Mathematical Modeling and Analysis of the Mechanical Properties of a Nonferromagnetic Panel Under the Action of a Quasi-Steady Electromagnetic Field

A physical and mathematical model and a methodology for studying the mechanical properties of a nonferromagnetic conductive panel under the action of a quasi-steady electromagnetic field are proposed. A two-dimensional thermomechanics problem is formulated for the considered panel of a rectangular cross-section. The initial relations for finding the determinant functions, namely, the components of the quasi-static stress tensor, are given. The thermomechanical problem was addressed using the author’s approach, which involves approximating the defining functions by cubic polynomials along the thickness direction. This approach enabled the transformation of the initial two-dimensional boundary value problems into one-dimensional formulations based on the integral characteristics of the defining functions. Using a finite integral transformation in the transverse coordinate, the expressions of all integral characteristics and determinant functions were obtained. On the basis of the proposed mathematical model, a computer analysis of all components of the quasi-static stress tensor and stress intensity in a tungsten panel depending on the dimensionless Fourier time, the Biot criterion, and the induction heating parameters was carried out. The thermomechanical behavior of the panel was analyzed using two modes of near-surface and in-depth induction heating of the panel by a homogeneous quasi-steady electromagnetic field.