Thin plate bending analysis using an indirect Trefftz collocation method

  • Carlos M. Tiago Technical University of Budapest
  • Vitor M.A. Leitão Instituto Superior Tecnico
  • Anna Vásárhelyi Technical University of Budapest

Abstract

In this work, the application of an indirect Trefftz collocation method to the analysis of bending of thin plates (Kirchhoff's theory) is described. The deflection field approximation is obtained with the use of a set of functions satisfying a priori the homogeneous part of the differential equation of the problem. Each of the approximating functions is derived from a known thick plate solution. The boundary conditions are imposed by means of continuous (integral) and discrete (collocation) least squares methods. Numerical examples are presented and the accuracy of the proposed technique is assessed.

Keywords

Trefftz method, thin plates, point collocation, complex trial functions, least squares,

References

[1] E.D. Eason. A review of least-squares methods for solving partial differential equations. International Journal for Numerical Methods in Engineering, 10: 1021-1046, 1976.
[2] C.M.T.T. Fernandes. Utilização e Desenvolvimento de uma Formulação Indirecta de Trejjtz na Análise de Lajes Finas, (in Portuguese). MSc Thesis, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1999.
[3] C. Fernandes, V. Leitão. On a least squares Trefftz collocation method for plate bending. In: V. Kompiš, M. Žmindák, B. Hučko, eds., Numerical Methods in Continuum Mechanics, High Tatms, Slovak Republic, October 6- 9, 1998, pp. 7- 12. University of Žilina, 1998.
[4] J.R. Hutchinson. Analysis of plates and shells by boundary collocation. In: D.F. Beskos, ed., Boundary Element Analysis of Plates and Shells, pp. 341- 368. Springer-Verlag, 1991.
[5] J. Jiroušek, N. Leon. A powerful finite element for plate bending. Comp. Meth. Appl. Mech. Eng., 12: 77-96, 1977.
Published
Mar 27, 2023
How to Cite
TIAGO, Carlos M.; LEITÃO, Vitor M.A.; VÁSÁRHELYI, Anna. Thin plate bending analysis using an indirect Trefftz collocation method. Computer Assisted Methods in Engineering and Science, [S.l.], v. 8, n. 1, p. 1-16, mar. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1191>. Date accessed: 23 dec. 2024.
Citation Formats
Issue
Vol 8 No 1 (2001)
Section
Articles
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