Calculation of nonlinear deformation of a flexible rod

Author

Levin, Vladimir E.

Author_Institution

Novosibirsk State Tech. Univ., Russia

Volume

3

fYear

2000

fDate

2000

Firstpage

43

Abstract

The class of nonlinear tasks for flexible rods, even in the case of flat deformation, is rather complicated. Closed form solutions are possible only for some special cases. An algorithm of numerical integration of the nonlinear equations of equilibrium of a flat rod by a Runge-Kutta method is considered. The boundary conditions on the extremity of a rod are satisfied approximately. The projection equations are obtained from the common vectorial equations of equilibrium. As solving functions the projections of a transition vector and internal forces vector on global axes, angle of a normal´s turn to the rod axis, and internal flexing, are chosen

Keywords

Newton method; Runge-Kutta methods; bending; boundary-value problems; integration; nonlinear differential equations; vectors; Newton method; Runge-Kutta method; bending moment; boundary conditions; circular rod; closed form solutions; flat rod; flexible rod; internal forces vector; nonlinear deformation; nonlinear equations of equilibrium; numerical integration algorithm; projection equations; transition vector; vectorial equations; Boundary conditions; Capacitive sensors; Extremities; Nonlinear equations; Programmable logic arrays;

fLanguage

English

Publisher

ieee

Conference_Titel

Science and Technology, 2000. KORUS 2000. Proceedings. The 4th Korea-Russia International Symposium on

Conference_Location

Ulsan

Print_ISBN

0-7803-6486-4

Type

conf

DOI

10.1109/KORUS.2000.866058

Filename

866058