General Theory And Its Practice Of Axisymmetric Deformation Of Annular Membrane

The film has been widely applied in many fields. Structural stability, reliability anddurability need to have a better understanding of the mechanical behavior of thesethin-film structures. As the thickness of the film is very thin, the deformation of thinfilm structure is usually with a strong nonlinear under the action of load, and thus itsanalytic study is usually more difficult. Axisymmetric deformation of the clampedcircular thin film under transverse loads, so far, has only four relatively matureanalytical research works:①the axisymmetric deformation of clamped circular thinfilm under the action of transverse uniform load, referred to as "the circular membraneproblem";②the axisymmetric deformation of circular thin film centrally connected to arigid plate under the action of centrally transverse concentrated load, referred to as “theannular membrane problem”;③the axisymmetric deformation of clamped circular thinfilm under the action of transverse local uniform load at its center, referred to as “thecircular-annular membrane problem”;④the axisymmetric deformation of clampedcircular thin film under the action of centrally transverse concentrated force, referred toas "the concentrated force problem". These classic theoretical works have laid animportant theoretical basis for the effective application of the thin-film structures.However, only “the circular membrane problem” has been given a complete analyticalsolution, while the remaining three problems only have been given a partial analyticalsolution. Therefore, it is necessary to do further research work to improve them.Our topic choses to study the deformation of circular thin film centrally connectedto a rigid plate under the action of centrally transverse concentrated load, using largedeflection theory of thin-film to establish the membrane equation, in accordance withthe pending constan(B) of the membrane equation may has three cases(B＞0, B=0, B＜0) in the range of real number, using an intermediate parameter1and acontrol parameter, adopting the shooting method to numerically solve the relateparameters of the membrane equation, and finally give a complete analytical solution ofthis problem. Moreover, In order to facilitate the practical application, base on a largenumerical calculations, this paper gives typical diagrams corresponding functionrelationship of all pending parameters and Poisson’s ratio(ν=0.1~0.6).In addition, weuse the complete analytical solution to derive the complete analytical solution of the"the concentrated problem ".In order to reflect the actual value of the theoretical research, as to the delamination study of film-substrate system in blister test、the measurement ofmembran-membrane or membrane-substrute interfacal adhension in the field ofbiomedical engineering、the simultaneous measurement of Poisson’s ratio and Young’smodulus of elasticity of thin film materials、and the development of capacitive pressuresensor and so on.The thesis mainly consists of six chapters: the introduction, basictheory, the general theory of the annular membrane, results and analysis, the practice ofanbular membrane, conclusions and outlook.“The annular membrane problem” and "the concentrated force problem", havecontributed to improve the classical theory.