We use a method recently introduced by some of the authors to obtain a semi-analytical solution to a problem of deformation of a long cylindrical conductor carrying a steady axial current, in the quasi-electrostatic approximation. The method relies on the expansion of the unknown harmonic functions arising in the process of solution in terms of Cartesian polynomial and rational harmonic functions. The normal cross-section of the conductor is taken to be nearly circular and the thermal and magnetic parts are solved independently of each other and of the elastic problem. Numerical results and plots are provided and discussed. A comparison with the case of a circular crosssection allows to assess the influence of imperfection of the cross-sectional shape on the quantities of practical interest. The effect of the dependence of the magnetic permeability on strain is investigated as well.
A method proposed earlier, relying on the use of harmonic Cartesian polynomial and rational functions, is extended here to find a semi-analytical solution to the uncoupled, two-dimensional problem of thermo-magnetoelasticity for a system of long parallel, non-intersecting, transversely isotropic elastic cylindrical electrical conductors. Results are presented for two conductors of equal circular normal cross-sections carrying currents of equal densities flowing along the same direction, subjected to Robin-type thermal boundary conditions. Quantities of practical interest are represented graphically and discussed. Consideration of a system of electrical conductors is of practical importance in power plants and in various technological instruments, where it is required to assess the interaction between conductors. The obtained formulas for the magnetic vector potential may be of importance for the determination of the coefficients of self- and mutual inductance of long electric conductors, otherwise difficult to calculate by standard methods. Comparing the results with those of a single conductor allows us to assess the interaction between conductors.
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