Trefftz method for large deflection of plates with application of evolutionary algorithms
Abstract
The large deflection of thin plates by means of Berger equation is considered. An iterative solution of Berger equation by the method of fundamental solutions is proposed. In each iterative step the Berger equation can be considered as an inhomogeneous partial differential equation of the fourth order. The inhomogeneous term is interpolated by radial basis functions using thin plate splines. For the optimal choice of parameters of the fundamental solutions method an evolutionary algorithm is used. Numerical results for square plate with simply supported edges are presented to compare the obtained results with previous solutions.
References
[1] M.R. Akella, G.R. Katamraju. Trefftz indirect method applied to nonlinear potential problems. Engineering Analysis with Boundary Elements, 24: 459- 465, 2000 .
[2] J. Arabas. Lectures on Evolutionary Algorithms (in Polish: Wykłady z algorytmów ewolucyjnych). WN-T, Warszawa, 200l.
[3] K. Balakrishnan, A. Ramachandran. A particular solution Trefftz method for non-linear Poisson problems in heat and mass transfer. Journal of Computational Physics, 150: 239- 267, 1999.
[4] H.M. Berger. A new approach to the analysis of large deflections of plates. Journal of Applied Mechanics, 22: 465- 472, 1955.
[5] C.S. Chen. The method of fundamental solutions for non-linear thermal explosions. Communications in Numerical Methods in Engineering, 11: 675- 681 , 1995
[2] J. Arabas. Lectures on Evolutionary Algorithms (in Polish: Wykłady z algorytmów ewolucyjnych). WN-T, Warszawa, 200l.
[3] K. Balakrishnan, A. Ramachandran. A particular solution Trefftz method for non-linear Poisson problems in heat and mass transfer. Journal of Computational Physics, 150: 239- 267, 1999.
[4] H.M. Berger. A new approach to the analysis of large deflections of plates. Journal of Applied Mechanics, 22: 465- 472, 1955.
[5] C.S. Chen. The method of fundamental solutions for non-linear thermal explosions. Communications in Numerical Methods in Engineering, 11: 675- 681 , 1995
Published
2022-11-17
Issue
pp. 407-416
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
Klekiel, T., & Kołodziej, J. A. (2022). Trefftz method for large deflection of plates with application of evolutionary algorithms. Computer Assisted Methods in Engineering and Science, 13(3), 407-416. https://cames3.ippt.pan.pl/index.php/cames/article/view/942
