静力学问题的求解实例—扳手的受力分析
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课堂教学实施方案点作逆时针方向转动. 应该注意,力臂是OD,注意:负号必须标注,正号可标也可不标。
一般不标注。
平面汇交力系的合力对其平面内任一点的矩等于所有各分力对本题有两种解法。
按力矩的定义计算由图中几何关系有:=(AB-DB)sinα=(AB- BCctgα)sinαα)sinα-bcosα在日常生活和工程实际中经常见到物体受动两个大小相等、方向相反,但不在同一直线上的两个平行力作用的情况。
(图a)司机转动驾驶汽车时两手作用在方向盘上的力;(图b)工人用丝锥攻螺纹时两手加在扳手上的力;(图c)以及用两个手指拧动水龙头所加的力等等。
▪力偶:在力学中把这样一对等值、反向而不共线的平行力称为力偶。
▪用符号( F ,F′) 表示。
▪两个力作用线之间的垂直距离称为力偶臂。
▪两个力作用线所决定的平面称为力偶的作用面。
偶使物体逆时针方向转动时,力偶矩为正,反之为负。
在国际单位制中,力矩的单位是牛顿•米(N•m)或千牛顿•米力和力偶是静力学中两个基本要素。
力偶与力具有不同的性质:)力偶不能简化为一个力,即力偶不能用一个力等效替代。
因此力偶不能与一个力平衡,力偶只能与力偶平衡。
)无合力,故不能与一个力等效;结论:只要保持力偶矩不变,力偶可在作用面内任意移动或转动,其对刚体的作用效果四力的平移定理力的平移定理:作用于刚体上的力可以平行移动到刚体上的任意一指定点,但必须同时在该力与指定点所决定的平面内附加一力偶,其力偶矩等于原力对指定点之矩。
力的平移定理只适用于刚体力的平移定理表明,可以将一个力分解为一个力和一个力偶;反过来,也可以将同一平面内的一个力和一个力偶合成为一个力。
学号:S2*******程序版本:ANSYS 10作业一:带孔平板圆孔应力集中分析问题描述:如右图所示,一个承受单向拉伸的无限大板,在中心位置有一个小圆孔。
材料属性为弹性模量a P E 6101⨯=,泊松比为0,拉伸的均布载荷Pa p 7101⨯=,平板厚度mm t 1=。
ANSYS 10 分析步骤:1. 定义工作文件名:Utility Menu>File>Change Jobname>输入Plate>OK2. 定义工作标题:Utility Menu>File>Change Title>输入The Ansysis of Plate withsmall Circle>OK3. 重新显示:Utility Menu>Plot>Replot4. 设置系统单位制:命令输入窗口,输入命令/UNITS,SI 并回车5. 设置计算类型:ANSYS Main Menu>Preferences>选Structural>OK6. 选择单元类型:ANSYS Main Menu>Preprocessor>Element Type>Add/Edit/Delte>Add>选Solid Quad 4node 42>OK>Options>K3:Plate Strs w/thk>OK>Close7. 定义实常数:ANSYS Main Menu>Preprocessor>Real Constants> Add/Edit/Delte>Add>OK>在THK 输入1 >OK>Close8. 定义材料特性:ANSYS Main Menu>Preprocessor>Material Props> Material Models>双击选Structural>双击Linear>双击Elastic>双击Isotropic>在EX 输入1e6,PRXY 输入0>OK>点击“X”关闭9. 生成平面方板:ANSYS Main Menu>Preprocessor>Modeling>Create>Areas>Rectangle>By2 Corners>输入WP X:0 WP Y:0 Width:10 Height:10 >OK10. 生成圆孔平面:ANSYS Main Menu>Preprocessor>Modeling>Create>Areas>Circle>SolidCircle>输入WP X:5 WP Y:5 Radius:1 >OK11. 布尔运算生成孔:ANSYS Main Menu>Preprocessor>Modeling>Operate>Booleans>Subtract>Areas>选方板>点OK(Multi Entities 窗)>OK(Subtract Areas 窗) 选方板>点NEXT>OK(Multi Entities 窗)>OK(Subtract Areas 窗)12. 网格划分:ANSYS Main Menu>Preprocessor>Meshing>MeshTool>Size Control:Global>set>在NDIV 输入6>OK> MeshTool> Mesh>Pick All>Close(Warning)> Close(MeshTool)13. 施加约束:(1): ANSYS Main Menu>Solution>Define Loads>Apply>Structural>Displacement>OnNodes>点选结构左侧所有节点>OK>Lab2 DOFs:UX,VALUE:0>OK (2):ANSYS Main Menu>Solution>Define Loads>Apply>Structural>Displacement>On Nodes>点选结构左下侧(0,0)节点>OK>Lab2 DOFs:UX,UY,VALUE:0>OK14. 施加均布载荷:ANSYS Main Menu>Solution>Define Loads>Apply>Structural>Pressure>OnLines>点选结构右侧所有节点>OK>VALUE:-1E7> OK>Close15. 分析计算:ANSYS Main Menu>Solution>Solve>Current LS>OK>Yes>Close>关闭文字窗16. 结果显示:ANSYS Main Menu>General Postpro>Plot Results>Deformed Shape>点选Def+undeformed>OK> Plot Results>Contour Plot>Nodal Solu>选Stress 选von Mises stress>Def+undeformed Model>OK17. 退出系统图1 带孔平板变形形状的结果图2带孔平板应力分布的结果作业二:内六角扳手静力分析如右图所示,截面宽度为10mm的内六角扳手,在手柄端部施加扭转力100N,以及垂直向下的力20N,分析在两种载荷的作用下扳手的应力分布。
静力学问题的求解——扳手的受力分析利用ANSYS对空间问题进行静力学分析,下面就以扳手的受力分析为例,说明ANSYS 的分析方法、步骤和过程。
1、改变工作名称在通用菜单上选择“File”→“Change Jobname”。
在弹出图1的对话框中输入文件名,单击“OK”按钮。
图1 改变工作名称2、创建单元类型在主菜单中选择“Preprocesso r”→“Element Type”→“Add/Edit/Delete”。
弹出如图2的对话框,然后在其中单击“Add”按钮;弹出如图3的对话框,在对话框中选择单元的类型。
图2单元类型图3 单元类型选择对话框3、定义材料特性在主菜单中选择“Preprocesso r”→“Material Props”→“Material Models”。
在弹出的如图4的菜单中选择“Structural”→“Linear”→“Elastic”→“Isotropic”,弹出如图5的对话框,在EX文本框中输入2e11, 在PRXY文本框中输入0.3 ,然后点击 OK 按钮。
图4 材料模型图5 材料特性在主菜单中选取“Preprocessor”→“Modeling”→“Create”→“Areas”→“Polygon”→“Hexagon”。
在弹出的菜单如图6中,在“WP X”、“WP Y”和“Radius”文本框中分别输入0、0和0.01,单击OK按钮。
创建六边形、改变视角并显示关键点和线号如图7所示。
图6创建六边形图7创建六边形及显示关键点、线号在ANSYS主菜单中选取“Preprocessor”→“Modeling”→“Create”→“Keypoints”→“In Active CS”。
在弹出的对话框图8中创建点7,X、Y、Z坐标为0,0,0,单击“Apply”按钮,继续创建关键点8,坐标为0,0,0.05,单击“Apply”按钮,创建点9,坐标为0,0.1,0.05,单击OK按钮。
第1例关键点和线的创建实例—正弦曲线/PREP7K,100,0,0,0CIRCLE,100,1,,,90CSYS,1KFILL,2,1,4,3,1K,7,1+3.1415926/2,0,0CSYS,0KFILL,7,1,4,8,1KGEN,2,7,11,1,,1LSTR,8,13LSTR,9,14LSTR,10,15LSTR,11,16LANG,5,6,90,,0LANG,4,5,90,,0LANG,3,4,90,,0LANG,2,3,90,,0BSPLIN,1,17,18,19,20,12LSEL,U,,,14LDELE,ALLLSEL,ALLKWPA VE,12CSYS,4LSYMM,X,14NUMMRG,KP,,,,LOWLCOMB,ALL,,0第2例工作平面的应用实例—相交圆柱体/PREP7CYLIND,0.015,0,0,0.08,0,360CYLIND,0.03,0,0,0.08,0,360/VIEW,1,1,1,1/PNUM,VOLU,1WPOFF,0,0.05,0.03WPROT,0,60CYLIND,0.012,0,0,0.055,0,360CYLIND,0.006,0,0,0.055,0,360VSEL,S,,,2,3,1CM,VV1,VOLUVSEL,INVECM,VV2,VOLUVSEL,ALLVSBV,VV1,VV2BLOCK,-0.002,0.002,-0.013,-0.009,0,0.008WPSTYLE,,,,,,1CSYS,4VGEN,3,1,,,,120VSBV,5,1VSBV,4,2VSBV,1,3WPROT,0,0,90VSBW,ALLVDELE,1,4,3V ADD,ALLVPLOT/REPLOT第3例复杂形状实体的创建实例—螺栓/PREP7CSYS,1K,1,0.008,0,-0.002K,2,0.008,90,-0.0015K,3,0.008,180,-0.001K,4,0.008,270,-0.0005K,5,0.008,0,0/VIEW,1,1,1,1L,1,2L,2,3L,3,4L,4,5LGEN,7,ALL,,,,,0.002NUMMRG,KP,,,,LOWLCOMB,ALLK,80,0.008+0.0015/4,90,0.012+0.002/4K,81,0.008+2*0.0015/4,180,0.012+2*0.002/4K,82,0.008+3*0.0015/4,270,0.012+3*0.002/4K,83,0.008+4*0.0015/4,0,0.012+4*0.002/4L,35,80L,80,81L,81,82L,82,83CSYS,0K,90,0.008,0,-0.00025K,91,0.006918,0,-0.002K,92,0.006918,0,0/PNUM,KP,1/PNUM,LINE,1GPLOTLSTR,1,90LSTR,91,92LANG,7,90,60,,0LANG,7,1,120,,0AL,6,9,10,11VDRAG,1,,,,,,1,2,3,4,5/PNUM,KP,0/PNUM,LINE,0/PNUM,AREA,1/PNUM,VOLU,1CYLIND,0.0079,,0,0.04,0,360VSEL,U,,,6CM,VVV2,VOLUALLSVSBV,6,VVV2/REPLOTK,93,0.0065,0,0K,94,0.0095,0,0.003K,95,0,0,0K,96,0,0,0.03LSTR,93,94AROTA T,6,,,,,,95,96,360ASEL,S,,,1,4,1VSBA,7,ALLASEL,ALLVDELE,1,,,1RPRISM,0.04,0.05,6,,0.0131CONE,0.03477,0.00549,0.03,0.055,0,360 VINV,1,3/REPLOTVPLOTFINISH第4例复杂形状实体的创建实例—杯子/PREP7K,1,0,0,0K,2, 0.0395,0,0K,3, 0.05,0.12,0K,4, 0.047,0.12,0K,5, 0.03675,0.003,0K,6, 0,0.003,0LSTR,1,2LSTR,2,3LSTR,3,4LSTR,4,5LSTR,5,6LSTR,6,1LFILLT, 1, 2, 0.02LFILLT, 4, 5, 0.017AL,ALLVROTA T, ALL, , , , , , 1,6, 360K,31, 0,0.103,0K,32, 0.078,0.103,0K,33, 0.078,0.046,0K,34, 0,0.0011,0LSTR,31,32LSTR,32,33LSTR,33,34LFILLT, 54,55, 0.013LFILLT, 55, 56, 0.028K,41, 0,0.103+0.002,0.005K,42, 0,0.103+0.002,-0.005K,43, 0,0.103-0.002,-0.005K,44, 0,0.103-0.002,0.005LSTR,41,42LSTR,42,43LSTR,43,44LSTR,44,41LFILLT,59,60,0.001LFILLT,60,61,0.001LFILLT,61,62,0.001LFILLT,62,59,0.001AL, 59,63,60,64,61,65,62,66VDRAG,33, , , , , , 54,57,55,58,56VSEL,S,,,5,9,4ASEL,S,,,4,28,24VSBA,ALL,ALL ALLSEL,ALLVDELE,10,,,1VDELE,13,,,1/PNUM,VOLU,1/NUMBER,1/COLOR,VOLU,ORAN,ALL /REPLOTFINISH第5例杆系结构的静力学分析实例—平面桁架/CLEAR/FILNAME, EXAMPLE5L=0.1A=1e-4/PREP7ET,1,BEAM3R,1,AMP,EX,1,2E11MP,PRXY,1,0.3N,1N,2,LN,3,2*LN,4,L,LE,1,2E,2,3E,1,4E,2,4E,3,4FINISH/SOLUD,1,UXD,1,UYD,3,UYF,4,FY,-2000SOLVEFINISH/POST1ETABLE,FA,SMISC,1ETABLE,SA,LS,1PRETAB,FA,SAFINISH第6例杆系结构的静力学分析实例—悬臂梁/CLEAR/FILNAME, EXAMPLE6/PREP7ET,1, BEAM3R,1,14.345e-4,245e-8,0.1MP,EX,1,2E11MP,NUXY,1,0.3K,1,0,0,0K,2,1,0,0LSTR,1,2LESIZE,1,,,50LMESH,1FINISH/SOLUDK,1,UXDK,1,UYDK,1,ROTZFK,2,FY,-10000SOLVEFINISH/POST1PLDISPFINISH第7例平面问题的求解实例—厚壁圆筒问题/CLEAR/FILNAME, EXAMPLE7/PREP7ET,1,PLANE183,,,2MP,EX,1,2E11MP,PRXY,1,0.3PCIRC, 0.1, 0.05, 0, 90LESIZE, 4,,,6LESIZE, 3,,,8MSHAPE,0MSHKEY,1AMESH,1FINISH/SOLUDL,4,,UYDL,2,,UXSFL,3,PRES,10E6SOLVESA VEFINISH/POST1PATH,P1,2PPATH,1,30PPATH,2,1PDEF,SR,S,XPDEF,ST,S,YPLPATH,SR,STFINISH第8例静力学问题的求解实例—扳手的受力分析/CLEAR/FILNAME, EXAMPLE8/PREP7ET,1,PLANE42ET,2,SOLID45MP,EX,1,2E11MP,PRXY,1,0.3RPR4, 6, 0, 0, 0.01K,7,0,0,0K,8, 0,0,0.05K,9, 0,0.1,0.05LSTR,7,8LSTR,8,9LFILLT, 7, 8, 0.015LSTR,1,4ASBL, 1, 10LESIZE,2,,,3LESIZE,3,,,3LESIZE,4,,,3LESIZE,7,0.01LESIZE,8,0.01LESIZE,9,0.01MSHAPE,0MSHKEY,1AMESH,ALLVDRAG, ALL,,,,,,7,9,8ACLEAR, 2,3,1FINISH/SOLUDA,2,ALLDA,3,ALLKSEL,S,,,24,29,1FK,ALL,FX,100KSEL,ALLSOLVESA VEFINISH/POST1/VIEW,1,1,1,1 PLDISP, 2 PLNSOL,S,EQV,0,1 NWPA VE,159/TYPE,1, SECT/CPLANE,1/REPLOTFINISH第9例各种坐标系的应用实例—圆轴扭转分析/CLEAR/FILNAME, EXAMPLE9/PREP7ET,1,PLANE183ET,2,SOLID186MP,EX,1,2.08E11MP,PRXY,1,0.3RECTNG,0,0.025, 0,0.12LESIZE,1,,,5LESIZE,2,,,8MSHAPE,0MSHKEY,1AMESH,1EXTOPT,ESIZE,5EXTOPT,ACLEAR,1VROTA T,1,,,,,,1,4,360/VIEW,1,1,1,1WPROT,0,-90CSWPLA,11,1,1,1NSEL,S,LOC,X,0.025NROTA T,ALLFINISH/SOLUD,ALL,UXNSEL,R,LOC,Z,0.12F,ALL,FY,1500ALLSEL,ALLDA,2,ALLDA,6,ALLDA,10,ALLDA,14,ALLSOLVESA VEFINISH/POST1PLDISP,1RSYS,11NSEL,S,LOC,Z,0.045NSEL,R,LOC,Y,0PRNSOL,U,Y!NSEL,S,LOC,Z,0,0.045 !命令前加“!”号为注释语句,!ESLN,R,1 !去掉“!”号即可执行该命令,!PLESOL,S,YZ !三个注释语句用于显示剪应力。