固支边界的矩形板在横向载荷作用下弯曲问题的解及其应用

鉴于用文献方法求解固支矩形板横向弯曲问题时计算量大且难以理解,本文提出了一种以上述方法为基础,但较之简单的计算方法,在各向同性板中得到了文献相吻合的结果后,进一步应用到正交各向异性材料中,得到大量计算结果。另外,在各向同性介质中,平面热应力问题与弯曲问题是可以相互比拟的。将这种比拟推广到正交各向异性介质中去,可以由弯曲问题的解求得平面热应力问题的解。

SOLUTION METHOD OF THE LATERAL BENDING PROBLEM OF CLAMPED PLATE AND ITS APPLICATION

The present paper is concerned with the lateral bending problem ofrectangular plate with four sides clamped under the uniformly distributed load. To solve this problem, a new superposition method is developed, which is considerably simpler than, but based on the similar method developed bv S. Timoshenko. A series of satisfactorily calculated solutions of isotropic plate and orthotropic plate are obtained by using the new method. Furthermore, by means of the analogical characteristics between the thermal problem in an orthotropic medium and the lateral bending problem of clamped orthotropic plate, the thermal stresses can straightforwardly be obtained from the bending moments of the orthotropic plate which has the same shape as the section of the orthotropic body in the thermal problem, and vice versa. As examples, numerical solutions to a rectangular plate are listed.