Study On Large Deflection Problem Of Circular Membrane Under Axisymmetric Linearly-distributed Loads

Thin film has been found more and more applications in many fields, e.g., the useof thin film to improve and better the surface properties of materials in the advancedsurface treatment and coating systems. Structural reliability, stability and durability needto have a better understanding of the mechanical behavior of these thin film structures.However, the mathematical equations of membrane problem usually has a strongnon-linear, making it difficult to obtain its accurate analytical solution, generally onlynumerical solution can be obtained. At present, there are only a few analytical solutionsof circular membrane problems, and this situation affects the application of thin film insome fields of engineering.This thesis completely solved the problem of large deflection of circular membraneunder the action of axisymmetric linearly-distributed loads based on the existinganalysis works of the problem of large deflection of circular membrane: using largedeflection theory of thin-film to establish the membrane equation, and the completeanalytical solution is given in accordance with the pending constant(B) of themembrane equation may has three cases(B0, B0, B0) in the range of real number,using an intermediate parameter1and a control parameter, adopting the shootingmethod to numerically solve the intermediate variables and the integration using anintermediate parameter1and a control parameter, and a series of typical charts thatreflect the function relationship among parameters concerned are given; We obtain theanalytical solution of “Concentrate problem” by the limiting form of analytical solutionof the problem of large deflection of the circular membrane fixed at its edge under theaction of axisymmetric linearly-distributed loads. In addition, the correctness of theanalytical solution is proved by a confirmatory test. This analytical solution can be usedfor the research of mechanical properties testing of surface and interface, and this papermainly discuss the measurement of interface adhension of membrane-substrute andsimultaneous measurement of Young’s modulus of elasticity and Posisson’s ratio of thinfilm materials.Thesis consists of seven Chapters: the introduction, basic theory, the researchstatus of the problem of large deflection of the circular membrane fixed at its edge, theproblem of large deflection of the circular membrane fixed at its edge under the actionof axisymmetric linearly-distributed loads, confirmatory test, the application of the research results of this thesis, and conclusions of this thesis and prospects of futureresearch.The exact analytical solution obtained by this thesis, not only further promote thedevelopment of theoretical research of circular membrane, but also provide themechanical model and theoretical formulas for the engineering application of thin filmtechnology, making the analysis of test with a more accurate theory.