Describing Non-Axisymmetric Elastic Fields Generated by Volume Forces in Anisotropic Solids of Revolution

Abstract

The paper presents a technique for plotting elastic fields in transversely isotropic bodies bounded by coaxial surfaces of revolution, subjected to non-axisymmetric volume forces. Our theory uses the ideas of the boundary state method, which is based on state spaces describing a medium. Fundamental polynomials form the basis of the internal state space. A polynomial is placed in any displacement vector position in a planar auxiliary state, then transition formulas can be used to determine the spatial state. A set of such states forms a finite-dimensional basis that is used after orthogonalisation to expand the desired elastic field characteristics into Fourier series with identical coefficients. These series coefficients are dot products of given and base volume force vectors. The search for an elastic state is reduced to solving quadratures. We provide guidelines for constructing an internal state basis depending on the type of volume forces given by various cyclic functions (sine and cosine). We analysed a solution to a specific theory of elasticity problem concerning a transversely isotropic circular cylinder subjected to non-axisymmetric volume forces. We analysed the series convergence and graphically evaluated the solution accuracy