缓倾斜薄板初次破断与周期破断运移规律分析

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关键词：倾斜薄板；运移规律；最小势能原理；MATLAB；力学模型

中图分类号：TD313 文献标志码：A 文章编号：1005-8249（2026）02-0085-09

DOI：10.19860/j.cnki.issn1005-8249.2026.02.014

Analysis of Movement Laws for Initial and Periodic Fractures in Gently Dipping Thin Plates

GUO Yanhua’，LI Yifan1，HAN Xiangang¹，WANG Chao （1. Hebei University of Engineering School of Civil Engineering，Handan O56038，China; 2. Jinan Cultural & Tourism Development Group Co.，Ltd.， Jinan 25OoOO，China）

Abstract：Inorder tosolvetheproblemofthemigrationlawofinclinedsheet，basedonthethree-dimensional model，the migrationlawof theinitialandperiodicbreakingoftheroofundertheconditionofcertaininclinationangleandheterogeneous loadisanalyzedindepthAccordingtothetheoryofminimumdeflectionofthinplateandWinkel’shypothesis，themechanical modelof inclinedthinplateunderdiferentboundaryconditionsisestablised，andthemechanicalanalysisoftheinitialand periodic breaking models iscariedoutrespectively.UsingtheprincipleofminimumpotentialenergyandWinkel’shypothesis， thedeflectionformulasofthetwo mechanicalmodelsarederived，andthecorresponding bending momentsand stressesare calculated.The deflection curve，bending moment curveand stresscurve of the engineering example are drawn by MATLAB software，andthemigrationlawof themaximumprincipal stress oftheinclinedshtwiththeadvancementoftheworking face andthe position ofthe maximum deflection pointareobtained.Theresultsshow that the maximum deflectionpointof the inclined sheet moves upwards compared with the horizontal sheet，and the bending moment ∣Mx∣>∣My∣ is also greater thanthebendingmomentinthecenterof therof，whichcauses thelongsideoftheroftoreachtheultimatebending moment andbegin tofail.Further analysis shows thatthe principal stresson theupperand lowersurfacesof therof presents the distribution characteristics of σxmax>σymax ，and the maximum principal stress on the upper surface is located near the long side region.Thisstudyprovidesaniportanttheoreticalbasisfortheanalysisoftheworkingresistancecharacteristicsofthescaold during the periodic breaking process.

Keywords：inclined thin plate；migration patern；principleof minimum potential energy；MATLAB；mechanical model

0 引言

顶板事故长期以来被视为采矿过程中风险较高的突发性灾害，无论是周期破断还是初次破断，都会直接影响矿井的安全性和作业效率。（剩余4257字）