Unsymmetrical Nonlinear Bending Problem of Circular Thin Plate With Variable Thickness
-
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,其结果和物理概念完全吻合.Abstract: 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 unsym-metrical 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.
-
Key words:
- variable thickness /
- unsymmetrical bending /
- modified iteration method /
- deflection
-
[1] 叶开沅,刘平.非均匀变厚度圆盘的定常热传导[J].应用数学和力学,1984,[STHZ]. 5[STBZ]. (5):619—624. [2] 叶开沅,刘平.在定常温度场中非均匀变厚度高速旋转圆盘等强度的计算[J].应用数学和力学,1986,7(9):769—778. [3] 王新志.变厚度圆薄板在均匀载荷下的大挠度问题[J].应用数学和力学,1983,4(1):163—112. [4] 王新志,王林祥.边缘载荷下变厚度环形板大挠度问题[J].应用力学学报,1986,3(1):91—94. [5] 王新志,王林祥,徐鉴.圆薄板非轴对称大变形问题[J].科学通报 ,1989,34(1):1276—1277. [6] 王新志,王林祥,洪小波,等.圆薄板非轴对称大变形位移解[J].自然科学进展,1983,3(2):133—144. [7] 王新志,任冬云,王林祥,等.扁薄球壳非轴对称大变形问题[J].应用数学和力学,1996,17(8):669—683. [8] 王新志,赵永刚,叶开沅.扁薄锥壳非轴对称大变形问题[J].应用数学和力学,1998,19(10):847—857. [9] 王新志,赵永刚,叶开沅,等.正交各向异性板的非对称大变形问题[J].应用数学和力学,2002,23(9):881—888.
计量
- 文章访问数: 3048
- HTML全文浏览量: 168
- PDF下载量: 559
- 被引次数: 0