Theoretical And Experimental Research On Self-Equilibrated Tensegrity Cable Domes

Cable dome is a kind of long-span cable-strut structure with high stiffness to mass ratio.However,the cable dome must be supported on a rigid circular beam or truss to keep prestressed.Thus,it is not a real self-equilibrated tensegrity by definition.Due to the many benefits of tensegrity structures,this paper proposes a novel self-equilibrated tensegrity cable dome on top of a tensegrity torus.The study shows that the two parts promote each other in a positive feedback manner.That is,since the torus has a relatively high radial stiffness,it can balance the radial forces from cable dome.Meanwhile,the cable dome also enhances the in/out-plane stiffness of tensegrity torus.In this paper,the tensegrity cable dome design is studied from these different prospectives:form-finding,optimization,static and dynamic analysis,construction simulation,etc.Finally,an experimental model is designed and manufactured to verify the construction and loading process.The main research contents of this article include:(1)Static and dynamic equation of tensegrity structuresFor statics,the equilibrium equations of tensegrity structures are first developed based on variation principles.In the statics formulation,nodal positions are chosen as the generalized coordinates,which significantly simplifies the derivation.Then,by linearizing the equilibrium equation,the tangent stiffness matrix and theoretical form of the eigenvalue buckling force of any tensegrity structure are given.For dynamics,the Lagrangian method is implemented to obtain the explicit dynamic expression from a systematic level.The derived dynamic equations are capable of dealing both structures with boundary constraints and structural elements with large displacements and nonlinear material problems.The modal analysis and time history analysis are verified to have consistent results with commercial software ANSYS.(2)Form-finding mothod of tensegrity structuresThree form-finding methods are studied in this paper.Firstly,a form-finding method for tensegrity structures based on the Levenberg-Marquardt method is proposed.From the nonlinear equilibrium equations,the form-finding process yields a nonlinear least-squares(NLS)problem.The Levenberg-Marquardt method is implemented to solve the NLS problem because of the advantage of the L-M method in dealing with the singularity of the stiffness matrix.Then,a form-finding method based on pseudo inverse is given by using the least norm solution of the underdetermined equilibrium equation.Another form-finding method based on optimization of potential energy is also proposed.Instead of solving equilibrium equations,this method is performed by solving a unconstrainted optimization problem,in which the modified Newton method is used to guarantee the results converge to a stable equilibrium configuration.Force and torque equilibrium equations are innovatively derived for rigid bodies connected by strings.The form-finding algorithm of the structure configuration and prestress of the generalized tensegrity are calculated in an iterative manner.Finally,a numerical form-finding method for rigid body generalized tensegrity structures is studied and analyzed.(3)Optimization design of self-equilibrated tensegrity cable domeThe topology optimization of the tensegrity torus is first studied.Using ring stiffness as an objective function,the genetic algorithm is implemented to optimize the torus topology,configuration,prestress,and cross-sectional area of the structure.Then,the topology and configuration of a new tensegrity torus are proposed and parameterized.For the given configuration,the minimal mass design in two states is used to design the prestress and cross-sectional area of the torus in the presence of structural member failure stress and global stability constraints.The configuration parameters are then formulated as a constrained optimization problem.Then,by conducting a similar procedure,the design of the cable dome,its minimal mass,and configuration parameters are studied.Finally,a new self-equilibrated tensegrity cable dome is proposed by combing the tensegrity torus and cable dome together.The prestress and cross-sectional area of the new structure system is designed and analyzed.(4)Research on mechanical properties and tensile construction process of the self-equilibrated tensegrity torusA self-equilibrated tensegrity torus experimental model with a 100m span and 15m height is first designed and manufactured.Then,the static mechanical properties are studied by exerting full span vertical force,half span vertical force,and horizontal force to the structure.The modal analysis of the structure is also studied with different structure parameters.To verify the dynamic behavior of the structure subject to an earthquake,a study on the time history of the self-equilibrated cable dome in the presence of the 1940 El-Centro earthquake is conducted.In the end,the tensile construction process of the tensegrity torus and cable dome is simulated by the positional FEM method.(5)Experimental research on the self-equilibrated tensegrity cable domeThe static and dynamic similitude laws of scale models of cable-strut structures are first studied.For static similitude laws,the Newton-Raphson method and inductive method are used to derive the nonlinear static similitude principles.For dynamic similitude principles,free vibration and time history analysis are studied by dimensional analysis of the dynamic equations.In the experimental study,a self-equilibrated tensegrity cable dome model in a 5m span is designed and manufactured.The construction and loading process is then tested and compared with FEM simulation results.