Общее решение второй основной задачи для упругого кольца при нулевых главных векторах сил, приложенных к его границам

Abstract

For the first time formulated and solved the problem for the ring with the set on the border of the radial displacement, in the form of Fourier series. The technique differed from used in the classic monograph N.I. Muskhelishvili has been developed and applied to the solution of the first boundary value problem for elastic ring. The solution demonstrates the flexibility of the method of analytic functions, allowing analytically solve the boundary problems which have almost arbitrary complexity. In addition, the convenience of application of is computer algebra system Mathematica was demonstrated. It allows to build a stress distribution with help of complex analytic functions, without prior separation of the real and imaginary parts. A comparison of the stress state of the ring at the given variable radial displacement of borders based on the results of calculations in Mathematica and ANSYS 10 ED was fulfilled. It is found that the results coincide with a high accuracy both qualitatively and quantitatively. For the first time the possibility of program application of the piecewise constant approximation of the variables static loads applied to the body was demonstrated. It was shown that arbitrary mathematical functions can be used for boundary conditions.