Affiliations: [a] Department of Mathematics, Faculty of Science,
Damanhour University, Damanhour, Egypt | [b] Department of Mathematics, Faculty of Science, Cairo
University, Giza, Egypt | [c] College of Business and Economics, Qassim University,
Buraydah, Kingdom of Saudi Arabia
Correspondence:
[*]
Corresponding author: A.F. Ghaleb, Department of Mathematics,
Faculty of Science, Cairo University, Giza 12613, Egypt. E-mail:
[email protected]
Abstract: The static, uncoupled problem of thermomagnetoelasticity for long
cylinders carrying a steady, axial current is investigated in stresses within a
numerical approach by a boundary integral method in terms of real harmonic
functions.This is the numerical realization of the field equations, boundary
conditions and other relations presented in [1]. The method is complemented by
the use of boundary collocation method to evaluate some path-independent line
integrals needed in the representation of the mechanical displacement field.
The material of the cylinder is assumed homogeneous and isotropic, and linear
dependence of the magnetic permeability on strain is taken in consideration
through two material constants. Formulae are obtained for the boundary values
of functions of practical interest like stress and mechanical displacement.
Evaluation in the bulk may then be carried out by quadrature on the basis of
well-known formulae of the theory of potential. The special case of an elliptic
boundary is treated and the results are compared to the analytical solution
established in [11]. It is concluded that the proposed numerical scheme
performs efficiently in this case, and may thus be used for other forms of the
boundary, subject only to smoothness condition.
Keywords: Plane problem, thermo-magnetoelasticity, electric current, magnetic field, thermomagnetic stresses, Maxwell stress, boundary method, boundary integrals, numerical methods
