正交各向异性木质平板在均布载荷下挠曲面的研究

胶合板、细木工板、刨花板等用作家具及木结构构件时的变形,可按正交各向异性平板理论进行理论分析,且用微分方程来描述。本文通过广义简支边法和直接求解法,对在均布载荷下,两对边简支,另两对边自由的正交各向异性平板弯曲微分方程的解进行了理论推导及分析。得出如下结论:①两种推导方法所得结果可变换成完全相同的表达形式;②不同条件下级数解的收敛速度均很快;③纠正了日本学者平岛义彦关于此问题研究的部分失误;④理论计算值与部分实测值之间尚存在一定偏差,有待于进一步研究。

STUDY ON THE BENDING SURFACE OF PERPENDICULAR HETEROGENEOUS WOODBASED PANEL UNDER UNIFORMLY DISTRIBUTED LOAD

Deformation of the plywood, joinery board, particle board and so on which were used in making furnitures and other wood structures could be analysed by using the theory of perpendicular heterogeneous panel and described by partial differential equation. In this paper, the rigorous solutions of partial differential equation of bending of perpendicular heterogeneous panel with two opposite edges simply supported and the other two free under an uniformly distributed load were deduced and analysed by broad sense simply supporting edges method and directly deriving solutions method. The conclusions are as follows: (1) The results of two kinds of deducing method can be written in the same form. (2)The convergence speeds of rigorous solutions in different conditions are all rapid. (3) Some errors from Japanese scholor Yoshihiko Hirashima have been corrected. (4) There are some errors between calculated values and observed ones. We should study in them continuously.