Skip to main content
SpringerLink
Log in

The Background Concept in Structural Analyses: with Remarks on Deformation Control

  • Published:
International Applied Mechanics Aims and scope

Abstract

A review of the modern multiple field theory is given. The theory is derived from the classical two-field theory of linearized thermo-elasticity. Extensions of Maysel's formula are described. They allow formulating an optimal solution strategy using the Green function. Various applied problems are solved and commented on. The advantages of the multiple field theory are discussed

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. V. M. Maysel, Dokl. Akad. Nauk USSR, 30, 115 (1941).

    Google Scholar 

  2. F. Ziegler and H. Irschik, “Thermal stress analysis based on Maysel's formula,” in: R. B. Hetnarski (ed.), Thermal Stresses II, Elsevier, London (1987), pp. 120–188.

    Google Scholar 

  3. H. Irschik, P. Fotiu, and F. Ziegler, “Extension of Maysel's formula to the dynamic eigenstrain problem,” J. Mech. Behav. Mater., 5, 59–66 (1993).

    Google Scholar 

  4. T. Mura, Micromechanics of Defects in Solids, Kluwer Academic Publisher, Dordrecht (1991).

    Google Scholar 

  5. H. Irschik and F. Ziegler, “Uniaxial dissipative elastic waves due to high velocity impact,” in: J. D. Achenbach, et al. (eds.), Proc. IUTAM Symp. on Elastic Wave Propagation and Ultrasonic Nondestructive Evaluation, North Holland, Amsterdam (1990), pp. 333–338.

    Google Scholar 

  6. H. Irschik and F. Ziegler, “Dynamic processes in structural thermoviscoplasticity,” Appl. Mech. Rev., 48, No. 6, 301–316 (1995).

    Google Scholar 

  7. P. Fotiu and F. Ziegler, “The propagation of spherical waves in rate-sensitive elastic-plastic materials,” Int. J. Solids Struct., 33, No. 6, 811–833 (1996).

    Google Scholar 

  8. F. Ziegler, H. Irschik, and H. Holl, “Spherical elastic-plastic waves,” J. Vibr. Contr., 1, No. 3, 345–360 (1995).

    Google Scholar 

  9. F. Ziegler, “Acoustic emission from plastic sources,” J. Comp. Acoust., 9, No. 4, 1329–1346 (2001).

    Google Scholar 

  10. Y.-H. Pao and R. R. Gajewski, “The generalized ray theory and transient responses of layered elastic solids,” Phys. Acoust., 13, 183–266 (1977).

    Google Scholar 

  11. F. Ziegler and P. Borejko, “The method of generalized ray revisited,” The Chinese J. Mech., 16, 37–44, Erratum:125–126 (2000).

    Google Scholar 

  12. B. A. Boley and A. D. Barber, “Dynamic response of beams and plates to rapid heating,” J. Appl. Mech., 24, 413–420 (1957).

    Google Scholar 

  13. H. Irschik and F. Ziegler, “Thermal shock loading of elastoplastic beams,” J. Therm. Stress., 8, 53–69 (1985).

    Google Scholar 

  14. H. Irschik and F. Ziegler, “Dynamics of linear elastic structures with self-stress: A unified treatment for linear and nonlinear problems,” Z. Angew. Math. Mech., 68, 199–205 (1988).

    Google Scholar 

  15. P. Fotiu, H. Irschik, and F. Ziegler, “Dynamic plasticity: structural drift and modal projections,” in: W. Schiehlen (ed.), Proc. IUTAM Symp. on Nonlinear Dynamics in Engineering Systems, Springer-Verlag, Berlin (1990), pp. 75–82.

    Google Scholar 

  16. F. Moon, Chaotic Vibrations, Wiley & Sons, New York (1987).

    Google Scholar 

  17. P. Fotiu, H. Irschik, and F. Ziegler, “Micromechanical foundations of dynamic plasticity with application to damaging structures,” in: E. Brüller, V. Mannl, and E. Najar (eds.), Advances in Continuum Mechanics, Springer-Verlag, Berlin (1991), pp. 338–349.

    Google Scholar 

  18. Y. F. Dafalias, “Elastic-plastic coupling within a thermodynamic strain space formulation in plasticity,” Int. J. Non-Linear Mech., 12, 327–337 (1977).

    Google Scholar 

  19. P. Fotiu, “Elastodynamics of thin plates with internal dissipative processes,” Part I. Theoretical Foundations, Acta Mech., 95, 29–50 (1992).

    Google Scholar 

  20. P. Fotiu, “Part II. Computational aspects,” Acta Mech., 98, 187–212 (1993).

    Google Scholar 

  21. H. Irschik, C. Adam, R. Heuer, and F. Ziegler, “An exact solution for static shape control using piezoelectric actuation,” in: Y. A. Bahei-El-Din and G. J. Dvorak (eds.), Proc. IUTAM Symp. on Transformation Problems in Composite and Active Material, Kluwer Academic Publ., Dordrecht (1998), pp. 247–258.

    Google Scholar 

  22. H. Irschik and F. Ziegler, “Eigenstrain without stress and static shape control of structures,” AIAA J., 39, 1985–1990 (2001).

    Google Scholar 

  23. H. Irschik, M. Krommer, and U. Pichler, “Shaping distributed piezoelectric self-sensing layers for static shape control of smart structures,” J. Struct. Contr., 7, 173–189(2000).

    Google Scholar 

  24. Y. I. Nyashin, V. Y. Kiryukhin, and F. Ziegler, “Control of thermal stress and strain,” J. Therm. Stress., 23, 309–326 (2000).

    Google Scholar 

  25. H. Irschik, R. Heuer, and F. Ziegler, “Statics and dynamics of simply supported polygonal Reissner-Mindlin plates by analogy,” Arch. Appl. Mech., 70, 231–244 (2000).

    Google Scholar 

  26. H. Irschik and F. Ziegler, “Dynamics of composite structures based on lower order eigenstrain analysis,” in: G. P. Cherepanov (ed.), Fracture: A Topical Encyclopedia of Current Knowledge, Krieger Publ., Malabar, Florida (1998), pp. 840–852.

    Google Scholar 

  27. E. Betti, “Teori della elasticita,” II Nuovo Ciemento, Ser. 2, 7–10 (1872).

  28. J. D. Achenbach, A. K. Gautesen, and H. McMaken, Ray Methods for Waves in Elastic Solids, Pitman, Boston (1982).

    Google Scholar 

  29. A. T. DeHoop, Handbook for Radiation and Scattering of Waves, Academic Press, London (1995).

    Google Scholar 

  30. J. D. Achenbach, “Calculation of wave fields using elastodynamic reciprocity,” Int. J. Solids Struct., 37, 7043–7053 (2000).

    Google Scholar 

  31. W. Nowacki, Dynamic Problems of Thermoelasticity, Noordhoff Int., Leyden (1975).

    Google Scholar 

  32. H. Irschik and F. Ziegler, “Maysel's formula generalized for piezoelectric vibrations: Application to thin shells of revolution,” AIAA J., 34, 2402–2405 (1996).

    Google Scholar 

  33. K. Washizu, Variational Methods in Elasticity and Plasticity, 2nd ed., Pergamon Press, Oxford (1975).

    Google Scholar 

  34. J. C. Nagtegaal, “Some recent developments in combined geometric and nonlinear finite element analysis,” in: E. Hinton, D. R. J. Owen, and C. Taylor (eds.), Recent Advances in Nonlinear Computational Mechanics, Pineridge Press, Swansea (1982), pp. 87–118.

    Google Scholar 

  35. S. Mukherjee and A. Chandra, “Boundary element formulation for large strain-large deformation problems of plasticity and viscoplasticity,” in: P. K. Banerjee and S. Mukherjee (eds.), Developments in Boundary Element Methods-3, Elsevier, London (1984), pp. 27–58.

    Google Scholar 

  36. P. Fotiu, H. Irschik, and F. Ziegler, “Forced vibrations of an elastic-plastic and deteriorating beam,” Acta Mech., 69, 193–203 (1987).

    Google Scholar 

  37. C. Adam and F. Ziegler, “Moderately large forced oblique vibrations of elastic-viscoplastic deteriorating slightly curved beams,” Arch. Appl. Mech., 67, 375–392 (1997).

    Google Scholar 

  38. C. Adam and F. Ziegler, “Forced flexural vibrations of elastic-plastic composite beams with thick layers,” Composites. Part B, 28B, 201–213 (1997).

    Google Scholar 

  39. R. Heuer, “Static and dynamic analysis of transversely isotropic, moderately thick sandwich beams by analogy,” Acta Mech., 91, 1–9 (1992).

    Google Scholar 

  40. H. Rubin and U. Vogel, Baustatik ebener Stabwerke. Stahlbauhandbuch, Vol. 1, Teil A, 3rd. ed., Stahlbau-Verlags GmbH, Koln (1993).

  41. C. Adam, H. Irschik, and F. Ziegler, “Composite beam dynamics under conditions of inelastic interface slip,” in: H. Mang and F. Rammerstorfer (eds.), Proc. IUTAM/IACM Symp. on Discretization Methods in Structural Mechanics II, Kluwer Academic Publ., Dordrecht (1999), pp. 291–298.

    Google Scholar 

  42. C. Adam and F. Ziegler, “Dynamic response of elastic-viscoplastic sandwich beams with asymmetrically arranged thick layers,” in: Y. A. Bahei-El-Din and G. J. Dvorak (eds.), Proc. IUTAM Symp. on Transformation Problems in Composite and Active Material, Kluwer Academic Publ., Dordrecht (1998), pp. 221–232.

    Google Scholar 

  43. C. Adam, R. Heuer, and A. Jeschko, “Flexural vibrations of elastic composite beams with interlayer slip,” Acta Mech., 125, 17–30 (1997).

    Google Scholar 

  44. C. Adam, R. Heuer, A. Raue, and F. Ziegler, “Thermally induced vibrations of composite beams with interlayer slip,” J. Therm. Stress., 23, 747–772 (2000).

    Google Scholar 

  45. C. Adam and F. Ziegler, “Vibrations of layered beams under conditions of damaging and slipping interfaces,” Int. J. Fract., 98, 393–406 (1999).

    Google Scholar 

  46. E. F. Crawley, “Intelligent structures for aerospace: a technology overview and assessment,” AIAA J., 32, 1689–1699 (1994).

    Google Scholar 

  47. S. F. Rao and M. Sunar, “Piezoelectricity and its use in disturbance sensing and control of flexible structures,” Appl. Mech. Rev., 47, 113–123 (1994).

    Google Scholar 

  48. D. A. Saravanos and P. R. Heyliger, “Mechanics of computational models for laminated piezoelectric beams, plates, and shells,” AMR, 52, 305–320 (1999).

    Google Scholar 

  49. H. S. Tzou, Piezoelectric Shells, Kluwer, Dordrecht (1993).

  50. H. Irschik and U. Pichler, “Dynamic shape control of solids and structures by thermal expansion strains,” J. Therm. Stress., 24, 565–576 (2001).

    Google Scholar 

  51. H. Irschik, A. K. Belyaev, and K. Schlacher, “Eigenstrain analysis of smart beam-type structures,” in: M. Acar, J. Makra, and E. Penney (eds.), Mechatronics: The Basis for New Industrial Developments, Comp. Mechanics Publ., Southampton (1994), pp. 487–492.

    Google Scholar 

  52. H. Irschik, A. K. Belyaev, and K. Schlacher, “Anwendung der Mohrschen Analogie auf intelligente Konstruktionen,” Z. Angew. Math. Mech., 75, T81–T82 (1995).

    Google Scholar 

  53. H. Irschik, M. Krommer, A. K. Belyaev, and K. Schlacher, “Shaping of piezoelectric sensors/actuators for vibrations of slender beams: coupled theory and inappropriate shape functions,” Int. J. Intellig. Mater. Syst. Struct., 9, 46–54 (1999).

    Google Scholar 

  54. M. Krommer and H. Irschik, “On the influence of the electric field on free transverse vibrations of smart beams,” J. Smart Mater. Struct., 8, 401–410 (1999).

    Google Scholar 

  55. H. Irschik, M. Krommer, and U. Pichler, “Annihilation of beam vibrations by shaped piezoelectric actuators: coupled theory,” in: Proc. Joint Meeting: 137th regular meeting of the Acoustical Soc. America, 2nd convention EAA: Forum Acusticum—25th German Acoustics DAGA Conference, Acoustical Society of America, Berlin (1999), pp. 14–19.

  56. H. Irschik, M. Krommer, and U. Pichler, “Shaping of distributed piezoelectric sensors for flexural vibrations of smart beams,” in: V. V. Varadan (ed.), Proc. SPIE's 6th Annual Int. Symp. on Smart Structures and Materials: Mathematics and Control in Smart Structures, SPIE, 3667 (1999), pp. 418–426.

  57. H. Irschik, K. Schlacher, and W. Haas, “Output annihilation and optimal H2 control of plate vibrations by piezoelectric actuation,” in: D. Van Campen (ed.), Proc. IUTAM Symp. on Interactions Between Dynamics and Control in Advanced Mechanical Systems, Kluwer, Dordrecht, (1997), pp. 159–166.

    Google Scholar 

  58. R. Heuer, H. Irschik, and F. Ziegler, “Thermo-piezoelectric vibrations of three-layer elastic plates,” in: R. B. Hetnarski and N. Noda (eds.), Proc. 2nd Int. Symp. on Thermal Stresses and Related Topics, RIT, Rochester, N.Y. (1997), pp. 451–454.

    Google Scholar 

  59. H. Irschik, M. Krommer, and F. Ziegler, “Dynamic Green's function method applied to vibrations of piezoelectric shells,” in: F. L. Chernousko and A. L. Fradkov (eds.), Proc. 1st Int. Conf. on Control of Oscillations and Chaos (COC'97), St. Petersburg, IEEE, Piscataway, NJ 08855-1331, Vol. 3 of 3 (1997), pp. 381–388.

  60. H. Irschik, R. Heuer, and F. Ziegler, “Static shape control of redundant beams and trusses by thermal strains without stress,” in: R. B. Hetnarski and N. Noda (eds.), Proc. 2nd Int. Symp. on Thermal Stresses and Related Topics, R.I.T., Rochester, N.Y. (1997), pp. 469–472.

    Google Scholar 

  61. A. L. Kalamkarov and A. D. Drozdov, “On the theory of smart composite structures,” in: Y. A. Bahei-El-Din and G. J. Dvorak (eds.), Proc. IUTAM Symp. on Transformation Problems in Composite and Active Materials, Kluwer, Dordrecht (1998), pp. 259–270.

    Google Scholar 

  62. J. R. Vinson, The Behavior of Shells Composed of Isotropic and Composite Material, Kluwer, Dordrecht (1992).

  63. H. Irschik, A. K. Belyaev, P. Raschl, “Eigenstrain-based algorithm for viscoelastic uniaxial wave propagation due to impact,” in: B. Ravani (ed.), Proc. Design Engrg. Techn. Conf. Sacramento, ASME, New York, ASME Paper No. DETC97/VIB-3927 (1997), pp. 1–7.

    Google Scholar 

  64. T. Jimma and T. Masuda, “An analysis of elastic-plastic waves by the continuum theory of dislocations,” in: K. Kawata and J. Shiori (eds.), Proc. IUTAM Symp. on High Velocity Deformation of Solids, Springer-Verlag, Berlin (1978), pp. 289–294.

    Google Scholar 

  65. P. Borejko, “Reflection and transmission coefficients for three-dimensional plane waves,” Wave Motion, 24, 371–393 (1996).

    Google Scholar 

  66. P. Borejko, C. F. Chen, and Y.-H. Pao, “Application of the method of generalized rays to acoustic waves in a liquid wedge over elastic bottom,” J. Comp. Acoust., 9, 41–68 (2001).

    Google Scholar 

  67. F. Ziegler, “Acoustic emission from strain-determined sources,” Int. J. Solids Struct., 39, 5465–5479 (2002).

    Google Scholar 

  68. F. Ziegler, Mechanics of Solids and Fluids, 2nd ed., Springer-Publ., New York (1998).

    Google Scholar 

  69. D. H. Alien, “Thermomechanical coupling in inelastic solids,” Appl. Mech. Rev., 44 (8), 361–371 (1991).

    Google Scholar 

  70. N. Jones, “Recent studies on the dynamic plastic behavior of structures,” Appl. Mech. Rev., 42 (4), 95–115 (1989).

    Google Scholar 

  71. N. Ohno, “Recent topics in constitutive modeling of cyclic plasticity and viscoplasticity,” Appl. Mech. Rev., 43 (11), 283–295 (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technical University of Vienna, Austria

    Franz Ziegler

Authors
  1. Franz Ziegler
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ziegler, F. The Background Concept in Structural Analyses: with Remarks on Deformation Control. International Applied Mechanics 39, 1–19 (2003). https://doi.org/10.1023/A:1023681614964

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1023681614964

Search

Navigation