Construction And Study On Elastic Buckling Model Of Rectangular Thin Plate With Hole

Rectangular thin plate structures with holes are widely used in aerospace,marine and other engineering fields.Due to the existence of holes,the elastic buckling load capacity of the structure is changed.The study on the stability of rectangular plates with holes has important theory and engineering significance for understanding the buckling failure.However,the current modeling methods for elastic buckling of rectangular plates with holes mainly focus on numerical methods,lacking mathematical models for rectangular plates with different opening shapes,which is not conducive to uniform study of boundary conditions,hole size,hole shape and other factors effected on the elastic buckling behavior of the structure.Therefore,this paper proposes a method combining the independent coordinate coupling method,the Rayleigh-Ritz method and the improved Fourier series method,aiming at constructing a general elastic buckling model of a rectangular plate with holes under arbitrary complex boundary conditions.In this paper,the following research work is carried out around the construction method of elastic buckling model of rectangular plate with holes:The construction method of elastic buckling model of rectangular thin plate with rectangular holes,combined with the advantages of independent coordinate coupling method,Rayleigh-Ritz method and improved Fourier series method,the model is satisfied the arbitrary complex boundary conditions.The specific details are: in the independent coordinate system of the rectangular hole domain and the rectangular plate domain,the buckling deflection function of the rectangular hole domain adopts the orthogonal polynomial beam function,and the buckling deflection function of the rectangular plate domain adopts the improved Fourier series.According to the Rayleigh-Ritz method and the deflection matching condition,the energy equation and characteristic equation of the elastic buckling of rectangular thin plates with rectangular holes are derived.The numerical examples of elastic buckling of rectangular thin plates with rectangular holes are used to verify the accuracy of the modeling method.The effects of boundary conditions,rectangular hole size and rectangular hole position on the elastic buckling behavior of rectangular plates with rectangular holes are analyzed.The elastic buckling model construction method of rectangular plate with rectangular holes is extended to establish the elastic buckling model of rectangular plates with circular holes under arbitrary boundary conditions.The specific details are that the rectangular plate domain follows the elastic buckling model of the rectangular plate domain under arbitrary boundary conditions,and the buckling deflection function of the circular hole domain adopts the combination of the orthogonal polynomial function and the triangular series.According to the stress relationship in the Cartesian coordinate system and the polar coordinate system,the elastic buckling energy equation of the circular hole domain are obtained.The numerical examples of elastic buckling of rectangular plates with circular holes are used to verify the accuracy of the elastic buckling of rectangular plates with circular holes.The effects of boundary conditions and circular hole size on the elastic buckling behavior of rectangular plates with circular holes are verified.And through the numerical examples of the rectangular plate with rectangular hole and circle hole with the same orifice area ratio,the influence of the shape of the hole on the elastic buckling behavior of the rectangular plate with holes is analyzed.The elastic buckling experimental scheme of a rectangular plate with rectangular hole and rectangular plate with circular hole under the condition of loading edge simply supported boundary and non-loading edge free boundary is designed.The critical buckling load of rectangular plates with different structural parameters is obtained,and the calculation results of the theoretical model are obtained.For comparison,the correctness of the modeling method is verified from the experimental point of view.