The analytical solution of the bending problem for a clamped rectangular plate with a variable in-plane stiffness is found by using the method of superposition. The flexural rigidity of the plate varies across its width according to an exponential function. First, the analytical solution for a simply supported rectangular plate with a variable in-plane stiffness is obtained, and then the bending problem for the plate clamped at its four edges is solved analytically by the superposition of one simply supported plate under the transverse load and two simply supported plates under pure bending. The influence of the variable in-plane stiffness, aspect ratio, and different boundary conditions on the deflection and bending moment is studied by numerical examples. The analytical solution presented here may be helpful for the design of rectangular plates with a variable in-plane stiffness.

通过叠加方法，求出了平面内刚度变化的矩形板的弯曲问题的解析解。板的抗弯刚度根据指数函数在其整个宽度上变化。首先，获得平面内刚度可变的简单支撑矩形板的解析解，然后通过在横向载荷和力的作用下叠加一个简单支撑的板，以解析方式解决夹在其四个边缘处的板的弯曲问题。纯弯曲下的两个简单支撑的板。通过数值算例研究了可变的面内刚度，纵横比和不同的边界条件对挠曲和弯矩的影响。