Lorentz force-induced stresses in long current-carrying conductors

Semi-analytical solution by Cartesian harmonic polynomials for a problem of deformation of a long, current-carrying elastic cylindrical conductor

“…Abou-Dina and Ghaleb [11] presented a boundary integral formulation of the problem of deformation of a long current-carrying conductor. The calculation of Lorentz force-induced stresses in long straight conductors carrying a uniform current was treated by Deviatkin [12], with application to cylinders of elliptic or narrow rectangular cross-section having a stress-free lateral surface. The magnetic scalar potential was used for the solution.…”

Cartesian harmonic polynomials for a problem of deformation of a long, current-carrying elastic cylindrical conductor of nearly-circular normal cross-section

“…It is easily verified that 5A Dirichlet thermal condition is taken at the boundary: (6) The temperature distribution generates "temperature displacements", which will be included in the expressions for the mechanical displacement. These are [8]: (7) where and are Poisson's ratio and the coefficient of linear thermal expansion respectively. Here is an arbitrarily chosen point in the domain of the cross-section, usually taken to coincide with the origin , is the general point at which the function is calculated.…”

“…The deformation of long, current-carrying wires has been the subject of active research for fifty years or so. We only cite the following references by Ghaleb [4] for the circular boundary, Ayad [5] for the elliptical boundary, Abou-Dina and Ghaleb [6] for a boundary integral formulation of the problem, Deviatkin [7] for cylinders of elliptic or narrow rectangular cross-sections, El Dhaba et al [8,9,10] for the elliptic or square boundaries by boundary integrals, including a numerical approach, El Dhaba [11] and El Dhaba and Ghaleb [12] for a rod with square normal cross-section in an initially uniform transverse magnetic field by boundary integrals. Recently, the authors have investigated the elliptic and the rectangular contours under the Dirichlet thermal condition and uniform normal extension on the boundary [13].…”

Deformation of an elastic magnetizable square rod due to a uniform electric current inside the rod and an external transverse magnetic field

“…Once the boundary values of the functions A h , A c h , A à r , A *c r  à T have been obtained, one can find all of the physical quantities related to the magnetic potential. The numerical method is next applied to the four functions F, F c , C, and C c (equations (58), (59), (61) and (62)), the two boundary conditions (equations (41), (42)) and the seven boundary conditions (equations (49), (50), (51), (52), (53), (54) and (55)). The resulting system of linear algebraic equations is…”