正交各向异性板的非对称大变形问题

基金项目: 甘肃工业大学科研基金(92114)

Unsymmetrical Large Deformation Problem of Orthotropic Plates

1.
Department of Basic Science, Gansu University of Technology, Lanzhou 730050, P. R. China;
2.
Physics College, Lanzhou University, Lanzhou 730050, P. R. China

摘要: 从各向异性板的基本理论出发,推导出正交各向异性圆板的非对称大变形基本方程,利用Fourier级数把问题的偏微分方程转化为一组可积分求解的非线性常微分方程,并给出利用迭代法求解该问题的基本方法.
- 正交各向异性 /
- 圆薄板 /
- 非对称 /
- 大变形 /
- 迭代法
Abstract: Based upon the theory of anisotropic plates, the unsymmetrical large deformation equations of orthotropic circular plates were derived. By using Fourier series, the partial differential equations of this problem can be transformed into sets of non-linear differential equations. And the procedure to solve the problem using the iterative method is given.
- orthotropic /
- circular thin plates /
- unsymmetrical /
- large deformation /
- iterative method

[1]	刘人怀.夹层圆板的非线性弯曲[J].应用数学和力学,1981,2(2):173-190.
[2]	刘人怀,施云方.夹层圆板大挠度问题的精确解[J].应用数学和力学,1982,3(1):11-24.
[3]	王震鸣,刘国玺,吕明身.各向异性多层扁壳的大挠度方程[J].应用数学和力学,1982,3(1):49-65.
[4]	Chia C Y.Geometrically nonlinear behavior of composite plates[J].A Review Appl Mech,1988,41(12):439-451.
[5]	尹帮信.复合材料多层板壳大挠度非线性问题的迭代解[J].应用数学和力学,1999,20(7):721-728.
[6]	王新志,王林祥,徐鉴.圆薄板非对称问题[J].科学通报,1989,34(16):83-85.
[7]	王新志,王林祥,洪小波,等.圆薄板非轴对称大变形的位移解[J].自然科学进展,1993,3(2):133-144.
[8]	王新志,任冬云,王林祥,等.扁薄球壳非对称大变形问题[J].应用数学和力学,1996,17(8):667-684.
[9]	叶开沅,刘人怀,李思来.在对称线布载荷作用下圆底扁薄球壳的非线性稳定问题[J].兰州大学学报(自然科学),1965,18(2):10-33.
[10]	YEH Kai-yuan,WANG Xin-zhi.Modified iteration method in the problem of large deflection of thin circular plates with nonuniform thickness[A].In:Chien Wei-zang Ed.ICNM-I[C].Shanghai:Science Press,1985,398-403.