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The governing equation for viscoplastic simultaneous torsion and bending of a prismatic bar is derived. Then a certain particular closed-form solution of this equation is found; it corresponds to an elliptic cross-section with the ratio of semi-axes depending on the bending-to-torsion ratio. This solution proves to be optimal if the optimization constraint is imposed on initiation (nucleation) and growth of material damage and if the material properties conform to the Huber-Mises-Hencky failure hypothesis.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
751--770
Opis fizyczny
Bibliogr. 48 poz.
Twórcy
autor
- Institute of Mechanics and Machine Design, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland
autor
- Institute of Mechanics and Machine Design, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland
Bibliografia
- 1. J. S. Arora, T. H. Lee and J. B. Cardoso, Structural shape sensitivity analysis: relation between material derivative and control volume approaches, A1AA Journal, 30, 1638 - 1648, 1992.
- 2. J. S. Arora, T. H. Lee and V. Kumar, Design sensitivity analysis of non-linear structures III: shape variation of viscoplastic structures, publ. AIAA, Washington, 447 485, 1993.
- 3. B. Bochenek, Z. Kordas and M. Życzkowski, Optimal plastic design of a cross section under torsion and small bending, J. Struct. Mech., 11, 3, 383 -400, 1983.
- 4. E. Cegielski, Optimization of rigid-viscoplastic bars and beams under dynamic loadings, in Proc. IV Bulg. Congr. Mech. Varna, vol. 1, 484 489, 1981.
- 5. E. Cegielski, Problems of optimization of a cantilever viscoplastic beam under quasistatic load (in Polish], Mech. Teor. Stos., 23, 3/4, 381 396, 1985.
- 6. E. Cegielski, Parametric optimization of viscoplastic bars under dynamic twisting loadings, Mech. Teor. Stos., 28, 1/2, 35-44, 1990.
- 7. E. CEGIELSKI, Optimal design of rigid-viscoplastic beams subject to dynamical bending and axial forces, Z. Angew. Math. Mechanik, 72, 6, 540-542, 1992.
- 8. E. Cegielski and M. Życzkowski, Parametric optimization of viscoplastic bars under dynamic axial loading, Rozprawy Inż., 29, 1, 27 37, 1981.
- 9. E. Cegielski and M. Życzkowski, Optimization of some viscoplastic structires under variable loads, in Proc. Euromech Coll. 174 on Inelastic Structures, Palerno 1983, COGRAS, 105 116, Palermo 1984,
- 10. E. Cegielski and M. Życzkowski, Optimal design of viscoplastic, structures under dynamic loadings, in Proc. GAMM Seminar Discretization Meth. and Struct. Optimiz., Siegen 1988, Springer 1989. 102 109.
- 11. A. Gajewski, Optymalne kształtowanie wytrzymałościowe w przypadku materiału o nieliniowości fizycznej, Zeszyty Nauk. Polit. Krak. 5, Kraków 1975 (Polish ful text); Effect of physical nonlinearities on optimal design of structures, in Proc. IUTAN Symp. on Physical Nonlinearities, Senlis 1980, publ. Springer 1981, 81 84 (English summary).
- 12. D. R. Hayhurst, Creep rupture under multiaxial state of stress, J. Mech. Phys Solids, 20, 6, 381 390, 1972.
- 13. R. Hill, The mathematical theory of plasticity, Clarendon Press, Oxford 1950.
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- 15. S. Y. Jao and J. S. Arora, Design optimization of non-linear structures with rate- dependent and rate-independent constitutive models, Int. J. Numer. Meth. Eng., 36 2805 2823, 1993.
- 16. L. M. Kachanov, Tune of the rupture process under creep conditions [in Russian], Izv. AN SSSR, Otd. Tekh. Nauk. 8, 26-31, 1958.
- 17. D. Krajcinovic, Damage mechanics, Elsevier, Amsterdam, 1996.
- 18. M. Kulkarni and A. K. Noor, Sensitivity analysts of the non-linear dynamic viscoplastic response of 2D - structures with respect to material parameters, Int. J. Numer Meth. Eng., 38, 2, 183-198, 1995.
- 19. J. H. Lau and G. K. Listvinsky, Bending and twisting of internally pressurized thin- walled cylinder with creep, J. Appl. Mech., 48, 2, 439-441, 1981.
- 20. T. H. Lee, J. S. Arora and V. Kumar, Shape design sensitivity analysis of viscoplastic structures, Comp. Meth. Appl. Mech. Eng., 108, 237-259, 1993.
- 21. J. Lemaitre, A course on damage mechanics, Springer, Berlin 1992.
- 22. J. Lemaitre [Ed.], Handbook of materials behavior models, vol. 1/3, Academic Preis, San Diego 2001.
- 23. K. J. Leu and S. Mukherjee, Sensitivity analysis and shape optimization in nonlinear solid mechanics, Eng. Anal. Bound. Elements, 12, 4, 251 260,1993.
- 24. K. J. Leu and S. Mukherjee, Implicit objective integration for sensitivity anal/sis in nonlinear solid mechanics, Int. J. Numer. Meth. Eng., 37, 3843-3868, 1994.
- 25. S. A. Meguid, J. D. Campbell and L. E. Malvern, On the elastic-viscoplastic proportional combined twist and stretch of a circular bar of rate-sensitive material, J. Mech. Phys. Solids, 27, 4, 331 343, 1979.
- 26. P. M. Morse and II. Feshbach, Methods of theoretical physics, Me Graw-Hill, Nev York - Toronto - London, 1953.
- 27. P. Oberweis and M. ŻYCZKOWSKI, On Pala’s method for plastic bending with torsion. J. Appl. Mech., 64, 2, 435-437, 1997.
- 28. P. Perzyna, The constitutive equations for rate sensitive plastic materials, Quart. Appl. Math., 20, 321-332, 1963.
- 29. P. Perzyna, The constitutive equations for work-hardening and rate sensitive plastic materials, Bull. Acad. Pol. Sci., Ser.Sci. Techn., 12, 199-206, 1964.
- 30. P. Perzyna, Fundamental problems in viscoplasticity, Adv. Appl. Mech., 9, 243-377, 1966.
- 31. P. Perzyna, Theory of viscoplasticity, (in Polish), IPPT PAN-PWN, Warszawa 1966.
- 32. P. Perzyna, Internal state variable description of dynamic fracture of ductile solids, Int. J. Sol. Structures, 22, 797- 818, 1986.
- 33. P. PERZYNA, Constitutive modelling for brittle dynamic fracture in dissipative solids. Arch. Mechanics, 38, 725 738, 1986.
- 34. P. Perzyna, Thermo-elasto-viscoplasticity and damage, in (21], Sec. 9.5, 821 -834, 2001.
- 35. P. Perzyna and A. Drabik, Description of micro-damage process by porosity parameter for nonlinear viscoplasticity, Arch. Mechanics, 41, 895 908, 1989.
- 36. S. Piechnik, Steady-state creep of solid bar under combined load, Kungl. Tekniska Hogskolans Handlingar, Mech. Engng., 7, Stockholm 1962.
- 37. Yu. N. Rabotnov, Creep of structural elements, Nauka, Moskva 1966 (Russian original); North Holland, Amsterdam 1969 (English translation).
- 38. M. Rysz and M. Życzkowski, Optimal design of a thin-walled cross-section subject to bending with torsion against creep rupture, Int. J. Mech. Sci., 30, 2, 127- 136, 1988.
- 39. V. P. Sdobyrev, A long-time strength criterion for heat-resisting alloys under multiaxial states of stress [in Russian], Izv. AN SSSR, Otd. Tekhn. Nauk., 6, 93 99, 1959.
- 40. J. SKRZYPEK and A. Ganczarski, Modeling of material damage and failure of structures, Springer, Berlin 1999.
- 41. W. Świsterski, A. Wróblewski and M. Życzkowski, Geometrically nonlinear eccentrically compressed columns of uniform creep strength vs. optimal columns, Int J. Non linear Mech., 18, 4, 287 -296, 1983.
- 42. O. Zhang, S. Mukherje and A. Chandra, Design sensitivity coefficients for elasto-viscoplastic problems by boundary element methods, Int. J. Numer. Meth. Eng., 34, 3, 947-966. 1992.
- 43. M. Życzkowski, Combined loadings in the theory of plasticity, PWN-Nijhoff, Warszawa Alphen aan den Rijn 1981.
- 44. M. Życzkowski, Optimal structural design under creep conditions, Appl. Mech. Rev., 49. 9, 433 -446, 1996.
- 45. M. Życzkowski, Optimal plastic design for combined torsion with bending, Proc. Second World Congr. Str. Optimiz., Zakopane, W. Gutkowski and Z. Mróz |Eds.|, vol.2, 809 814, 1997.
- 46. M. Życzkowski, Optimal plastic design of statically indeterminate beams under bending with torsion, Festschrift Prof. Peter Gummert, TU Berlin, 251-262, 1998.
- 47. M. Życzkowski, Creep damage evolution equations expressed in terms of dissipated power, lilt. J. Mech. Sci., 42, 755-769, 2000.
- 48. M. Życzkowski and E. Cegielski, Parametric optimization of rigid-viscoplastic beams under dynamic loads (in Polish), Arch. Inż. Lądowej, 32, 1, 95 104, 1986.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0002-0090
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