Form-finding And Mechanics Property Analysis Of Multistable Tensegrity Structures

The tensegrity is a new type of structure system which is in a self-equilibrated and stable state.The process to determine its geometrical configuration and prestress is called form-finding.A new and efficient form-finding method is proposed which combines the classical Force Density Method with a swarm intelligence optimization algorithm--Particle Swarm Optimization(PSO).Firstly,the equilibrium equation of a tensegrity in a self-equilibrated state is set up based on the principle of Force Density Method.The process of form-finding is turned into a problem to find a set of force densities which makes the equilibrium matrix singular.Consequently,a set of feasible coordinate vectors of nodes are obtained.Then PSO is used as the global search tool to find suitable force densities by minimization of fitness functions.A two-dimensional tensegrity and three threedimensional tensegrities are used to verify the feasibility of the new form-finding method as examples.Their geometrical configurations and convergence curves are present respectively.The new method solves the problem of low efficiency of traditional Force Density Method and shows a good convergence,which can be served as an effective form-finding tool of tensegrities.The geometry obtained has diversity,and it can be used as the basis of the tensegrity with special coordinate requirements or shape requirements.Tensegrity structures have certain energy which will change as the length of members changes.A stable and equilibrated tensegrity may jump into another equilibrated state with higher energy under loading-unloading cycles.Dynamic Relaxation Method is used as a form-finding method to find tensegrities with the same initial conditions but different energy,which proves the multistable phenomenon of tensegrities.Then the new form-finding method combines the classical Force Density Method with PSO is used to verify the validity of the solution of multistable tensegrities.Considering the practical application of tensegrities,several tensegrities with geometric constraints are designed and modified Dynamic Relaxation Method is proposed as the form-finding method.A tensegrity with lower energy will turn nonlinear and prominent deformation as one of its node is fixed and other nodes bear random loads.As a result,its system energy increases continuously.The structure with higher energy will deform to a state of lower energy after the loads removed and finally recovers to a stable and equilibrated state.This stable and equilibrated state can be either the original state or a new state.If the latter occurs,the transition of tensegrities with different energy succeeds.Dynamic Relaxation Method and Vector Form Intrinsic Finite Element(VFIFE)are respectively used to verify the feasible of the transition.The results show the feasibility of both methods.The conclusions of the two methods all indicate that the transitions of different energy with the same initial conditions are accompanied by energy absorption or dissipation.Based on the form-finding method combines the classical Force Density Method with PSO,two methods to find target configurations of tensegrities are proposed by the linear combination of eigenvectors corresponding with zero eigenvalues.Several examples are used to prove the feasibility of both methods.Tensegrities satisfy special coordinate requirements or special coordinate requirements can be obtained using these two methods,which provides a reference to build modularized tensegrity structures.Based on the two methods,two linear type,one flat type,one circular type and two free type of modularized tensegrity structures are designed.Fitness functions are especially built corresponding to each tensegrity element and all target configurations are obtained successfully.Both methods show a good convergence and applicability.Tensegrities show distinct geometric nonlinearity.As a result,finite element method considering geometric nonlinearity is used to analyze mechanics property of tensegrities.The software of finite element analysis—ANSYS is used as static analysis tool for tensegrity elements and modularized tensegrity structures.Tensegrities with different rigidity of section are analyzed and made contrasts.The importance of structural stiffness to resistance to external loads was verified.