Research On Modeling And Numerical Method For Dynamic Response Analysis Of Tensegrity Structure

As a kind of novel and charming structure made of struts and cables,tensegrity structure has recently received extensive interests from academic and engineer circles,given its lightweight,controllable,shape-changeable properties.However,these unique structural properties also cause a great deal of complicated dynamic phenomena in applications.Such as,the structure is composed of a lot of flexible cables,making the structural stiffness can be significantly lower than that of traditional spatial structures,and thus exhibiting strong geometric nonlinearities;the cables can only be subjected to tensile force and almost cannot be subjected to compressive force,which exhibits typical constitutive nonsmooth phenomena.The structure may contain a large number of complicated dynamic phenomena induced by,such as,friction of sliding cables,cable slacking and strut collision,which yields serious challenges for the mechanical response analysis.Current researches of tensegrity structures usually focus on morphology analysis,while investigation of dynamic response analysis,in particular of the nonlinear and nonsmooth dynamic response,is rarely seen.These investigations,however,have a great significance in deepening the theoretical research of this kind of structure which will further expanding its multidisciplinary application.This dissertation follows the main line of investigating the structural dynamic response,centers around developing modeling and numerical method for analyzing compictaed dynamic phenomena induced by classical,sliding cables,and strut collision,with the aim to explore the common and difficult discipline problems involved in this kind of structure.The main content of this dissertation are summarized as followsFirstly,a multibody dynamic model of classical tensegrity structures is established.The absolute coordinated formulation of multi rigid body dynamics is adopted for the structural analysis.Struts are modeled as rigid bodies,and classical cables are modeled as spring-damper-actuator(SDA).To ensure efficiency of implicit dynamic analysis and static equilibrium analysis,additional tangent stiffness matrix and damping matrix of SDA,absent from general multibody monograph,are derived.Numerical examples are presented to demonstrate the importance of these matrices in the analysis.Based on the concept of dynamic relaxation,an approach combining SDA with multibody dynamic analysis is proposed for from finding analysis of tensegrity structures.Comparisons with configurations of classical tensegrity structures show the validity and correctness.Secondly,to analyze the dynamic response of sliding cables involved in clustered tensegrity structures,a frictionless sliding cable element based on multibody modeling method of absolute coordinate's formulation is proposed.The generalized force vector,and the additional tangent stiffness matrix and damping matrix are first derived.This element is then extended to flexible mulitibody dynamic analysis.This element can be considered as an extension of SDA,a classical force element in multibody system,as well as an extension of traditional sliding cable that described based on finite element formulation.Finally,by using the proposed element in combination with the multibody dynamic methodology,static and dynamic deployment performance of clustered tensegrity structures is investigated.Thirdly,to analyze the sliding cable that described based on nodal position formulation considering sliding induced friction,a linear complementarity based approach is proposed.In the analysis of each time/iteration step,this approach handles the calculation of sliding length of each conctact point as a linear complementarity problem(LCP).Contrasted to traditional predictor-corrector-based approach,the proposed approach is not only robust,but also mathematically elegant and easy to implement,and thus is very convenient for engineering applications.Uniqueness of sliding length of conctact points under a designated configuration has been proved by using linear complementarity theory.Multiply examples are presented to demonstrate the diverse motion state of conctact points and the complex nonlinear and nonsmooth mechanical response induced by sliding friction.Fourthly,based on the ideology of parametric variational principle,a linear complementarity framework is developed for analysis of classical tensegrity structure with a large number of slacking cables.This framework is valid for the case that a combination of either large or small and either static or dynamics analysis,which is commonly encountered in structural analysis.The complementarity condition is first obtained in the element level and the nonsmooth constitutive relation can be transformed into a unified constitutive relation containing parametric variable.By using the equilibrium equation that based on nodal coordinates modeling strategy and in combination with the previous complementarity condition,the governing equation can be finally transformed into a LCP.Numerical examples demonstrate the stability and accuracy of the proposed approach in dealing with mechanical response analysis of tensegrity structures with a large number of slacking cables.Finally,to investigate the strut collision phenomenon in classical and clustered tensegrity structures,a dynamic model based on the absolute coordinated formulation and the continuous contact force method,is developed.This model is suitable for the thick strut collision analysis in tensegrity structures.The struts are considered as ideal cylindrical rigid body and the strut collision condition is first obtained.By using the Lankarani-Nikravesh normal collision force model and the modified Coulomb's tangential friction model,the continuous contact force is thus established.The generalized force vector and the related tangential stiffness and damping matrix are derived.Representative example are presented to show the influence of strut collision phenomenon to the structural mechanical response.