初次断裂前矩形顶板的差分解

Difference analysis of the rectangle flat roof before the first falling

给出弹性地基四边夹支平板简化模型,分析初次跨落前顶板的受力机理。采用小挠度弯曲理论的微分方程,建立简化模型的边界条件,用差分法求解方程,并给出算例。结果表明:老顶顶板从中心点开始破坏,破坏沿平行于长边中心线向两边传播。当中心部位破断冒落后,破坏以"O"形向外传递。此结果与已有结论[2]一致,说明差分法可用于顶板破断分析。为"O"形圈理论和顶板来压预报提供了新的理论证据。

The paper gives a simplified model of flat panel with four sides fixed on a flexible foundation and analyzes the mechanic regularity of flat roof before the first falling. The minor deflection bending theorem is used to set up the differential equation and boundaries condition. After deriving the difference equation and analyzing the boundary condition,this paper provides one numeric example. The result shows that the main roof starts to break from the central point, with the break spreading to both sides along the central line parallel with the long side. When the central part breaks and then drops, the break will spread outwardly in the form of 'O'. The result is consistent with the existed conclusion,which proves that the method can be used for analyzing the first break of the main roof, and gives new theory evidence for theory of 'O' and forecasting the first break of the main roof.