一种正交各向异性板的等效各向同性板计算法

上、下表面平整的正交各向异性板的有效抗扭刚度是2个主方向抗弯刚度的几何平 均值. 根据这一特性、从正交各向异性板挠曲面的偏微分方程出发，保持一个主方向尺寸不变， 另一主方向的尺寸做线性缩放，保持弹性模量与第一主方向相同，泊松比取2个主方向泊松 比的几何平均值，将这类正交各向异性板等效为一块各向同性板；通过分析得到：各向同性 板任意点的挠度就是原正交各向异性板对应点的挠度，各对应点内力之间存在简单的比例关 系，该文的方法将为工程技术人员提供方便，同时可以更加直观的认识正交各向异性板的受 力.

ANALYSIS METHOD OF A KIND OF ORTHOTROPIC PLATES BY EQUIVALENT ISOTROPIC PLATES

The effective torsional rigidity is equal to the geometric mean of two principal bending rigidities, as is characteristic of the orthotropic plates with smooth up and down surfaces. According to that characteristic and based on the differential equation of the deformed surface of the orthotropic plate, with one principal direction size fixed, changing another principal direction size linearly, maintaining elasticity coefficient the same as in the first principal direction and Poisson ratio equal to the geometric mean of two principal Poisson ratios, the original orthogonal plate is equivalent to an isotropic plate. Results obtained show that the deflections of the equivalent isotropic plate are the same as the deflections of the original orthotropic plate at the corresponding points, the forces of the correspondent points have simple relations. The method of the paper will be easy to use for engineers and technicians.