Buckling analysis of the shell of a refuge chamber in a coal mine under uniform axial compression

Intemational Jourmal of Mining Science and Technology 22(2012)85-88Contents lists available at Sciverse Science Direct8" 9 International Journal of Mining Sciend technologyELSEVIERjournalhomepagewww.elsevier.com/locate/iimstBuckling analysis of the shell of a refuge chamber in a coal mine under uniformaxial compressionFang Haifeng" Ge Shirong, Cai Lihua, Hu eryiSchool of Mechanical and Electrical Engineering China Uriversity of Mining 6 Technalogy. Xuzhou 221116, ChinaARTICLE INFOA BSTRACTA stiffened cylindrical shell is normally used in refuge chambers of a coal mine Based on the method ofReceived 20 Apnl 2011pplication and shape characteristics of a refuge chamber, we simplified its shell as an orthotropic cylineived in revised form 12 May 2011der the basic buckling equation of the stiffened cylindrical shell under uniform axial compression wAvailable online 9 March 2012deduced by using a Donnel! function. The factors affecting its buckling capacity were studied by theoretcai analysis and numerical calculations. The results reveal that the torsional rigidity of the longitudinstiffener had little effect on the bucking capacity of the shell and that the critical load of an extermallystiffened cylindrical shell is higher than that of an intemally stiffened cylindrical shell.a 2012 Published by Elsevier B, V, on behalf of China University of Mining Technology.stiffened cylindrical she1 Introductionprocess of thin elastic cylindrcal shells under symmetrical axialmpression and suggested an elal formula for bucklingn China, the security situation of coal mines is under severe stress in cylindrical shells subject to axial compreess because of complex terrain,geological conditions of 111-16 More recently, plastic buckling and post-buckling of thincoal beds. the large number of gas containing coal mines and the cylindrical shells under axial compression have been studied.frequent accidents of gas explosions, water bursts, fires and roofand Anhobtained a numerical elastoplastic solution forcollapses [1-6. According to investigations into mine accidentsand post-buckling of thin shells [17 The most importantin a number of countries. more miners have been killed by a severefecting stiffened plates and shells has been analyzed byoxygenhunger and thirst after accidentsthe buckling deformation patten of these structures onthan by direct damage of gas explosions and fires. Therefore, in combined loads(18-20 Given the method of application andorder to offer a safe and airtight space for distressed miners, these shape characteristics of refuge chambers in coal mines. their shellscountries have been energetically studying coal mine refuge cham- were simplified as orthotropic cylinders. The basic buckling equa-bers [7-10)tions of stiffened cylindrical shells under uniform axial compres-The shell is a very important module of a refuge chamber, which sion were deduced by using a Donnell function. we studied theshould have strong impact resistance and a high level of security. factors affecting their buckling capacity by theoretical analysisiffened cylindrical shells are normally used in coal mine refuge and numerical calculations.chambers. Critical stress in buckling of stiffened shells is muchgher than that of non-stiffened shells of equal quality. In orderto reduce the impact of gas explosions on refuge chambers, these 2. Theoretical analysischambers are always placed in pre-existing underground cham-bers. Therefore, the lateral pressure and shear stress to whichOnly the end of a shell would be subject to the impact of theshells are subject are very small and only the buckling problem explosion when gas explosions occur. Circumferential stiffenersof stiffened cylindrical shells under uniform axial compression only can act as a support for the boundary. Therefore, a cylindricalshould be under discussion. Theoretical and experimental research shell with longitudinal stiffeners was applied in the design of theon buckling of thin shells has been studied at a relatively early shell of a refuge chamber. The frame of the axes is shown in Fig. 1stage. Some investigators have studied the overall deformationThe surface of the shell in the middle was set as the coordinatesurface xy. The z axis, in the direction of the center curvature, isI is the length ofesponding author. Tel: +86 13645stiffenV凵中国煤化工rature and h the thickailaddress:fhf@cumtedu.cn(HFaCNMHGe longitudinal stiffener095-2686/ see front matter e 2012 Published by Elsevier B, V, on behalf of Chln University of Mining Technologyk:10.1016jmst201106008H Fang et aL/mtemarional Journal of Mining Science and Technology 22(2012)85-88rrelitable values forresults indicate that KN can reach this minimum whennder uniform axial compression. Therefore, when心1. Diagram of modeLwe take m as 1 and g as n/B, Eq (5)can be expressed as follows:K=男+2(1+40g2+g2+1(+g)-the distance between stiffeners. the shell of the refur was simplified as an orthotropic cylinder The basic buckAssuming g to be an approximately continuous variable, theling equations of a stiffened cylindrical shell under uniform axial minimum condition of this equation is ak,2)=0. Thereforecompression were derived by using a Donnell function with simplethe following equation can be obtained:supported ends. The equation can be written as:K1=e(-u+g2)+v+b(9+原“-b(12R ax2xe+20+2814+g)-where:v=+壽=酃+孬+凯v=The expression for KN is obtained, when g is eliminated bysubstituting Eq(7)into Eq(6). It follows that KN is not a function+十飄昌,n=1+晶-a5y=舞ofB1yJ=面b=1+Fthe elastic modulus, D= ofma- the bending stiffness of the shell 3. Numencal computational analysisand v Poisson's coefficient. I= JA zdA is the moment of inertia ofthe longitudinal stiffeners to the center curvature of the shell and eters ie a& ly alde s above there are four independent param-Based on the analysiis a function of By. but not an indeperS=AzdA. the static moment of longitudinal stiffeners to its center dent parameter. The effect of these parameters on the criticalcurvature. G is the moment of shear elasticity and j the moment of buckling load is discussed by means of a numerical computation.twist inertia of the longitudinal stiffeners. A free torsional formula The computational results of &or0 and &0=0.006 are compared inwas used in the calculation of the stiffeners The simple support Table 1. The differences are all less than 5%. In general, o is lesstions are given bythan 0.006 for the stiffeners of the thin-walled open section beam=M=N=D=0,X=0,l(2) Therelore. the effect of the torsional rigidity of the longitudinalto be oAssuming the buckling displacement function to be a double trian-gular series, we can express this as:are considered te be s and o3 resp ined .poissonsto the variable nx to the left side of the equation, the following3) equations are obtained.number in axial direction and n the wave Km-,-+2+d+ Mt2)-%srnumberparameteial direction. The following dimensionless K=6-0.3+g)+t-fa c quad x(4+2(6+28, 8 (1 +g)-]The computation is conducted based on the common ranges forB-T,e,",the parameters ey, ey and g. The allowable range for the parameterey is(0, 1), for the parameter ey this range is [-10, 10) and for theparameter g it is 1,3l. which is taken as the discrete integers 1.212(1-2)弓-Vb°Va+71+(-p)dm2and 3. The relationships of KNo -na. e and ey are shown inFig. 2. These diagrams show that the critical buckling load in-creases with a decrease in the value of the independent parameterKI=pRVD2)1+y)Pey(ey>0 for internal stiffened shells, e, <0 for external stiffenedRhened shell is higher than that of the internal stiffened shell underEq(4)is obtained by substituting Eq(3)into Eq(1), shown as uniform axial compression.follows4. Simulation results,p,,哪::m(4 of the eder to oma are the r sites el che s w ta tie haraeteastics.eterss中国煤化工 software. The structuralACN MH Gulations and simulationThe critical buckling load of the shell under uniform axial compres- results presented ir Table 3. This proves thatsion can be obtained by solving this equation.the method to compute the critical buckling load is correct, whichH. Fang et aL/Intemational Joumal of Mining Science and Technology 22(2012)85-88Table 1Effect of torsional rigidity of stiffeners on KNK1=20K1=100K1=400ey·13nx5087ey=16nx-50131ey=09nx100b=0006b=0Difference (zey-15nx:100b0·0006b0=0Difference(寫3%13F30(b)g=22. Relations between KN, -nr By and eyTable 2Structural parameters of stiffened cylindrical shell.(2)The critical buckling load of an external stshell isgher than that of an intermal stiffenedaxial compression. Therefore, externalshould be used in the design of refuge chambers.I (mm)AcknowledgmentsComparison of theoretical calculations and the simulation results of the buckling load.The authors would like to thank the engineering technicians ofenforcement method Theoretical(kN) Simulation(kN) Difference (3)the wuxi Baoshen Mine Safety Equipment Factory for their de-Extemalvoted help. Financial support from the National Hi-tech ResearchInternal1622620and Development Program of China is much appreciateshowed excellent agreement with the results of our numerical sim-ReferencesIt also shows that the critical buckling load of the externald shell is higher than that of the internal stiffened shell un- [11QSR, Wang YS. Research status of the disaster rescue robot and its2ui YL Failure analysis of air fan blades. J China Univ Min5. Co3 ion for an s uper- urgenin d highly ass mine inchina niy Min TechinGiven the method of application and shape characteristics of a [4] Fang HF. Ge SR, L Yw Obstacle performance analysis of four-track robotrefuge chamber of a coal mine its shell was simplified as an ortho-tropic cylinder. The basic buckling equations of a stiffened cylindri[51 Liang YT. Analysis of reaction kinetic for gas explosion in enclosed space. Jcal shell under uniform axial compression were deduced by using aDonnell function. Based on a theoretical analysis and numerical [6] Yang RS. Yue Zw, Dong JC dynamics experiment of blasting crackcalculations, we draw the following conclusions.中国煤化工 ning intelligent response(1)The torsional rigidity do of longitudinal stiffeners has littleeffect on the critical buckling load of a stiffened shell; theaccidents in ourdifferences were all less than 5%. therefore, the effect of tor-CN MH GoI (n Chinese9) Lin BQ Chang JH, Zhai C Analysis on coal mine safety situation in China and itssional rigidity of longitudinal stiffeners can be neglected.rmeasures. China Saf Sci J 2006: 16(5): 42-6[ In ChineseH. Fang et al/ intemational Joumal of Mining Science and Technology 22(2012)85-88[10] Mu Z Dou UM, Ni XH. Research on the influence of roof strata on rock burst [16] Zhang SY. Zhang T Axial dynamic buckling parametric resonance and chaoticction of a closed cylindrical shell J Vib shock 2010: 29(12):34-8[12] Zhu EC Calladine CR Buckling of thin cylindrical shells under locally axial 11819]Sh114) Zhu pr ssion J Harbin Univ Civil Eng Archit 2000: 33: 12-5ression and bending. J Construct Steelin cylindrical shells [20] Tan ML Wu G. Buckling analysis of rectangular thin plates under parabolicer axial compression Chind Civil Eng J 2001:34: 18-2at edges in hamilton system. Chin Solid Mech115] Yang F. Qianng w]. Constit2010,31(153-8.nus with buckling considered at high temperatures. Mech Eng201032(6)27-32中国煤化工CNMHG