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Application of the Trefftz method to nonlinear potential problems

100%

Uściłowska A.

Computer Assisted Mechanics and Engineering Sciences

2008

tom Vol. 15, No. 3/4

377-390

In this paper some types of nonlinear potential problems are discussed and some of these problems are solved by the Trefftz method. The attention is paid to Fundamental Solutions Method (FSM) supported by Radial Basis Functions (RBF) approximation. Application of FSM to nonlinear boundary problem requires certain modifications and special algorithms. In this paper two methods of treating the nonlinearity are proposed, One on them is Picard iteration. Due to some problems of application of this method the Homotopj Analysis Method (HAM) is implemented for nonlinear boundary-value problems. The results of numerical experiment arc presented and discussed. The '(inclusion is that the method based on FSM for solving nonlinear boundary-value problem gives result with demanded accuracy.

The calculation of the eigenfrequencies of the torsional free vibrations of the bars using the method of fundamental solutions

63%

Uściłowska A. , Fraska A.

tom Vol. 25

429--434

This work concerns an application of the method of fundamental solutions to the calculation of the eigenfrequencies of the torsional natural vibrations of the bars. The problem of the torsional free vibrations of the bar is an initial-boundary value problem. In the solution process of this problem, the method of variables separation is used. The boundary value problem is solved by the method of fundamental solutions. The different shapes of the bar cross-section are taken into account. The numerical calculations are performed for the rods made of the materials with the different characteristics (mass, density, shear modulus, etc.). To check the accuracy of the proposed methods the results of numerical experiment are included.