:1445–1466
Arslan E, Mack W, Eraslan AN (2008) Effect of a temperature cycle on a rotating elastic-plastic shaft. Acta Mech 195:129–140
You LH, Zhang JJ (1999) Elastic-plastic stresses in a rotating solid disk. Int J Mech Sci 41:269–282
You LH, Tang YY, Zhang JJ, Zheng CY (2000) Numerical analysis of elastic-plastic rotating disks with arbitrary variable thickness and density. Int J Solids Struct 37:7809–7820
You XY, You LH, Zhang JJ (2004) A simple and efficient numerical method for determination of deformations and stresses in rotating solid shafts with non-linear strain-hardening. Commun Numer Methods Eng 20:689–697
Eraslan AN, Argeso A (2002) Limit angular velocities of variable thickness rotating disks. Int J Solids Struct 39:3109–3130
Debski R, Zyczkowski M (2002) On decohesive carrying capacity of variable-thickness annular perfectly plastic disks. Z Angew Math Mech 82:655–669
Vivio F, Vullo L (2010) Elastic-plastic analysis of rotating disks having non-linearly variable thickness: residual stresses by overspeeding and service stress state reduction. Ann Solid Struct Mech 1:87–102
Budiansky B, Mangasarian DL (1960) Plastic stress concentration at a circular hole in an infinite sheet subjected to equal biaxial tension. Trans ASME J Appl Mech 27:59–64
Papanastasiou P, Durban D (1997) Elastoplastic analysis of cylindrical cavity problems in geomaterials. Int J Numer Anal Mech Geomech 21:133–149
Durban D, Papanastasiou P (1997) Cylindrical cavity expansion and contraction in pressure sensitive geomaterials. Acta Mech 122:99–122
Bradford IDR, Durban D (1998) Stress and deformation fields around a cylindrical cavity embedded in a pressure-sensitive elastoplastic medium. Trans ASME J Appl Mech 65:374–379
Chen PCT (1973) A comparison of flow and deformation theories in a radially stressed annular plate. Trans ASME J Appl Mech 40:283–287
Roberts SM, Hall FR, Bael AV, Hartley P, Pillinger I, Sturgess CEN, Houtte PV, Aernoudt E (1992) Benchmark tests for 3-D, elasto-plastic, finite-element codes for the modeling of metal forming processes. J Mater Process Technol 34:61–68
Helsing J, Jonsson A (2002) On the accuracy of benchmark tables and graphical results in the applied mechanics literature. Trans ASME J Appl Mech 69:88–90
Ball DL (1995) Elastic-plastic stress analysis of cold expanded fastener holes. Fat Fract Eng Mater Struct 18:47–63
Hill R (1950) The mathematical theory of plasticity. Clarendon Press, Oxford
Bland DR (1956) Elastoplastic thick-walled tubes of work-hardening material subject to internal and external pressures and to temperature gradients. J Mech Phys Solids 4:209–229
Rees DWA (1990) Autofrettage theory and fatigue life of open-ended cylinders. J Strain Anal Eng Des 25:109–121
Luxmoore AR, Light MF, Evans WT (1977) A comparison of finite-element and experimental studies on plane stress crack geometries. J Strain Anal Eng Des 12:208–216
Simo JC, Taylor RL (1986) A return mapping algorithm for plane stress elastoplasticity. Int J Numer Meth Eng 22:649–670
Jetteur P (1986) Implicit integration algorithm for elastoplasticity in plane stress analysis. Eng Comput 3:251–253
Kleiber M, Kowalczyk P (1996) Sensitivity analysis in plane stress elasto-plasticity and elasto-viscoplasticity. Comput Meth Appl Mech Eng 137:395–409
Valoroso N, Rosati L (2009) Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part 1: Theoretical formulation. Int J Solids Struct 46:74–91
Triantafyllou SP, Koumousis VK (2012) An hysteretic quadrilateral plane stress element. Arch Appl Mech 82:1675–1687
Rees DWA (2006) Basic engineering plasticity. Elsevier, Amsterdam
Yoshida S, Oguchi A, Nobuki M (1971) Influence of high hydrostatic pressure on the flow stress of copper polycrystals. Trans Jpn Inst Met 12:238–242
Spitzig WA, Sober RJ, Richmond O (1976) The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory. Metall Trans 7A:1703–1710
Spitzig WA (1979) Effect of hydrostatic pressure on plastic-flow properties of iron single crystals. Acta Metall 27:523–534
Kao AS, Kuhn HA, Spitzig WA, Richmond O (1990) Influence of superimposed hydrostatic pressure on bending fracture and formability of a low carbon steel containing globular sulfides. Trans ASME J Eng Mater Technol 112(1):26–30
Wilson CD (2002) A critical reexamination of classical metal plasticity. Trans ASME J Appl Mech 69:63–68
Liu PS (2006) Mechanical behaviors of porous metals under biaxial tensile loads. Mater Sci Eng 422A:176–183
Drucker DC, Prager W (1952) Soil mechanics and plastic analysis for limit design. Q Appl Math 10:157–165
Alexandrov S, Alexandrova N (2001) Thermal effects on the development of plastic zones in thin axisymmetric plates. J Strain Anal Eng Des 36:169–176
Alexandrov S, Jeng Y-R, Lomakin E (2011) Effect of pressure-dependency of the yield criterion on the development of plastic zones and the distribution of residual stresses in thin annular disks. Trans ASME J Appl Mech 78:031012
Alexandrov SE, Lomakin EV, Jeng Y-R (2012) Solution of the thermoelasticplastic problem for a thin disk of plastically compressible material subject to thermal loading. Dokl Phys 57:136–139
Alexandrov S, Jeng Y-R, Lyamina E (2012) Influence of pressure-dependency of the yield criterion and temperature on residual stresses and strains in a thin disk. Struct Eng Mech 44:289–303
Pirumov A, Alexandrov S, Jeng Y-R (2013) Enlargement of a circular hole in a disc of plastically compressible material. Acta Mech 224:2965–2976
Alexandrov S, Jeng Y-R, Lomakin E (2014) An exact semi-analytic solution for residual stresses and strains within a thin hollow disc of pressure-sensitive material subject to thermal loading. Meccanica 49:775–794
Alexandrov S, Lyamina E, Jeng Y-R (2012) Design of an annular disc subject to thermomechanical loading. Math Prob Eng 2012, Article ID 709178
Wang Y-C, Alexandrov S, Jeng Y-R (2013) Effects of thickness variations on the thermal elastoplastic behavior of annular discs. Struct Eng Mech 47:839–856
Alexandrov S, Lyamina E, Jeng Y-R (2013) Plastic collapse of a thin annular disk subject to thermomechanical loading. Trans ASME J Appl Mech 80:051006
Alexandrov S, Wang Y-C, Aizikovich S (2014) Effect of temperature-dependent mechanical properties on plastic collapse of thin discs. Proc IMechE Part C: J Mech Eng Sci 228:2483–2487
Alexandrov S, Wang Y-C, Jeng Y-R (2014) Elastic-plastic stresses and strains in thin discs with temperature-dependent properties subject to thermal loading. J Therm Stresses 37:488–505
Alexandrov S, Pham C (2014) Plastic collapse mechanisms in thin disks subject to thermo-mechanical loading. Asia Pacific J Comput Eng 1:7
Alexandrov S, Mustafa Y (2014) A qualitative comparison of flow rules of pressure-dependent plasticity under plane stress conditions. J Eng Math 89:177–191
Alexandrova N, Alexandrov S (2004) Elastic-plastic stress distribution in a plastically anisotropic rotating disk. Trans ASME J Appl Mech 71:427–429
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Alexandrov, S. (2015). Axisymmetric Thermo-Elastic-Plastic Problem Under Plane Stress Conditions. In: Elastic/Plastic Discs Under Plane Stress Conditions. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-14580-8_1
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DOI: https://doi.org/10.1007/978-3-319-14580-8_1
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