Mathematic Model and Analytic Solution for a Cylinder Subject to Exponential Function

作     者：LIU Wen SHAN Rui 

作者机构：College of Science Yanshan University Qinhuangdao 066004 China 

出 版 物：《Chinese Journal of Mechanical Engineering》 (中国机械工程学报（英文版）)

年 卷 期：2009年第22卷第4期

页      面：587-593页

核心收录：

学科分类：080704[工学-流体机械及工程] 08[工学] 0807[工学-动力工程及工程热物理] 

基　　金：supported by National Natural Science Foundation of China (Grant No. 50875230) 

主　　题：cylinder analytic solution distributed pressure in the form of exponential function stress function biharmonic equations 

摘      要：Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lam6 solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.