轴对称圆板(含叠层板)的三维非线性分析

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

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.

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 solvs the complicated nonlinear three-dimension differential equations of equilibrium. The basic idea of this perturbation method is using the two-dimensional solutions as a basic form of the corresponding three-dimension solutions, and then processing the perturbation procedure to obtain the threa-dimension perturbation solutions. The nonlinear three-dimension results in analytic expressions and in numerical forms for ordinary plates and multilayered plates are presented. Each of the plate stresses is shown in figurss. The results show that this perturbation method used tojanalyse nonlinear three-dimension problems of plates is effective.