双模量矩形板的大挠度弯曲计算分析

LARGE DEFLECTION BENDING CALCULATION AND ANALYSIS OF BIMODULOUS RECTANGULAR PLATE

双模量矩形板在外载荷作用下,会形成各向同性的拉伸区和压缩区,把双模量矩形板看成两种各向同性材料组成的层合板,采用弹性力学理论建立了双模量矩形板在外载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量矩形板的中性面位置,推导出了双模量矩形板的大挠度弯曲变形微分方程。用加权残值法求得了双模量矩形板的大挠度弯曲变形时板中点挠度,把该方法计算结果与有限元计算结果进行了比较,说明了该计算方法是可靠的,并讨论分析了双模量对矩形板大挠度弯曲变形的影响。

A bimodulous rectangular plate could form an isotropic compression and a tensile area under external loads. Thusly, a bimodulous rectangular plate was regarded as a laminated plate composited of two kind of isotropic material. The static equilibrium equation of the bimodulous rectangular plate under the condition of external loads was established by using elastic mechanics theory. The location of the neutral plane in the bimodulous rectangular plate was determined by the utilization of static equilibrium equations. The large deflection bending deformation differential equations of the bimodulous rectangular plate was derived, and the middle point deflection of the bimodulous rectangular plate was gained with method of weighted residuals. Then the calculation results were compared with that obtained by finite element method, and it show that the method above is reliable. Meanwhile the effect of the bimodulous on the large deflection bending deformation of a rectangular plate was discussed and analyzed.