Study On Morphology Of Tensegrity Structures Using Optimization Methods

Morphology problem involving both structural geometry and prestress distribution is the key issue in the investigation and design of tensegrity structures.Referring to the previous researches,this thesis divides the morphology problem into six distinct sub-problems,called form-finding,structural stability,initial prestress design,load analysis,static control and erection process respectively.Then they are investigated carefully by means of matrix analysis,nonlinear programming theory,finite element method,dynamic relaxation method,genetic algorithms and so on.Nonlinear programming method is employed for form-finding of tensegrity structures.An improved optimization model is put forward for the purpose of finding more unknown self-equilibrium states.The dynamic relaxation technology is incorporated into the traditional gradient method to speed up the convergence and achieve higher precision.The Moore-Penrose generalized inverse is utilized to modify the nodal coordinates,while the kinetic damping is adopted to attenuate the kinetic energy of the system.Furthermore,this form-finding algorithm,based on free-standing self-equilibrium states,is extended to consider the anticipated dead loads and boundary conditions without the increment of constraint equations.In the orthogonal complement space of rigid-body motion space,two linear spaces spanned by internal mechanisms and internal affine motions,termed as Vinmand Vina respectively,are determined through singular value decomposition and Schmidt orthogonalization.Several stability conditions of tensegrity structures are given on the basis of the logical relations between Vinm and Vina.How the global stiffness changes as the level of prestress changes is explored.The practical classification of tensegrity structures is also proposed in view of their respective stability properties.For a tensegrity structure merely satisfying prestress-stability condition,a new optimization model is presented to determine its critical buckling state,while a real-coded genetic algorithm is developed to solve this problem.Two distinct methods are proposed to compute the symmetric self-stress modes of tensegrity structures with given shapes.The first one is to apply singular value decomposition on the so-called constrained equilibrium matrix.The other is an energy method making use of eigenvalue analysis,which is developed to overcome the drawback resulting from the manual classification of member groups.For structures with multiple symmetric self-stress modes,a novel optimization model for the purpose of maximizing the global rigidity is presented to determine the combination coefficient of each mode.For comparative study,two strategies of the genetic algorithms termed as simple genetic algorithm and isolation niche genetic algorithm are carried out successively to solve this optimization problem.Starting from the force method,the axial force variables and displacement variables are decoupled by means of linear algebra and Moore-Penrose generalized inverse theory.The finally obtained fundamental equations for static analysis include generalized equilibrium equations and generalized compatibility equations.The similarities in mathematic essence between dynamic relaxation method(DR)and nonlinear conjugate gradient method(NCG)are also revealed.Moreover,a mixed algorithm termed as NCG-DR is presented,which can be effectively used for static analysis of cable-strut systems.Regarding the active adjustments of actuators as the decision variables,a nonlinear programming model is established with multiple objectives for static control.In order to enhance the efficiency and robustness of the algorithm,the non-dominated sorting genetic algorithm NSGA-? is improved from the following three aspects-the calculation strategy of the non-dominated sort and crowding distance,the definition of the dominant relationship,the prevention of the duplicated individuals.Two carefully chosen examples are taken into account to demonstrate the effectiveness of the proposed method.An erection scheme is developed for a kind of prismatic tensegrity structures with additional cables.To simulate such scheme,we suppose that the active cables are eliminated following the inverse track of the erection process.Then the dynamic relaxation method is carried out to determine the slack equilibrium states under the gravity,where a new computational format of the kinetic energy peak is incorporated.In practice,the elimination and slackness of the cables are simulated by updating their material properties automatically,so that the topology of the structures remains invariant during the analysis.The work is motivated by promoting the development of morphology of tensegrity structures.Actually,it provides theoretical evidences and technical supports for the applications of tensile structures in civil engineering as well as other interdisciplinary fields.At the end of thesis,the limitations and problems that need to be studied further are pointed out.