变厚度圆薄板非对称非线性弯曲问题  

Unsymmetrical Nonlinear Bending Problem of Circular Thin Plate With Variable Thickness

作　　者：王新志[1] 赵永刚[1] 踞旭 赵艳影[1] 叶开沅[1] 

机构地区：[1]兰州理工大学理学院,兰州730050

出　　处：《应用数学和力学》2005年第4期386-393,共8页Applied Mathematics and Mechanics

基　　金：甘肃省自然科学基金资助项目(ZS021_A25_007_Z)

摘　　要：　首先将直角坐标系中的横向变厚度薄板的大挠度方程,转化到极坐标系中的变厚度圆薄板的非对称大挠度方程·　此方程和极坐标系中径向、切向两个平衡方程联立求解·　将物理方程和中面应变非线性变形方程,代入3个平衡方程,可得用3个变形位移表示的3个非对称非线性方程·　用Fourier级数表示的解代入基本方程,获得相应的基本方程·　在周边夹紧边界条件下,用修正迭代法求解·　作为算例,研究了余弦形式载荷作用下的问题,还给出了载荷与挠度的特征曲线,曲线依据变厚度参数变化而变化。Firstly, the cross large deflection equation of circular thin plate with variable thickness in rectangular coordinates system was transformed into unsymmetrical large deflection equation of circular thin plate with variable thickness in polar coordinates system. This cross equation in polar coordinates system is united with radical and tangential equations in polar coordinates system, and then three equilibrium equations were obtained. Physical equations and nonlinear deformation equations of strain at central plane are substituted into superior three equilibrium equations, and then three unsymmetrical nonlinear equations with three deformation displacements were obtained. Solution with expression of Fourier series is substituted into fundamental equations; correspondingly fundamental equations with expression of Fourier series were obtained. The problem was solved by modified iteration method under the boundary conditions of clamped edges. As an example, the problem of circular thin plate with variable thickness subjected to loads with cosin form was studied. Characteristic curves of the load varying with the deflection were plotted. The curves vary with the variation of the parameter of variable thickness. Its solution is accordant with physical conception.

关 键 词：变厚度 非对称 修正迭代法 挠度 

分 类 号：O322.5[理学—一般力学与力学基础] O326[理学—力学]