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A Finite Element Formulation for the Analysis of Local Effects

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Abstract

The paper reviews the progress achieved in the analysis of geometry and load dependent local effects, based on an alternative FE formulation known as the hybrid-Trefftz (HT) FE model. A brief description with examples presents the developments which have lead to a simple p-adaptive analysis of structures with stress-raisers (e.g., holes, cracks and corners) in presence of multiple load cases, including local concentrated loads.

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References

  1. E. Trefftz. Ein Gegenstück zum Ritzschen Verfahren. Proc. 2nd Intl. Cong. Appl. Mech., Zürich, pp. 131–137 (1926).

    Google Scholar 

  2. J. Jirousek and N. Leon. A powerful finite element for plate bending. Comp. Meths. Appl. Mech. Engrg. 12, 1, pp. 77–96 (1977).

    MathSciNet  MATH  Google Scholar 

  3. J. Jirousek. Basis for development of large finite elements locally satisfying all field equations. Comp. Meth. Appl. Mech. Engrg. 14, 1, pp. 65–92 (1978).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. I. Babuska, J.T. Oden and J.K. Lee. Mixed hybrid finite element approximations of second-order elliptic boundary value problems, Part 2–Weak-hybrid methods. Comp. Meth. Appl. Mech. Engrg. 14, 1, pp. 1–22 (1978).

    MathSciNet  MATH  Google Scholar 

  5. A.P. Zielinski and O.C. Zienkiewicz. Generalized finite element analysis with T-complete boundary solution functions. Int. J. Num. Meth. Engrg. 21, pp. 509–528 (1985).

    Google Scholar 

  6. J. Jirousek and P. Teodorescu. Large finite element method for the solution of problems in the theory of elasticity. Comp. Struc. 15, pp. 575–587 (1982).

    Google Scholar 

  7. J. Jirousek and Lan Guex. Hybrid-Trefftz finite element model and its application to plate bending. Int. J. Num. Meth. Engrg. 23, pp. 651–693 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Jirousek and A. Venkatesh. Adaptivity in hybrid-Trefftz finite element formulation. Int. J. Num. Meth. Engrg. 29, pp. 391–405 (1990).

    Article  Google Scholar 

  9. J. Jirousek and A. Venkatesh. A simple stress error estimator for hybrid-Trefftz Aversion elements. Int. J. Num. Meth. Engrg. 28, pp. 211–236 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Jirousek. Hybrid-Trefftz plate bending elements with p-method capabilities. Int. J. Num. Meth. Engrg. 24, pp. 1367–1393 (1987).

    Article  MATH  Google Scholar 

  11. J. Jirousek and A. Venkatesh. Hybrid-Trefftz plane elasticity elements with p-method capabilities. Int. J. Num. Meth. Engrg. To appear.

    Google Scholar 

  12. A.K. Rao, I.S. Raju and A.V.K. Murthy. A powerful hybrid method in finite element analysis. Int. J. Num. Meth. Engrg. 3, 3, pp. 389–403 (1971).

    Article  MATH  Google Scholar 

  13. K.Y. Lin and P. Tong. Singular finite elements for the fracture analysis of v-notched plate. Int. J. Num. Meth. Engrg. 15, pp. 1343–1354 (1980).

    Article  MATH  Google Scholar 

  14. R. Piltner. Spezielle finite Elemente mit Löchern, Ecken and Rissen unter Verwendung von analytischen Teillösungen. Fortschritt-Berichte der VDI Zeitschriften 1, 96, VDI-Verlag GmbH, Düsseldorf (1982).

    Google Scholar 

  15. T. D. Gerhardt. A hybrid/finite element approach for stress analysis of notched anisotropic materials. J. Appl. Meth. Trans. ASME 51, pp. 804–810 (1984).

    Article  ADS  MATH  Google Scholar 

  16. A. Venkatesh and J. Jirousek. Accurate FE analysis of thin plates under concentrated loading. IREM Internal Report 89/6, Dept. of Civil Engineering, Swiss Federal Institute of Technology, Lausanne, June 1989.

    Google Scholar 

  17. J. Jirousek. Implementation of local effects into conventional and non-conventional finite element formulations. Local Effects in the Analysis of Structures. Ed. P. Ladevèze. Elsevier, pp. 279–298 (1985).

    Google Scholar 

  18. B.A.Szabo. Estimation and control of error based on p-convergence. Accuracy Estimates and Adaptive Refinements in Finite Element Computations. Ed. I. Babuska, O.C. Zienkiewicz, J. Gado and E.R. de A. Oliveira. Wiley, pp. 61–78 (1986).

    Google Scholar 

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© 1992 Springer-Verlag Berlin Heidelberg

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Venkatesh, A., Jirousek, J. (1992). A Finite Element Formulation for the Analysis of Local Effects. In: Křupka, V., Drdácký, M. (eds) Contact Loading and Local Effects in Thin-walled Plated and Shell Structures. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02822-3_27

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  • DOI: https://doi.org/10.1007/978-3-662-02822-3_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-02824-7

  • Online ISBN: 978-3-662-02822-3

  • eBook Packages: Springer Book Archive

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