缓倾斜弹性薄板顶板力学模型分析

Analysis of Mechanical Model of Slow Inclined Elastic Sheet

针对缓倾斜顶板稳定性分析问题,基于三维模型进一步分析在一定倾角以及受非均布荷载情况下顶板的破坏规律。根据弹性薄板小挠度理论对缓倾斜顶板建立不同边界条件下的薄板力学模型,分别对四边固支薄板、两边固支两边简支薄板以及四边简支薄板模型进行力学分析,运用伽辽金法计算各薄板力学模型的挠度公式,并求出相应弯矩以及应力解。运用MATLAB软件绘出工程实例的挠度曲线和弯矩曲线,分析得到顶板应力分布特征以及破断机理。结果表明,顶板形成“长边—短边—中部”的破坏机制,由整体破坏过程来看,也可看作顶板形成“O-X”型的破断模式,可为缓倾斜顶板支护以及顶板破断机理分析提供了理论依据。

Aiming at the stability analysis of the gently inclined roof,the failure law of the roof under a certain inclination angle and non-uniform load is further analyzed based on the three-dimensional model.According to the small deflection theory of elastic thin plate,the mechanical models of thin plate under different boundary conditions are established for the gently inclined roof.The mechanical analysis is carried out for the four fixed sides,the two fixed sides and two simply supported sides thin plate and the four simply supported sides thin plate models respectively.The deflection formulas of each thin plate mechanical model are calculated by Galerkin method,and the corresponding bending moment and stress formulas are obtained.The deflection and bending moment curves of the engineering example are drawn by using MATLAB software,and the stress distribution characteristics and breaking mechanism of the roof are obtained through analysis.The results show that the failure mechanism of"long side-short side-middle"formed by the roof can also be regarded as the"O-X"failure mode formed by the roof from the perspective of the overall failure process,which can provide a theoretical basis for the analysis of gently inclined roof support and roof failure mechanism.