Study On The Buckling Characteristics Of High Temperature Superconducting Thin Circular Plate Under External Magnetic Field

Since the discovery of superconductivity,the understanding of superconducting materials has been continually deepening.The discoveries of material properties such as the Zero resistance effect,Meiners effect,and Josephson effect have laid the research value of the superconducting materials.High temperature superconducting materials,represented by copper oxide superconductors,have high critical transition temperature,making them widely used in fields such as transportation,military engineering,and aerospace.As a common structure in in the applications of superconducting material,superconducting thin circular plates are subjected to complex electromagnetic environments during their preparation and service,and are therefore influenced by strong electromagnetic forces.Considering the structural characteristics of superconducting thin circular plates,buckling of the plates under the action of electromagnetic force usually occurs before strength failure of the materials.Additionally,the presence of inevitable defects such as holes and non-uniformity of materials can also greatly influence the buckling behavior of the structure.The buckling phenomenon has important effects on the failure of superconducting materials,this leads to significant safety risks in superconducting components,so it is necessary to further study the buckling characteristics of superconducting thin circular plates.In this thesis,the buckling characteristics of the superconducting thin circular plate,the superconducting thin circular plate with a small concentric circular hole and the functionally graded superconducting thin circular plate with a small concentric circular hole under external magnetic field and mechanical load are studied by combining theoretical derivation with numerical calculation.The influences of external magnetic field,mechanical boundary conditions,holes,critical state model and material non-uniformity on the buckling characteristics of the thin superconducting plate are analyzed in order to provide basic conclusions for the anti-buckling design of the plate superconducting structure.Specific contents and conclusions are as follows:(1)The distribution of electromagnetic force in the thin superconducting plate was analyzed based on the Bean critical state model.On this basis,the buckling differential equation of the superconducting thin circular plate under the action of electromagnetic force and mechanical load was derived.The critical buckling magnetic field and critical buckling load of superconducting thin circular plates with simply supported and clamped boundaries were numerically solved by using the initial value method.The results show that the critical buckling value of the superconducting thin circular plate increase with the increase of the thickness-to-diameter ratio.The critical buckling magnetic field of the superconducting thin circular plate with clamped is increased by 85% compared with that of the superconducting thin circular plate with simply supported.At the same time,when the external magnetic field and mechanical load act on the thin superconducting plate,the critical buckling load of the superconducting thin plate will decrease when the external magnetic field gradually increases,and vice versa.When the values of the two exceed a certain range,the thin superconducting plate will enter the buckling instability state.(2)Based on the Bean critical state model,the critical buckling magnetic field and the critical buckling load of a thin superconducting plate with a concentric small circular hole were studied by using the initial value method under multiple boundary conditions are applied to the plate boundary and hole boundary.The results show that the boundary conditions also significantly affect the critical buckling load and critical buckling magnetic field,among which the critical buckling value is the highest under the clamped-clamped boundary condition and the lowest under the free-simply supported boundary condition.Compared with the free-simply supported thin superconducting plates,the critical buckling magnetic field and the critical buckling load of thin plates with clamped-clamped are doubled and quadrupled,respectively.In addition,compared with other boundary conditions,the critical buckling load and the critical buckling magnetic field of the thin superconducting plate can be greatly improved when both the inner and outer boundaries are clamped.(3)The extended generalized Irie-Yamafuji critical state model was introduced to study the buckling characteristics of the functionally graded superconducting thin plate with a concentric small circular hole under external magnetic field and mechanical load.Considering that the material properties of the superconducting thin circular plate were distributed exponentially along the radial direction,the critical buckling magnetic field and critical buckling load of the functionally gradient superconducting thin plate with a hole under different boundary conditions,functional gradient indexes and model indexes were numerically solved by using the initial value method.The results show that the buckling resistance of thin superconducting circular plates can be improved effectively by increasing the thickness-diameter ratio and model indexes,as well as decreasing the functional gradient indexes.