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两种单元的结果为什么相差那么大,我添加了附加质量 ,beam188质量单元设置为ux uy uz ixx iyy izz ,beam3单元设置为ux uy uz ,当不加附加质量的简支梁用平面钢架单元matlab计算结果一致,为什么添加了附加质量,结果相差那么大(数据上有点小小误差)平面钢架元刚度矩阵
c=E*I/(L^3);
y=[E*A/L 0 0 -E*A/L 0 0;...
0 12*c 6*L*c 0 -12* c 6*L*c;...
0 6*L*c 4*L^2*c 0 -6*L*c 2*L^2*c;...
-E*A/L 0 0 E*A/L 0 0;...
0 -12*c -6*L*c 0 12*c -6*L*c;...
0 6*L*c 2*L^2*c 0 -6*L*c 4*L^2*c];
质量单元
m = (rho*A*L/420)*[140 0 0 70 0 0;
0 156 22*L 0 54 -13*L;
0 22*L 4*L^2 0 13*L -3*L^2;
70 0 0 140 0 0 ;
0 54 13*L 0 156 -22*L;
0 -13*L -3*L^2 0 -22*L 4*L^2 ] ;
beam188单元模型
- FINISH
- /CLEAR
- /prep7
-
- MP,EX,1,2.06E11 !ex: 弹性模量
- MP,DENS,1,7850 !密度
- MP,GXY,1,1E12 !gxy为剪切模量
- MP,PRXY,1,0.3 !泊松比
- ET,1,beam188,,,2 !=0时 (默认), 每节点有6个自由度。 分别是沿x,y,z的位移及绕其的转动。
- *DIM,DIAM,ARRAY,16 !定义直径数组
- DIAM(1) = 0.015
- DIAM(2) = 0.016
- DIAM(3) = 0.017
- DIAM(4) = 0.017
- DIAM(5) = 0.0205
- DIAM(6) = 0.029
- DIAM(7) = 0.0217
- DIAM(8) = 0.030
- DIAM(9) = 0.020
- DIAM(10) = 0.017
- DIAM(11) = 0.017
- DIAM(12) = 0.0205
- DIAM(13) = 0.017
- DIAM(14) = 0.017
- DIAM(15) = 0.016
- DIAM(16) = 0.0125
- *DO,I,1,16
- SECTYPE,I,BEAM,CTUBE !截面类型ID: 截面号TYPE: BEAM:定义此截面用于梁 CSOLID:圆形实心截面CTUBE: 圆管
- SECDATA,0.004,DIAM(I)/2,40 !Ri, Ro, N
- *ENDDO
- ET,3,COMBIN14 ! ELEMENT TYPE #3 : BEARINGS
- KEYOPT,3,2,2 ! Y DIRECTION
- ET,4,COMBIN14
- KEYOPT,4,2,3 ! Z DIRECTION
- R,30,164E+6 ! BEARINGS
- ET,32,mass21
- R,32,0.0248,0.0248,0.0248,0.0324,0.0162,0.0162
- ET,33,mass21
- R,33,0.0577,0.0577,0.0577,0.1188,0.05941,0.05941
- ET,34,mass21
- R,34,0.0577,0.0577,0.0577,0.1188,0.05941,,0.05941
- ET,38,mass21
- R,38,0.134,0.134,0.134,0.7199,0.3599,,0.3599
- ET,313,mass21
- R,313,0.0577,0.0577,0.0577,0.1188,0.05942,,0.05942
- ET,314,mass21
- R,314,0.0577,0.0577,0.0577,0.1188,0.05942,0.05942
- ET,315,mass21
- R,315,0.02051,0.02051,0.02051,0.0280,0.014,0.014
- ET,316,mass21
- R,316,0.06647,0.06647,0.06647,0.01235,0.06176,0.06176
- N,1,0
- N,2,0.0165
- N,3,0.03
- N,4,0.034
- N,5,0.044
- N,6,0.049
- N,7,0.0555
- N,8,0.0585
- N,9,0.065
- N,10,0.1122
- N,11,0.1172
- N,12,0.1377
- N,13,0.1427
- N,14,0.1527
- N,15,0.1575
- N,16,0.164
- N,17,0.187
- BRG =0 ! BEARING "LENGTH" FOR VISUALISATION
- N,18,0.034,BRG
- N,19,0.044,BRG
- N,20,0.1427,BRG
- N,21,0.1527,BRG
- N,22,0.034,,BRG
- N,23,0.044,,BRG
- N,24,0.1427,,BRG
- N,25,0.1527,,BRG
- TYPE,1
- MAT,1
- *DO,I,1,16
- E,I,I+1
- SECNUM,I !指定梁的截面号
- *ENDDO
- n,400001,0.022,0,0
- n,400002,0.085,0,0
- n,400003,0.1574,0,0
- n,400004,0.1755,0,0
- TYPE,32 !建立质量单元
- real,32
- e,400001
- TYPE,33
- real,33
- e,18
- TYPE,34
- real,34
- e,19
- TYPE,38
- real,38
- e,400002
- TYPE,313
- real,313
- e,20
- TYPE,314
- real,314
- e,21
- TYPE,315
- real,315
- e,400003
- TYPE,316
- real,316
- e,400004
- TYPE,3 ! y向弹簧单元
- REAL,30
- E,18,4
- E,19,5
- E,21,14
- E,20,13
- TYPE,4 ! z向弹簧单元
- REAL,30
- E,22,4
- E,23,5
- E,24,13
- E,25,14
- FINI
- eplot
- finish
- /SOLU
- D,18,ALL
- D,19,ALL
- D,20,ALL
- D,21,ALL
- D,22,ALL
- D,23,ALL
- D,24,ALL
- D,25,ALL
- D,ALL,UX ! 不考虑扭转和轴向移动
- D,ALL,ROTX
- /SOLU
- ANTYPE,MODAL
- CORIOLIS,ON,,,ON
- MODOPT,QRDAMP,30,,,ON
- MXPAND,30
- SOLVE
复制代码 beam3模型
- finish
- /clear
- /prep7
- RO = 7850
- PEX = 2.06E11
- MP,EX,1,PEX !ex: 弹性模量
- MP,DENS,1,RO !密度
- MP,GXY, 1,EX/2.6
- MP,PRXY,1,0.3
- ET,1,beam3,,,
- ET,32,mass21 !mass ux uy uz
- keyopt,32,3,4
- R,32,0.0248,0.0248,0.0248
- ET,33,mass21
- keyopt,33,3,4
- R,33,0.0577,0.0577,0.0577
- ET,34,mass21
- keyopt,34,3,4
- R,34,0.0577,0.0577,0.0577,
- ET,38,mass21
- keyopt,38,3,4
- R,38,0.134,0.134,0.134
- ET,313,mass21
- keyopt,313,3,4
- R,313,0.0577,0.0577,0.0577
- ET,314,mass21
- keyopt,314,3,4
- R,314,0.0577,0.0577,0.0577
- ET,315,mass21
- keyopt,315,3,4
- R,315,0.02051,0.02051,0.02051
- ET,316,mass21
- keyopt,316,3,4
- R,316,0.06647,0.06647,0.06647
- ET,2,COMBIN14 ! ELEMENT TYPE #3 : BEARINGS
- keyopt,2,2,2
- R,2,164e6
- ET,3,COMBIN14 ! ELEMENT TYPE #3 : BEARINGS
- keyopt,3,2,3
- R,3,164e6
- *DIM,DIAM,ARRAY,16 !定义直径数组
- DIAM(1) = 15E-3
- DIAM(2) = 16E-3
- DIAM(3) = 17E-3
- DIAM(4) = 17E-3
- DIAM(5) = 20.5E-3
- DIAM(6) = 29E-3
- DIAM(7) = 21.7E-3
- DIAM(8) = 21E-3
- DIAM(9) = 20E-3
- DIAM(10) = 17E-3
- DIAM(11) = 17E-3
- DIAM(12) = 20.5E-3
- DIAM(13) = 17E-3
- DIAM(14) = 17E-3
- DIAM(15) = 16E-3
- DIAM(16) = 12.5E-3
- *DIM,AERA,ARRAY,16 !定义横截面面积数组
- AERA(1) = 0.000126449104
- AERA(2) = 0.000150796447
- AERA(3) = 0.000176714587
- AERA(4) = 0.000176714587
- AERA(5) = 0.0002797980
- AERA(6) = 0.000610254372
- AERA(7) = 0.0003195707
- AERA (8) = 0.0002960951
- AERA(9) = 0.0002638938
- AERA(10) = 0.00017671459
- AERA(11) = 0.00017671459
- AERA(12) = 0.00027979808
- AERA(13) = 0.00017671459
- AERA(14) = 0.00017671459
- AERA (15) = 0.00015079645
- AERA(16) = 0.00007252981
- *DIM,IZZ,ARRAY,16 !定义截面惯性矩数组
- IZZ(1) = 0.022839869465450E-7
- IZZ(2) = 0.030159289474462E-7
- IZZ(3) = 0.038987655704901E-7
- IZZ(4) = 0.038987655704901E-7
- IZZ(5) = 0.084682642404833E-7
- IZZ(6) = 0.084682642404833E-7
- IZZ(7) = 0.106834468521627E-7
- IZZ(8) = 0.093455018336514E-7
- IZZ(9) = 0.076529197041447E-7
- IZZ(10) = 0.038987655704901E-7
- IZZ(11) = 0.038987655704901E-7
- IZZ(12) = 0.084682642404833E-7
- IZZ(13) = 0.038987655704901E-7
- IZZ(14) =0.038987655704901E-7
- IZZ(15) = 0.030159289474462E-7
- IZZ(16) = 0.009973605607059E-7
- *DO,I,1,16
- R,1,AERA(I),IZZ(I),DIAM(I)
- *ENDDO
- N,1,0
- N,2,0.0164
- N,3,0.029
- N,4,0.039
- N,5,0.049
- N,6,0.0555
- N,7,0.0585
- N,8,0.065
- N,26,0.09
- N,9,0.1122
- N,10,0.1172
- N,11,0.1222
- N,12,0.1272
- N,13,0.1377
- N,14,0.1477
- N,15,0.1577
- N,16,0.164
- N,17,0.187
- TYPE,1
- *DO,I,1,16
- E,I,I+1
- *ENDDO
- TYPE,32
- real,32
- e,2
-
- TYPE,33
- real,33
- e,3
- TYPE,34
- real,34
- e,4
- TYPE,38
- real,38
- e,26
- TYPE,313
- real,313
- e,13
- TYPE,314
- real,314
- e,14
- TYPE,315
- real,315
- e,15
- TYPE,316
- real,316
- e,16
- BRG =0 ! BEARING "LENGTH" FOR VISUALISATION
- N,18,0.039,BRG
- N,19,0.039,0,BRG
- N,20,0.049,BRG
- N,21,0.049,0,BRG
- N,22,0.1477,BRG
- N,23,0.1477,0,BRG
- N,24,0.1577,BRG
- N,25,0.1577,0,BRG
- TYPE,2 ! CREATE BEARING ELEMENTS
- REAL,2
- E,18,4
- E,19,4
- E,20,5
- E,21,5
- TYPE,3 ! CREATE BEARING ELEMENTS
- REAL,3
- E,22,14
- E,23,14
- E,24,15
- E,25,15
- finish
- /SOLU
- D,18,ALL
- D,19,ALL
- D,20,ALL
- D,21,ALL
- D,22,ALL
- D,23,ALL
- D,24,ALL
- D,25,ALL
- /SOLU
- ANTYPE,MODAL
- MODOPT,lanb,20,,,ON
- MXPAND,20
- SOLVE
- finish
复制代码 solid45模型
- FINISH
- /CLEAR
- /TITLE,MODAL analysis
- /FILENAME,MODAL analysis
- /Units,SI !公制单位
- /Show
- /PREP7
- !定义单元类型
- ET,1,PLANE42
- ET,2,solid45
- ET,32,mass21 !mass ux uy uz
- keyopt,32,3,4
- R,32,0.0248,0.0248,0.0248
- ET,33,mass21
- keyopt,33,3,4
- R,33,0.0577,0.0577,0.0577
- ET,34,mass21
- keyopt,34,3,4
- R,34,0.0577,0.0577,0.0577,
- ET,38,mass21
- keyopt,38,3,4
- R,38,0.134,0.134,0.134
- ET,313,mass21
- keyopt,313,3,4
- R,313,0.0577,0.0577,0.0577
- ET,314,mass21
- keyopt,314,3,4
- R,314,0.0577,0.0577,0.0577
- ET,315,mass21
- keyopt,315,3,4
- R,315,0.02051,0.02051,0.02051
- ET,316,mass21
- keyopt,316,3,4
- R,316,0.06647,0.06647,0.06647
- ET,2,COMBIN14 ! ELEMENT TYPE #3 : BEARINGS
- keyopt,2,2,2
- R,2,164e6
- ET,3,COMBIN14 ! ELEMENT TYPE #3 : BEARINGS
- keyopt,3,2,3
- R,3,164e6
- !定义材料属性
- MP,DENS,1,7800 !密度
- MP,EX,1,2.11e11 !弹性模量
- MP,PRXY,1,0.3 !泊松比
- R,1,82e6,0,0, , ,0, !实常数
- !建模
- rectng,0,0.03,0.004,0.008 !!!!!!!!!!!
- rectng,0.03,0.034,0.004,0.0085 !!!!!!!!!!!!!
- rectng,0.034,0.044,0.004,0.0085
- rectng,0.044,0.049,0.004,0.0085
- rectng,0.049,0.0555,0.004,0.01025
- rectng,0.0555,0.0585,0.004,0.0145
- rectng,0.0585,0.065,0.004,0.011
- rectng,0.065,0.117,0.004,0.018
- rectng,0.117,0.138,0.004,0.011 !!!!!!!!
- rectng,0.138,0.143,0.004,0.0085
- rectng,0.143,0.153,0.004,0.0085
- rectng,0.153,0.164,0.004,0.0085
- rectng,0.164,0.187,0.004,0.00625
- aadd,all
- lesize,1,,,15
- lesize,3,,,15
- lesize,53,,,3
- lesize,7,,,3
- lesize,55,,,8
- lesize,56,,,8
- lesize,57,,,3
- lesize,58,,,3
- lesize,19,,,5
- lesize,59,,,5
- lesize,23,,,3
- lesize,61,,,3
- lesize,27,,,5
- lesize,63,,,5
- lesize,31,,,26
- lesize,65,,,26
- lesize,35,,,7
- lesize,67,,,7
- lesize,39,,,2
- lesize,69,,,2
- lesize,72,,,5
- lesize,71,,,5
- lesize,74,,,5
- lesize,73,,,5
- lesize,51,,,8
- lesize,75,,,8
- lesize,68,,,3
- lesize,70,,,1
- lesize,76,,,1
- lesize,50,,,1
- lesize,54,,,1
- lesize,66,,,3
- lesize,4,,,2
- lesize,60,,,1
- type,1
- amesh,all
- k,53,0,0,0
- k,54,0.187,0,0
- TYPE,2
- MAT,1
- !扫掠体
- EXTOPT,ESIZE,10,0,
- EXTOPT,ACLEAR,1
- VROTAT,all, , , , , ,53,54,360,2,
- EPLOT
- NPLOT
- N,300001,0.034,0.0185,0,,,,
- N,300002,0.034,-0.0185,0,,,,
- N,300003,0.034, 0, 0.0185,,,,
- N,300004,0.034, 0, -0.0185,,,,
- N,300005,0.044, 0.0185, 0,,,,
- N,300006,0.044, -0.0185, 0,,,,
- N,300007,0.044, 0, 0.0185,,,,
- N,300008,0.044, 0, -0.0185,,,,
- N,300009,0.143,0.0185,0,,,,
- N,300010,0.143,-0.0185,0,,,,
- N,300011,0.143,0,0.0185,,,,
- N,300012,0.143,0,-0.0185,,,,
- N,300013,0.153,0.0185,0,,,,
- N,300014,0.153,-0.0185,0,,,,
- N,300015,0.153,0,0.0185,,,,
- N,300016,0.153,0,-0.0185,,,,
- !
- !
- n200001=node(0.034,0.0085,0)
- n200002=node(0.034,-0.0085,0)
- n200003=node(0.034,0,0.0085)
- n200004=node(0.034,0,-0.0085)
- !
- n200005=node(0.044,0.0085,0)
- n200006=node(0.044,-0.0085,0)
- n200007=node(0.044,0,0.0085)
- n200008=node(0.044,0,-0.0085)
- !
- n200009=node(0.143,0.0085,0)
- n200010=node(0.143,-0.0085,0)
- n200011=node(0.143,0,0.0085)
- n200012=node(0.143,0,-0.0085)
- !
- n200013=node(0.153,0.0085,0)
- n200014=node(0.153,-0.0085,0)
- n200015=node(0.153,0,0.0085)
- n200016=node(0.153,0,-0.0085)
- !
- n400001=node(0.022,0.008,0)
- n400002=node(0.085,0.0105,0)
- n400003=node(0.1574,0.008,0)
- n400004=node(0.1755,0.00625,0)
- TYPE,32 !建立质量单元
- real,32
- e,n400001
- TYPE,33
- real,33
- e,n200001
- TYPE,34
- real,34
- e,n200005
- TYPE,38
- real,38
- e,n400002
- TYPE,313
- real,313
- e,n200009
- TYPE,314
- real,314
- e,n200013
- TYPE,315
- real,315
- e,n400003
- TYPE,316
- real,316
- e,n400004
- TYPE,3
- REAL,1
- E,n200001,300001
- E,node(0.034,-0.0085,0),300002
- E,node(0.034,0,0.0085),300003
- E,node(0.034,0,-0.0085),300004
- E,n200005,300005
- E,node(0.044,-0.0085,0),300006
- E,node(0.044,0,0.0085),300007
- E,node(0.044,0,-0.0085),300008
- E,n200009,300009
- E,node(0.143,-0.0085,0),300010
- E,node(0.143,0,0.0085),300011
- E,node(0.143,0,-0.0085),300012
- E,n200013,300013
- E,node(0.153,-0.0085,0),300014
- E,node(0.153,0,0.0085),300015
- E,node(0.153,0,-0.0085),300016
- eplot
- /solu
- !
- D,300001,,0,0,300016,1,UX,UY,UZ !定义弹簧单元的外部节点的想x,y,z方向的位移约束
- !X=0.034处的弹簧内部节点
- D,n200001,,,,,,UX,,,
- D,node(0.034,-0.0085,0),,,,,,UX,,,,
- D,node(0.034,0,0.0085),,,,,,UX,,,,
- D,node(0.034,0,-0.0085),,,,,,UX,,,,
- !X=0.044处的弹簧内部节点
- D,n200005,,0,,,,UX,,,
- D,node(0.044,-0.0085,0),,,,,,UX,,,,
- D,node(0.044,0,0.0085),,,,,,UX,,,,
- D,node(0.044,0,-0.0085),,,,,,UX,,,,
- EPLOT
- !
- !
- /solu
- antype,modal
- modopt,lanb,10,,, !模态提取方法Method=LANB、SUBSP、REDUC、UNSYM、DAMP、QRDAMP。
- mxpand,10
- solve
- /POST1
复制代码
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