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Boundary/Field Variational Principles for the Elastic Plastic Rate Problem

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Boundary Integral Methods
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Summary

An elastic-plastic continuous solid body under quasi-statically variable external actions is herein addressed in the hypoteses of rate-independent material model with dual internal variables and of infinitesimal displacements and strains. The related analysis problem for assigned rate actions is first formulated through a boundary/field integral equation approach, then is shown to be characterized by two variational principles, one of which is a stationarity theorem, the other a min-max one.

This paper has been completed with the financial support of the Ministero dell’Università e della Ricerca Scientifica e Tecnologica, Italy.

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References

  1. Hodge, P.G. Jr.: Numerical applications of minimum principles in plasticity. In Heyman, J. and Leckie, F.A. (eds.) Engineering Plasticity, 237-256. Cambridge: University Printing House 1968.

    Google Scholar 

  2. Lemaitre, J.; Chaboche, J.L.: Mécanique des materiaux solides. Paris: Dunod 1985.

    Google Scholar 

  3. Drucker, D.C.: A definition of stable inelastic material. J. Appl. Mech. 26, Trans. ASME 81 (1959) 101–106.

    MathSciNet  Google Scholar 

  4. Banarjee, P.K.; Butterfield, R.: Boundary element methods in engineering science. London: Mc Graws-Hill 1981.

    Google Scholar 

  5. Brebbia, C.A.; Telles, J.C.F.; Wrobel, L.C.: Boundary element tecniques. Berlin and Heidelberger: Springer-Verlag 1984.

    Google Scholar 

  6. Cruse, T.A.: Mathematical foundations of the boundary-integral equation method in solids mechanics. Tech. Rep. AFOSR-TR-77, Pratt & Whitney Aircraft Group, East Hartfort, July 1977.

    Google Scholar 

  7. Maier, G.; Polizzotto, C.: A Galerkin approach to boundary element elastoplastic analysis. Comput. Meth. Appl. Mech. Engng. 60 (1987) 175–194.

    Article  ADS  MATH  Google Scholar 

  8. Polizzotto, C.: An energy approach to the boundary element method. Part I: elastic solids. Comput. Meth. Appl. Mech. Engng. 69 (1988) 167–184.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Rudolphi, T.J.; Krishnasamy, G.; Schmerr, L.W.; Rizzo, F.J.: On the use of the strengly singular integral equations for crack problems. In: Brebbia, C.A. (ed.), Boundary Elements X, Vol. 3, 249–263. Berlin Heildeberg: Springer-Verlag 1988. Southampton: Computational Mechanics Pubs. 1988.

    Google Scholar 

  10. Krishnasamy, G.; Schmerr, L.W.; Rudolphi, T.J.; Rizzo, F.J.: Hypersingular boundary integral equations: some applications in acoustic and elastic wave scattering. J. Appl. Mech. (to appear).

    Google Scholar 

  11. Zhang, J.-D.; Atluri, S.N.: A boundary/interior element method for quasi-static and transient response analyses of shallow shalls. Computers & Structures 24 (1986) 213–223.

    Article  MATH  Google Scholar 

  12. Polizzotto, C.: A symmetric-definite BEM formulation for the elastoplastic rate problem. In: Brebbia, C.A., Wendland, W.L. and Kunh, G. (eds.), Boundary Elements IX, Vol. 2, 315–334. Southamptom and Boston: Computational Mechanics Publications 1987.

    Google Scholar 

  13. Capurso, M.: Minimum principles for the incremental solution to elastic-plastic problems, Part I and II (in Italian). Rendiconti Accademia Nazionale dei Lincei, Serie VIII, Vol. XLVI, fascicoli 4-5, April–May 1969, 417–560.

    Google Scholar 

  14. Capurso, M.; Maier, G.: Incremental elastoplastic analysis and quadratic optimization. Meccanica 5 (1970), 107–116.

    Article  MATH  Google Scholar 

  15. Polizzotto, C.: A consistent formulation of the BEM within elastoplasticity. In: Cruse, T.A. (ed.), Advanced Boundary Element Methods, 315–324. Berlin Heildeberg: Springer-Verlag 1988.

    Chapter  Google Scholar 

  16. Polizzotto, C.: A boundary min-max principle as a tool for boundary element formulations Engng. Anal. (to appear).

    Google Scholar 

  17. Polizzotto, C.; Zito, M.: A variational formulation of the BEM for the elastic-plastic analysis. In: Kunh, G. and Mang, H. (eds.), Discretization methods in structural mechanics, 201–210. Berlin and Heidelberg: Springer-Verlag 1990.

    Chapter  Google Scholar 

  18. Panzeca, T.; Polizzotto, C.; Zito, M.: A boundary/field element approach to the elastic-plastic structural analysis problem. Proc. of the X Congresso Nazionale AIMETA, 165-168, 1990.

    Google Scholar 

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© 1991 Springer-Verlag Berlin, Heidelberg

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Panzeca, T., Polizzotto, C., Zito, M. (1991). Boundary/Field Variational Principles for the Elastic Plastic Rate Problem. In: Morino, L., Piva, R. (eds) Boundary Integral Methods. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85463-7_41

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  • DOI: https://doi.org/10.1007/978-3-642-85463-7_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-85465-1

  • Online ISBN: 978-3-642-85463-7

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