Analysis of Nonlinear Stresses and Strains in a Thin Current-Carrying Elastic Plate

Abstract

Two-dimensional magnetoelastic problems of a thin current-carrying plate under the interaction of an unsteady electromagnetic field and a mechanical field are studied. The nonlinear magnetoelastic kinetic equations, geometric equations, physical equations, electrodynamics equations, and expressions for the Lorentz force of a thin current-carrying plate under the action of a coupled field are given. The normal Cauchy form nonlinear differential equations, which include ten basic unknown functions in all, are obtained by the variable replacement method. Using the difference and quasi-linearization methods, the nonlinear magnetoelastic equations are reduced to a sequence of quasilinear differential equations, which can be solved by the discrete-orthogonalization method. Numerical solutions for the magnetoelastic stresses and strains in a thin current-carrying elastic plate are obtained by considering a specific example. The results that the stresses and strains in the thin current-carrying elastic plate change with variation of the electromagnetic parameters are discussed. The results show that the stress–strain state in thin plates can be controlled by changing the electromagnetic parameters. This provides a method of theoretical analysis and numerical calculation for changing the service conditions and intensity research of thin plates of engineering structures in the electromagnetic field