轴对称圆板(含叠层板)的三维非线性分析

江晓禹; 张相周

轴对称圆板(含叠层板)的三维非线性分析

西北工业大学强度所西安

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出版历程
- 收稿日期: 1991-11-28
- 刊出日期: 1993-08-15

Nonlinear Three-Dimension Analysis for Axially Sym-metrical Circular Plates and Multilayered Plates

Northwestern Polytechnical University, Xi'an

摘要

摘要: 本文提出了轴对称固支圆板(含叠层板)受均布横向载荷作用下的三维非线性摄动解答.文中所考虑的是一种中等大挠度的几何非线性,并采用一种发展的摄动方法对复杂的三维非线性平衡微分方程进行求解.该方法的基本思想是以二维解答为基础,对板的厚度参数进行摄动而求得相应的三维解答.文中给出了一般板及叠层板的三维非线性理论结果及数值结果,并图示出了各个应力的分布情况.而且,该三维非线性结果能退化为完全一致的相应的二维板理论非线性结果.结果表明,该方法对板的三维非线性分析是一种行之有效的方法.
- 三维分析 /
- 几何非线性 /
- 摄动法 /
- 轴对称
Abstract: Analytic nonlinear three-dimension solutions are presented for axially symmetrical homogeneous isotropic circular plates and multilayered plates with rigidly clamped boundary conditions and under transverse load.The geometric nonlinearity from a moderately large deflection is considered.A developmental perturbation method is used to solve the complicated nonlinear three-dimension differential equations of equilibrium.The basic idea of this perturbation method is using the two-dimension solutions as a basic form of the corresponding three-dimension solutions,and then processing the perturbation procedure to obtain the three-dimension perturbation solutions.The nonlinear three-dimension results in analytic expressions and in numerical forms for ordinary plates and multilayered plates are presented.All of the plate stresses are shown in figures.The results show that this perturbation method used to analyse nonlinear three-dimension problems of plates is effective.
- three-dimension analysis /
- geometric nonlinearity /
- perturbation method /
- axially symmetry

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参考文献(8)

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[2]	B,B.诺沃日洛夫,《非线性力学基础》,朱兆祥译,科学出版社,北京(1958),20-80.
[3]	徐芝纶.《弹性力学》,上、下册,高等教育出版社,北京(1987).
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[5]	Nayfeh,A.H.,Introduction to Perturbation Techniques,John Wiley and Sons(1981),40-100.
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[7]	Ahmed,K.Noor and W.Scott Burton,Three-dimensional solutions for antisymmetrically laminated anisotropic plates.ASME J.Appl.Mechanics.,57(1990),182-188.
[8]	江晓禹,复合材料层合板壳的三维线性及非线性,静力及动力分析,西北工业大学博士学位论义(1992).