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
