Thin plate bending analysis using an indirect Trefftz collocation method
Keywords:
Trefftz method, thin plates, point collocation, complex trial functions, least squaresAbstract
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.
References
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[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.
[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
2023-03-27
Issue
pp. 1-16
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Tiago, C. M., Leitão, V. M., & Vásárhelyi, A. (2023). Thin plate bending analysis using an indirect Trefftz collocation method. Computer Assisted Methods in Engineering and Science, 8(1), 1-16. https://cames3.ippt.pan.pl/index.php/cames/article/view/1191
