Construction of elastic fields in the problem from the action of body forces of a cyclic nature

D. A. Ivanychev ; E. Yu. Levina

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 28 (2024) no. 1, pp. 59-72

Résumé

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

Détail

Keywords: boundary state method, transversely isotropic materials, body forces, state space, non-axisymmetric deformation