Static And Dynamic Performance Analysis And The Shape Optimization Design Of Hybrid Ellipsoidal Paraboloid Shells

With the increase of people’s sports,recreation,tourism activities and the continuous emergence of new construction technologies and materials,Hybrid structures formed by combining different types of structural forms become the new direction of large-span spatial structure.The hybrid structure can give full play to the characteristics of each single-type space structure.It improves the mechanical performance,reduces total investment of the structural system and increases the space coverage of the space structure through reasonable hybridization,which has received good results.The hybrid ellipsoid paraboloid reticulated shell improves the disadvantages of stress concentration near the apex of the single-type reticulated shell and the large number of connecting rods,so that the distribution of the mesh is uniform and the mechanical performance of the structure is improved.In this paper,the parametric design language of APDL parametric design is used to develop a parametric design macro program for parametric ellipsoid paraboloid reticulated shells.A preliminary study is conducted on the static and dynamic performance and shape optimization design of this type of structure.The main work of this paper is as follows:(1)According to the ellipsoid paraboloid equation,z=f-4f(x2/S12+y2/S22),where S1 is the major axis span,S2 is the minor axis span,and fis the vector height.Referencing the modular method and the meshing form of circular horizontal projection hybrid saddle reticulated shell and rotating parabolic reticulated shell,Six hybrid ellipsoid paraboloid reticulated shell structures are established.(2)Applying static loads to the six hybrid ellipsoidal paraboloid reticulated shell structures,We can analyze the effect on of span S,vector height f,the number of the circumferential regions Kn,the number of turns of the superstructure radial nodes Ns,and the form of bearings on the ststic performance.The range of spans,vector heights,and number of grids for the six types of structures with good mechanical properties are summarized,which provides a theoretical basis for practical engineering design.(3)Taking the minimum steel consumption of the hybrid ellipsoidal paraboloid reticulated shell structure as the objective function,and taking the local constraints and the overall constraints as constraints,this paper analysis the minimum steel consumption in the case of different span S,vector height f,number of circumferential regions Kn and number of turns of superstructure radial nodes Ns.The optimal combination of the number of grids when the mesh shell has the minimum amount of steel consumption is obtained.According to the equation of the elliptic paraboloid surface,the relations between the lengths of three kinds of ellipsoidal paraboloid reticulated shells and the macroscopic and microscopic geometrical parameters are deduced.The numerical examples are based on the example of the Kiewitt-Lamella reticulated shell and the macroscopic and microscopic mathematical models can be used.The length of the rod and the range of the Nx values for the engineering are obtained to improve the design efficiency.(4)Earthquake response analyses are studied of the Kiewitt-Lamella and Kiewitt-Ribbed ellipsoid paraboloid shells.By analyzing the influence of the span S,the vector height f,the fraction of the circumferential zone Kn and the number of the radial nodes of the superstructure Ns on the natural vibration characteristics of the structure,the variation law of the natural vibration frequency and the formation of the structure is obtained.The displacement time-history curve of the structure node is obtained using the time-history analysis.The results provide a reference for the hybrid ellipsoid paraboloid reticulated shell structure under earthquake.Finally,this paper summarizes and prospects the analysis of hybrid ellipsoid paraboloid shells.