Analysis For Magnetostriction And Stress In A Thin Superconducting Disk With The Changing Magnetic Field

Recently,as a new sort of smart materials,superconducting materials have been further researched,and a set of theoretical systems have been established.Owing to the comparatively high critical transition temperature and excellent intrinsic electromechanical properties,high-temperature superconductors(HTS)have been widely applied in electric power,communication,mechanical manufacturing and other advanced technospheres.However,HTS are fragile materials,and there are unavoidable drawbacks such as holes.Serving the complex electromechanical conditions,HTS are susceptible to mechanics failure.In this paper,the magnetostriction,distributions of stresses and stress concentration of superconducting disks with various types of concentric holes have been researched by analytical method and numerical simulation.The details are as follows:First of all,the magnetostriction and distributions of stresses of a homogeneous superconducting disk under electromagnetic force are investigated by analytical method.Basing on the Irie-Yamafuji critical state model,the distributions of magnetic flux density and current density are obtained with the change of applied magnetic field.And then,according to Lorentz theorem,the flux pinning force is acquire,which pave the way for deriving the magnetostriction and distributions of stresses by elastic theory.Then,the further research is concentrated on the the magnetostriction and distributions of stresses of the superconducting disk with a concentric circle hole.As the same method,the Irie-Yamafuji critical state model is introduced and the effect of hole to electromagnetic field is ignored.The formulas of circumferential and radial stress can be derived by analytical method and the stress field is discussed.Further,this paper investigates the distributions of stresses and hole-edged stress concentration of the superconducting disk with a concentric elliptic hole.Overlooking the effect of hole and introducing the Irie-Yamafuji critical state model,electromagnetic force is obtained.Different with above,finite element method is used to calculate the related result and the effect of the shape of elliptic hole to stress concentration can be analyzed.Finally,the distributions of stresses and hole-edged stress concentration of the superconducting disk with a concentric elliptic hole under applied magnetic field are researched.With the same electromagnetic conditions,the numerical results are acquired by finite element method.According to the numerical examples,the effects of shape of hole,applied magnetic field and related electromagnetic parameters have been discussed.With above researches,the relationship between holes and mechanical properties of superconducting disk has been roundly analyzed.It will provide the superior theoretical foundations for the applications of superconducting materials.