The Analysis Of Thermo-Magneto-Elastic Stress And Deformation In The Thin Current-Carrying Truncated Conical Shell

Thermo-magneto-elastic theory studies the coupling effect of the electromagnetic field,the temperature field,and the deformation field.In modern industrial engineering,there are often structural components of thin shell that work in the environment of the coupling action of the electromagnetic field,the temperature field,and the mechanical field.The analysis of its stresses and deformations is of practical value and significance.The thermo-magnetic elasticity includes classic elastic theory,the heat conduction theory,and the electromagnetic field theory.On the basis of these theories,some problems on the elastic deformation and motion of the conductive bodies in the magnetic field are further solved,that is,solving the problems that the temperature field,the deformation field,and the electromagnetic field interact and influence each other.In this paper,the thermal-magneto-elastic problems in the thin current-carrying truncated conical shell subjected to mechanical loadings in a magnetic field are studied.The geometric relations of nonlinear strain,physical equations,magneto-elastic motion equations,electrodynamic equations,and Lorentz force component expressions of the thin shell are derived by theoretical deduction.The basic thermal-magneto-elastic equations of a thin truncated conical shell under the interaction of the electromagnetic field,the temperature field,and the mechanical field are established.Considering Joule’s thermal effect and the related knowledge of heat transfer,the equation of the temperature curve for the heat conduction of an object with internal heat source is derived.The temperature field and integral eigenvalue expressions of the temperature field T of thin current-carrying truncated conical shell are given.On this basis,eight partial differential equations are transformed into quasi-linear differential equations which can be solved by the discrete-orthogonalization method by using Newmark’s stable finite equidifferent formulas and the quasi-linearization method.By applying the discrete-orthogonalization method programming,the numerical solutions of the thermal-magneto-elastic stress and deformation of the thin current-carrying truncated conical shell are given.The changing rules between the stress,deformation,and temperature of the thin truncated conical shell in the coupling field and the external electromagnetic parameters are obtained.The calculation results and their changing rules are analyzed.We draw the corresponding curves.Through specific examples,it is proved that the changes in the parameters of the electric field,magnetic field,and mechanical field can be used to control the stresses,strains,and temperatures in the thin truncated conical shell.