Topology Optimization And Applications Of Tensegrity Tours

Tensegrity structure is the typical representative of modern flexible space structure.Thanks to the characteristics of the beautiful shape,strong spanning ability,and good economic benefits,cable dome has been widely used in engineering practice.The existing cable dome is supported by reinforced concrete ring beam or steel ring beam,so it is not a real tensegrity structure of the strict sense.Therefore,it is of great significance of theory and great value of engineering application to study the self-balanced cable dome with a tensegrity tori.The primary task of realizing a self-balanced cable dome is to find a feasible construction of tensegrity tori.In this thesis,the topology optimization,static and dynamitic charcateristics of tensegrity tori are studied,and its application in self-balanced cable dome is explored for the purpose of providing theoretical basis and technical support for the popularization of application of this kind of structure in engineering.In view of the fact that the tensegrity structure system must be provided with stiffness by external prestressing force in order to maintain the stability of geometric shape,the double singular value decomposition method based on equilibrium matrix and stiffness matrix based form-finding method of tensegrity structures are firstly introduced.The application scopes of the two methods are discussed.The corresponding MATLAB calculation programs are compiled in this thesis and the efficiency of the programs are verified by examples.A theoretical basis for the following topology optimization of tensegrity tour and static and dynamic performance analysis of self-balanced cable dome is provided.A topology optimization method based on improved genetic algorithm with the sharing function niche mechanism and pre-selection niche mechanism is proposed by considering the flexibility and mechanical properties of tensegrity torus.The minimum structural weight is taken as the objective function of the method.The five constraint conditions of the method are minimum number of bars connected by nodes,feasible integral structural prestressing,none-cross collision of bars,stress constraints of members and limitation of structure displacements.The efficiency of stiffness matrix based form-finding method of tensegrity structures for solving the self-balanced modes and static analysis of tensegrity torus of different topological conditions is proved by the topology optimization results in numerical examples.The improved genetic algorithm with the sharing function niche mechanism and pre-selection niche mechanism effectively improves the reliability and stability of traditional genetic algorithm.The proposed computing method is applicable to the topology optimization of tensegrity torus and other tensegrity structures.Low stiffness is one of the weaknesses of tensegrity structures,and it is also the biggest disadvantage for the application of tensegrity structures in practical engineering.Combining with the mechanical characteristics of cable dome and considering the additional constraint of vertical displacements on the basis of the constraints imposed in Chapter 3,the mechanical performance of tensegrity tori is studied.The optimal solution of topology optimization of the corresponding tensegrity tori is obtained.The influences of prestressing level and section areas of members on static and dynamic characteristics of optimal tensegrity tori are analyzed as well.The application of combining tensegrity tori with cable dome is further studied.The influence of stiffness of tensegrity tori on the mechanical properties of cable dome is analyzed,and the loading process of self-balanced cable dome under loading is simulated.The ultimate bearing capacity of structure is considered under the conditions of geometric and material nonlinearity,elastic-plastic buckling of compression bar,cable relaxation and cable yielding.The similarities and differences between self-balanced cable dome and traditional cable dome in displacement,member internal force,support reaction and ultimate bearing capacity under various working conditions as well as the dynamic characteristics are compared and analyzed.The analysis results show that the self-balanced cable dome has high stiffness,and the mechanical performance of the self-balanced cable dome has been improved due to the effect of the tensegrity tori.In this thesis,the improved genetic algorithm is used for topology optimization of tensegrity tori.The static and dynamic characteristics of the self-balanced cable dome are analyzed when the tensegrity tori is used as the ring beam,which provides theoretical basis and technical support for the practical engineering application of the self-balanced cable dome.