Non-linear Stability Theory Of Lattice Structures With Initial Imperfection And Its Applications

Damage, in its mechanical sense in solid matericals with initial micro-imperfectionsuch as microvids or microcracks subjected to unfavorable mechanical andenvironmental conditions, is the creation and growth of microvids or microcracks underexternal load and makes deterioration of the material. On the other hand, for thin-walledstructure as cold-formed thin-walled structure and lattice structure and so on, it occurredstatic deformation (i.e. intinal imperfection) from construction to occupation. Initialimperfection included intial physical imperfection and intial structure imperfection. Thelattice structure was sensitive structure to imperfection. So this dissertationsystematically studied non-linear dynamic stability of axial symmetrical and non-axialsymmetrical lattices taking the initial imperfection as research breakthrough point.Finally, using catastrophe theory, this dissertation studie d the overall stability of thelattices with the initial damage.Thus a series of useful throretical results were obtained,which was essential in the safety and durability of lattice structure.Firstly, the development in nonlinear theorier of stability and accident analysis forthe lattice structures was reviewed, which indicated theoretical significance andapplication prospect of this research. Secondly, taking account of the effects of theinitial imperfection, dynamic model of the lattices with initial imperfection wasestablished to analyse the characteristic nonlinear dynamic. And, considering the effectof the initial damaged, damage model of structure steel was presented. Then nonlinearbending of the lattices with initial damage was solved. Thirdly, nonlinear dynamic model of the lattices with initial damage was obtained to systematically study thenonlinear dynamic stability of the lattice with initial damage. This dissertation studiedlocal stability of the lattice with initial damage at the fixed point using bifurcationtheory and explained the chaotic characteristic and control chaotic motion by chaotictheory. Meanwhile, using the catastrophe theory, this dissertation studied the overallstability of the system with initial damage. Then, in order to take account of couplingfactor of the initial structure imperfection and the initial materials damage, nonlineardynamic model of the lattices with coupling the intial structure imperfection and intialdamage was estabilished. Finally, a cusp catastrophic mode of the lattices with theinitial damage was established using catastrophe theory. Summing up the above, thisdissertation studied systematically local stability and overall stability. The main worksand achievements of this dissertation were as follows:(1) This dissertation took deformation as initial imperfection and nonlineardynamic model of the lattices with initial imperfection was given. The problem of localstability at the equilibrium of the system was discussed by exponent Floquet underdifferent intial conditions and parameter. So theoretically critical condition of chaoticmotion was given using the Melnikov function method. The chaos motion of theshallow reticulated spherical shell with initial imperfection was simulated by computernumerical emulation under nonlinear forced vibration. And it was founded that theinitial imperfection made the chaos motion of the system easily occur.(2) The damage model of the structure steel was presented by theory of irreversiblethermodynamics. This model had clear physical meaning, simple form, providing anexpedient usage in steel structure design. Then the nonlinear large deflection equation ofthe initial damage was given by the model and the problem of nonlinear bending wassolved by the method of modified iteration.(3) The nonlinear dynamical equations of the shallow reticulated spherical shellwith initial damage were given by Galerkin method. An accurate solution of the shallowreticulated spherical shell with initial damage was solved. The problem of local stabilityat the equilibrium of the system was discussed by exponent Floquet under differentintial conditions and parameter. It was found that the initial damage had effect on localstability of the lattices. (4) Assuming the thin film tension consists of two items, the compatible equationswere simplified to two independent equations. Selecting the maximal amplitude in thecenter of the shallow reticulated spherical shell with damage as the perturbationparameter, the nonlinear vibration equation of the system with damage under theboundary conditions of fixed and clamped was solved by perturbation variation. So therelation of the lowest natural frequency and the maximal amplitude was obtained.Then,the nonlinear dynamical equations of the shallow reticulated spherical shell with initialdamage were given by Galerkin method. An accurate solution of the shallow reticulatedspherical shell with initial damage was obtained. Finally, theoretical critical condition ofchaotic motion was given by the Melnikov function method. The chaos motion of theshallow reticulated spherical shell with initial damage was simulated by computernumerical emulation under nonlinear forced vibration. And it was founded that theinitial damage makes the chaos motion of the system easily occur.(5) As the lattices had sensitive to the initial imperfection, this dissertation tookaccount of structure imperfections and phycisal imperfection. The lattices with twoimperfections were frail to collapse under rainstorm, blizzard and earthquake. So anonlinear dynamic model of the lattices with coupling the intial imperfection and initialdamage was obtained to reveal the plenty dynamics characteristic.(6) The nonlinear dynamical stability of the lattices with initial damage wasanalyzed by the method of catastrophe. Firstly, potential function?of the globecharacter was obtained. Then the static and dynamic cusp catastrophic model of thesystem was given separately. The equilibrium state of the system was dissussed.