非线性变厚度圆薄板轴对称弯曲问题的变分解答  

Axisymmetric Bending of a Thin Circular Plate with Nonlinear Variable Thickness a Variational Solution

作　　者：张迅炜[1] 周建方[1] 徐吉良[1] 

机构地区：[1]河海大学机电工程学院,常州213022

出　　处：《机械设计与制造》2013年第9期137-139,共3页Machinery Design & Manufacture

基　　金：中央高校基本科研业务费专项资金项目(2009B30014)

摘　　要：基于能量原理,推导出均布载荷作用下变厚度圆薄板轴对称弯曲的变分列式,应用计算代数系统Mathematica编制程序,计算得到不同板厚参数下的挠度方程和最大挠度因子。结果表明,里茨法的计算过程易于实现程序化,计算精度高,在求解变厚度圆薄板小挠度弯曲问题时是有效的。与等厚度板相比较,变厚度板在弯曲刚度、抗屈曲和振动的性能等方面都有明显提高,因而在工程中得到广泛应用。变厚度圆薄板的厚度通常仅是半径的函数,并且受到的载荷关于板轴线对称,求解板的变形、内力、应力等即形成变厚度圆薄板轴对称弯曲问题。Based on the energy principle, the variational formulation of a uniformly-loaded thin elastic plate with variable thickness is deduced. With the help of the computational algebra system mathematica, the deflection function for the middle surface of the plate is solved. Then, the maximum deflection factors with the different thickness parameters are calculated separately. Results show that, due to its process easy to be programmed and high computational accuracy, the Ritz method is effective in solving the little deflection of a variable thickness circular plate.Compared with the plate with uniform thickness, varying thickness plate is obviously improved in bending stiffness, buckling and vibration resistance, etc,and therefore is widely applied in engineering. Usually the thickness of variable thickness circular plate is only the function of radius, and has the formation of variable thickness circular plate axisymmetrical bending problems such as symmetric relation with the axis of the plate by the load, solving plate deformation, internal force, stress, etc.

关 键 词：变厚度圆板 轴对称弯曲 里茨法 最大挠度因子 MATHEMATICA 

分 类 号：TH16[机械工程—机械制造及自动化] TG115.54[金属学及工艺—物理冶金]