Redundancy Theory And It’s Application In Tensegrity Dome Comprised Of 3-Bar Prisms

Redundancy analysis is an important direction in the field of structural robustness and security research and has received extensive attention from domestic and foreign scholars.A variety of redundancy measures,including probabilistic redundancy measures,deterministic redundancy measures,life-cycle redundancy measures,sensitivity-related redundant measures,as well as redundancy measures that are related to the importance of components,are proposed in the previous studies.These measures are applied to the study of structural systems such as buildings,bridges,and hulls.However,researches on the redundancy of large-span spatial structures,especially on the redundancy of flexible space structures,are still lacking.As a new type and typical large-span flexible space structure,the tensegrity dome have a wide range of applications since it is novel,highly mass efficient and controllable.Simple Tensegrity domes and its Composition monomers have been the subject of several studies including form-finding,design optimization,static and dynamic analysis and control,while few studies focus on the tensegrity dome with high complexity.This paper aims to explore the redundancy theory of rigid and flexible structures respectively,and propose new redundancy measures to evaluate the rigid and flexible structures.Furthermore,this paper also aims to study a tensegrity dome comprised of 3-bar prisms.The geometry and topology of the structures would be studied firstly,and the construction methods and redundancy characteristics would then be explored.The main research contents of this article include:(1)Redundancy theory of rigid structuresTaking trusses and frames as the research object,a redundancy theory of rigid structures is proposed.The concept of redundancy is extended from system-level to the member-level in the proposed theory.Based on the relationship between element deformation and strain energy,the redundancy theories of trusses and frames are deduced,in which the redundancy distribution indexes of trusses and frames are defined and used as redundancy evaluation indexes.In addition,the sensitivity analysis and component importance analysis are performed on the basis of the proposed redundancy theory.A sensitivity index is proposed to evaluate the sensitivity of trusses,and a component importance index is proposed to find the importance sequence of the components in trusses and frames.(2)Redundancy theory of flexible structuresBased on the potential energy equations,the concept of redundancy is applied to the flexible cable-strut system,and the influence of the prestress on the redundancy is introduced into the redundant measurement.The geometry,topology,material properties and prestress of the flexible cable-strut system are comprehensively considered to reflect its redundancy properties.This paper discusses the redundancy of the cable-strut system from two perspectives--statically indeterminant redundancy and kinematically indeterminant redundancy.For the statically indeterminate redundancy,linear and nonlinear redundancy matrices are derived,and corresponding statically indeterminate redundancy indexes are proposed.For the kinematically indeterminant redundancy,the node mobility matrix and node rigidity matrix are derived respectively.The corresponding node mobility index and node rigidity index are proposed.Finally,through a case study of cable dome,the two sets of redundancy evaluation indexes are unified,and a set of comprehensive redundancy index of cable-strut system is proposed.(3)Tensegrity dome and its modular construction methodA method for systematically calculating the connectivity matrix and the node coordinates of the minial tensegrity plate is proposed.On the basis of the minimal tensegrity plate,a new type of tensegrity plate is proposed by adding additional strings.The connectivity matrix of new tensegrity plate is also deduced.Furthermore,tensegrity domes with spherical and parabolic surfaces are also proposed and characterized.A modular construction method is developed to construct the proposed dome.(4)Dynamic and open-loop control strategy of tensegrity domeBased on the matrix form of dynamic equations,an open-loop control strategy is proposed to realize the transformation from a tensegrity plate to a dome by shortening the rest-length of strings in bottom surface of the structure.According to the final shape of the overall dome,the effects of the control parameters and the initial goemetry parameters on the final shape of the structure are studied.Finally,a tensegrity dome is designed by the proposed control strategy and material selection is discussed.(5)Redundancy analysis of tensegrity domeThe system-level,member-level and node-level redundancy properties of tensegrity domes comprised of minimal regular 3-bar prisms are analyzed by utilizing the redundancy theory proposed in this paper.The redundancy indexes are also solved,which can be combined with stiffness indexes to provide the basis for the rational design of this kind of tensegrity domes.