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通过在顶板变形规律与受力特征的研究中引入弹性力学薄板理论,依据各阶段受力特征的不同,建立并完成了4种力学模型的求解。运用薄板理论的平衡微分方程求解问题转化为关于节点挠度的矩阵计算问题,然后运用Matlab软件求解差分法建立的矩阵,最后,运用编写的Visual Basic计算程序实现内力的求解。依据计算结果,预测了各种模型下薄板破断位置与破断特征。
Through the introduction of the theory of elastic mechanics sheet in the study of deformation law and force characteristics of roof, four kinds of mechanical models are established and completed according to the different stress characteristics of each stage. Using the theory of balance sheet differential equations to solve the problem, the problem of matrix deflection is transformed into the matrix calculation problem of node deflection. Then the Matlab software is used to solve the matrix established by the difference method. Finally, the calculation of internal force is realized by using Visual Basic program. According to the calculation results, the breaking position and breaking characteristics of the thin plate under various models are predicted.