Определение упругих полей в трансверсально-изотропных телах вращения, вызванных действием объемных сил

Abstract

The paper presents a method for determining the stress-strain state of transversely isotropic bodies of revolution under the action of non-axisymmetric stationary body forces. This problem solution involves the use of boundary state method definitions. The basis of the space of internal states is formed using the fundamental polynomials. The polynomial is placed in any position of a displacement vector of the plane auxiliary state; the spatial state is determined by transition formulas. A set of such states forms a finite-dimensional basis, in which after orthogonalization, the desired state is expanded into Fourier series with the same coefficients. The series coefficients are scalar products of the vectors of given and basic body forces. Finally, the determination of the elastic state is reduced to solving quadratures. The solutions to problems of elasticity theory for a transversely isotropic circular cylinder are analyzed in terms of the action of body forces given by various cyclic laws (sine and cosine). Recommendations are given for constructing the basis of internal states depending on the type of the function of the given body forces. The analysis of the series convergence and the estimation of the solution accuracy are given in a graphical form.