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LIU Wen
College of Science,
Yanshan University,
Qinhuangdao 066004, China
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MATHEMATIC MODEL AND ANALYTIC
SOLUTION FOR CYLINDER SUBJECT
TO UNEVEN PRESSURES
Abstract:
According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surfaces of cylinder. When borderline condition that is predigested according to the Saint-Venant’s theory is joined, an equation suit is constructed which meets both the biharmonic equations and the boundary conditions. Furthermore, its analytic solution is deduced with Matlab. When this theory is applied to hydraulic bulging rollers, the experimental results inosculate with the theoretic calculation. Simultaneously, the limit along the axis invariable direction is given and the famous Lamè solution can be induced from this limit. The above work paves the way for mathematic model building of hollow cylinder and for the analytic solution of hollow cylinder with randomly uneven pressure.
Key words:
Cylinder Analytic solution Cubic function distributed pressure Stress function Biharmonic equations
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