湖南大学桥梁结构仿真分析作业

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一、一根长度为150m的斜拉索,水平夹角为45°,截面0.0026m2,弹性模量为195000MPa,分析其索力在600kN至3600kN之间变化时(增量为200kN)索力与第一阶自振频率的关系曲线(边界条件按铰接考虑、不考虑垂度)。解:采用LINK10单元对斜拉锁进行模拟,拉锁分为100个单元。采用子空间迭代方法,计算一阶模态。有限元模型如下:图1斜拉索模型图通过ansys计算,索力与第一阶自振频率的关系曲线如图2所示:图2索力-频率关系曲线从上图可以明显观察到随着斜拉锁索力的增大,其刚度相应增大,振动频率增加。二、一跨径为6m等截面悬臂工字钢梁,采用下表中不同类型的工字钢,理想弹塑性材料本构关系,屈服强度为345MPa,加载模式如图所示,计算结构从开始加载一直到破坏的全过程曲线(要求给出荷载-跨中竖向位移曲线)。3mF3m图1(a)图1(b)表1工字钢截面参数表(mm)型号hbdtrr114140805.59.17.53.816160886.09.98.04.018180946.510.78.54.3解:采用beam189单元对工字钢梁进行模拟,为简化计算,截面形式采用ANSYS界面库中的H形截面模拟工字钢,上下翼缘厚度取相应工字钢的平均厚度。模型如下图所示:图3简支梁有限元模型14号工字钢计算结果:图414号简支梁Y方向变形图图514号简支梁X方向应力图图614号简支梁跨中荷载-位移曲线16号工字钢计算结果:图716号简支梁Y方向变形图图816号简支梁X方向应力图图916号简支梁跨中荷载-位移曲线18号工字钢计算结果:图1018号简支梁Y方向变形图图1118号简支梁X方向应力图图1218号简支梁跨中荷载-位移曲线从以上计算结果可以看出,当达到极限承载力时,工字梁跨中下缘应力均达到屈服强度。随着梁高的加大,极限荷载增大,但是跨中最大位移减小。三、一变截面桥墩,高80m、C30混凝土,墩底和墩顶截面布置如下图所示。要求分析其在墩顶作用活载竖向集中荷载20000kN下的特征值稳定安全系数和非线性屈曲(初始缺陷为10cm)稳定安全系数(要求给出荷载-位移曲线)。(用BEAM189单元)解:采用beam189单元对桥墩进行模拟,竖向共分为20个单元,考虑截面翘曲自由度。有限元模型如下图:图12桥墩模型图活载(本题中为集中荷载)的安全系数,需通过迭代获得。每次施加的荷载为上一次施加荷载与上一次所获得的freq的乘积,重复静力求解和特征屈曲求解,循环该步骤直至所求得的freq在一定误差内为1,此时施加的荷载数值等于稳定安全系数与集中力的乘积。弹性稳定安全系数计算结果见下图:图13桥墩变形图图14特征值稳定安全系数迭代计算结果由计算结果知在集中荷载20000KN作用下的特征值稳定安全系数为50.04,即当荷载为20000×50.04=1000800KN时,该桥墩失稳。施加10cm的初始缺陷后计算的结果如下图所示:图15荷载-位移曲线由荷载位移曲线可以看出,在初始缺陷为10cm的情况下,对该桥墩的稳定影响不大,在荷载达到弹性临界荷载之前,墩顶的侧向位移较小,而当荷载达到临界荷载时,位移急剧增大。命令流第一题/TITLE,VIBRATIONOFACABLEFINISH/CLEAR/PREP7ET,1,LINK10!前处理,定义单元和材料参数MP,EX,1,1.95E8MP,DENS,1,8.25*DIM,CSYB,ARRAY,16*DIM,F,ARRAY,16*DIM,FREQ,TABLE,16*DO,i,1,16!定义荷载加载步循环F(i)=600+(i-1)*200CSYB(i)=F(i)/0.0026/195000000*ENDDO*DO,j,1,16R,1,0.0026,CSYB(j)N,1N,101,106.066,106.066,0FILLE,1,2EGEN,100,1,1FINISH/SOLU!定义约束和求解类型ANTYPE,STATICD,1,ALLD,101,ALLACEL,0,10,0PSTRES,ONOUTPR,BASIC,1SOLVEFINISH/SOLU!模态分析,采用子空间迭代方法ANTYPE,MODALMODOPT,SUBSP,1MXPAND,PSTRES,ONSOLVE*GET,FREQ1,MODE,1,FREQ!输出索力频率曲线FREQ(j)=FREQ1*ENDDO*VPLOT,F,FREQ/AXLAB,X,F(kN)/AXLAB,Y,FREQ(HZ)第二题型号14/TITLE,beam14haoFinish/Clear/prep7span=6!定义截面b=0.08h=0.14t=0.0091d=0.0055P=26.798e3et,1,beam189keyopt,1,7,1mp,ex,1,2.06e11!定义材料属性mp,prxy,1,0.3tb,bkin,1!定义钢材破坏准则tbdata,1,345e6,0.0sectype,1,beam,i!建立模型secoffset,user,,hsecdata,b,b,h,t,t,dk,1k,2,span/2k,3,spank,100,span/2,span/2,0L,1,2$L,2,3latt,1,,1,,100,,1esize,0.1,0lmesh,alldk,1,ux!施加边界条件与荷载dk,1,uydk,1,uzdk,1,rotxdk,3,uydk,3,uz/eshape,1fk,2,fy,-Pfinishsave/solunsubst,15!求解outres,all,alsolveFINISH/POST1SET,LASTPLDISPPLNSOL,U,Y,0,1FINISH/post26!输出荷载位移曲线nsol,2,2,u,yprod,3,2,,,,,,-1000prod,4,1,,,,,,P/1E3/axlab,x,UY(mm)/axlab,y,F(kN)xvar,3plvar,4型号16/TITLE,beam14haoFinish/Clear/prep7span=6!定义截面b=0.088h=0.16t=0.0099d=0.006P=37.1e3et,1,beam189keyopt,1,7,1mp,ex,1,2.06e11!定义材料属性mp,prxy,1,0.3tb,bkin,1!定义钢材破坏准则tbdata,1,345e6,0.0sectype,1,beam,i!建立模型secoffset,user,,hsecdata,b,b,h,t,t,dk,1k,2,span/2k,3,spank,100,span/2,span/2,0L,1,2$L,2,3latt,1,,1,,100,,1esize,0.1,0lmesh,alldk,1,ux!施加边界条件与荷载dk,1,uydk,1,uzdk,1,rotxdk,3,uydk,3,uz/eshape,1fk,2,fy,-Pfinishsave/solu!求解nsubst,15outres,all,allsolveFINISH/POST1SET,LASTPLDISPPLNSOL,U,Y,0,1FINISH/post26!输出荷载位移曲线nsol,2,2,u,yprod,3,2,,,,,,-1000prod,4,1,,,,,,P/1E3/axlab,x,UY(mm)/axlab,y,F(kN)xvar,3plvar,4型号18/TITLE,beam14haoFinish/Clear/prep7span=6!定义截面b=0.094h=0.18t=0.0107d=0.0065P=48.91e3et,1,beam189keyopt,1,7,1mp,ex,1,2.06e11!定义材料属性mp,prxy,1,0.3tb,bkin,1!定义钢材破坏准则tbdata,1,345e6,0.0sectype,1,beam,i!建立模型secoffset,user,,hsecdata,b,b,h,t,t,dk,1k,2,span/2k,3,spank,100,span/2,span/2,0L,1,2$L,2,3latt,1,,1,,100,,1esize,0.1,0lmesh,alldk,1,ux!施加边界条件与荷载dk,1,uydk,1,uzdk,1,rotxdk,3,uydk,3,uz/eshape,1fk,2,fy,-Pfinishsave/solu!求解nsubst,20outres,all,allsolveFINISH/POST1SET,LASTPLDISPPLNSOL,U,Y,0,1FINISH/post26!输出荷载位移曲线nsol,2,2,u,yprod,3,2,,,,,,-1000prod,4,1,,,,,,P/1E3/axlab,x,UY(mm)/axlab,y,F(kN)xvar,3plvar,4第三题/TITLE,PIERfinish/clear/PREP7!前处理ET,1,beam189mp,ex,1,3.0e7!定义材料系数和单元截面mp,prxy,1,0.2mp,dens,1,2.5P=20000SECTYPE,1,BEAM,HRECSECDATA,6,10,0.9,0.9,0.9,0.9,0,0,0,0SECTYPE,2,BEAM,HRECSECDATA,4,10,0.6,0.6,0.6,0.6,0,0,0,0SECTYPE,3,TAPER,,SECDATA,1,SECDATA,2,0,80k,1,0,0,0!建模、添加约束、网格划分k,2,0,80,0k,3,0,1,1l,1,2DK,1,ALLlsel,alllesize,all,4lsel,s,,,1latt,1,,1,,3,,3lmesh,all/eshape,1eplotWUCHA=0.001!定义迭代容许误差PMODI=1.0*DOWHILE,WUCHAFINISH/SOLU!静力解ANTYPE,0ACEL,,10FKDELE,ALL,ALLFK,2,FY,-P*PMODIPSTRESS,ONSOLVEFINISH/SOLU!屈曲分析ANTYPE,BUCKLEBUCOPT,LANB,1MXPAND,1,,,1SOLVE*GET,FREQ1,MODE,1,FREQ*IF,ABS(FREQ1-1),LE,WUCHA,THEN*EXIT*ELSEPMODI=PMODI*FREQ1*ENDIF*ENDDO/POST1!输出稳定系数SET,LIST/POST1SET,LASTPLDISPPLNSOL,U,Y,0,1FINISH/prep7!定义初始缺陷upgeom,0.5,,,PIER,rstfinish/SOLU!求存在初始缺陷情况下的荷载位移曲线ANTYPE,STATICNLGEOM,ONKBC,0FK,2,FY,-1000800NSUBST,30OUTRES,ALL,ALLARCLEN,ON,10OUTRESS,,1SOLVEFINISH/POST26!输出荷载位移曲线NSOL,2,2,U,XRFORCE,3,1,F,YPROD,4,2,,,,,,1,1,1000/AXLAB,X,Deflections(mm)/AXLAB,Y,TotalLoad(kN)XVAR,4PLVAR,3

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