有限元法计算双层框架.doc

有限元法计算双层框架
双层双跨刚架如图F-2所示，材料的E ＝ 28GPa，各梁的惯性矩I1 = 0.5m4，横截面积A1 = 0.3m2，各柱的I2 =0.8 m4，A2 = 0.4 m2，刚架尺寸及作用荷载数值如表F-2所示，计算刚架的内力及变形，并绘制内力图。

图F-2 双层双跨刚架计算图
表F-2 尺寸及荷载
序号
结构
a
(m)
b
(m)
q1
(kN/m)
q2
(kN/m)
q3
(kN/m)
1
双层框架
4.4
3.6
3.4
1.0
0.5

1. 网格划分及节点、单元编号（剖分图）

2. 输入数据（可用数据文件）

在PFSAP.IN中输入如下数据：
1
example2-1 fig.2-4
9,18,10,2,0,6
1,2,3,0.0,0.0,4,5,6,4.4,0.0,7,8,9,8.8,0.0
10,11,12,0.0,-3.6,13,14,15,4.4,-3.6,16,17,18,8.8,-3.6
0,0,0,0.0,-7.2,0,0,0,4.4,-7.2,0,0,0,8.8,-7.2
1,2,1,2,3,1,4,5,1,5,6,1,1,4,2,4,7,2,2,5,2,5,8,2,3,6,2,6,9,2
2.8e7,0.3,0.5
2.8e7,0.4,0.8
1,1,1.0,1.0,2,1,1.0,1.0,3,1,3.4,3.4,4,1,3.4,3.4,
5,1,-0.5,-0.5,6,1,-0.5,-0.5
0
3. 有限元计算结果（可用计算机打印结果）
(NO.= 1)
example2-1 fig.2-4
NJ=: 9 N=:18 NE=:10
NM=: 2 NPJ=: 0 NPF=: 6
NO.(1)(2)(3) X Y
( 1) 1 2 3 .000 .000
( 2) 4 5 6 4.400 .000
( 3) 7 8 9 8.800 .000
( 4) 10 11 12 .000 -3.600
( 5) 13 14 15 4.400 -3.600
( 6) 16 17 18 8.800 -3.600

( 7) 0 0 0 .000 -7.200
( 8) 0 0 0 4.400 -7.200
( 9) 0 0 0 8.800 -7.200

ELEMENT NO.NODE-1 NODE-2 MATERIALS
1 1 2 1
2 2 3 1
3 4 5 1
4 5 6 1
5 1 4 2
6 4 7 2
7 2 5 2
8 5 8 2
9 3 6 2
10 6 9 2

NO.MAT ELASTIC MODULUS AREA MOMENT OF INERTIA
1 .280000E+08 .300000 .500000
2 .280000E+08 .400000 .800000

NON-NODEL LOADS
NO.E NO.LOAD.MODEL A C
1 1 1.000 1.000
2 1 1.000 1.000
3 1 3.400 3.400
4 1 3.400 3.400
5 1 -.500 -.500
6 1 -.500 -.500

**************************RESULTS OF CALCULATION**************************

NO.N X-DISPLACEMENT Y-DISPLACEMENT ANG.ROT.(RAD)
1 -.18025E-05 .44890E-05 .33462E-06
2 -.65250E-06 .57735E-05 .81355E-07
3 .26200E-06 .50118E-05 -.17765E-06
4 -.68918E-06 .35477E-05 .40884E-06
5 -.28392E-06 .49420E-05 .80045E-07
6 -.65134E-07 .39561E-05 -.17244E-06
7 .00000 .00000 .00000
8 .00000 .00000 .00000
9 .00000 .00000 .00000

NO.E N(1) Q(1) M(1) N(2) Q(2) M(2)
1 -2.1955 -2.9285 -2.4102 2.1955 -1.4715 -.79525
2 -1.7459 -1.1156 1.5965 1.7459 -3.2844 3.1750
3 -.77367 -8.1087 -5.8222 .77367 -6.8513 3.0561
4 -.41769 -5.9366 -1.2864 .41769 -9.0234 8.0775
5 -2.9285 2.1955 2.4102 2.9285 -.39554 2.2537
6 -11.037 1.1692 3.5685 11.037 .63079 -2.5993
7 -2.5871 -.44968 -.80127 2.5871 .44968 -.81758
8 -15.375 -.80567 -.95214 15.375 .80567 -1.9483
9 -3.2844 -1.7459 -3.1750 3.2844 1.7459 -3.1101
10 -12.308 -2.1635 -4.9674 12.308 2.1635 -2.8214

4．采用结构力学求解器计算的结果
位移计算
杆端位移值 ( 乘子 = 1)
--------------------------------------------------------------------------------------------
杆端 1 杆端 2
---------------------------------------- ------------------------------------------
单元码 u -水平位移 v -竖直位移 ?-转角 u -水平位移 v -竖直位移 ?-转角
--------------------------------------------------------------------------------------------
1 0.00000180 -0.00000449 -0.00000033 0.00000065 -0.00000577 -0.00000008
2 0.00000065 -0.00000577 -0.00000008 -0.00000026 -0.00000501 0.00000018
3 0.00000069 -0.00000355 -0.00000041 0.00000028 -0.00000494 -0.00000008
4 0.00000028 -0.00000494 -0.00000008 0.00000007 -0.00000396 0.00000017
5 0.00000180 -0.00000449 -0.00000033 0.00000069 -0.00000355 -0.00000041
6 0.00000069 -0.00000355 -0.00000041 0.00000000 0.00000000 0.00000000
7 0.00000065 -0.00000577 -0.00000008 0.00000028 -0.00000494 -0.00000008
8 0.00000028 -0.00000494 -0.00000008 0.00000000 0.00000000 0.00000000
9 -0.00000026 -0.00000501 0.00000018 0.00000007 -0.00000396 0.00000017
10 0.00000007 -0.00000396 0.00000017 0.00000000 0.00000000 0.00000000
--------------------------------------------------------------------------------------------
内力计算
杆端内力值 ( 乘子 = 1)
--------------------------------------------------------------------------------------------
杆端 1 杆端 2
---------------------------------------- ------------------------------------------
单元码 轴力 剪力 弯矩 轴力 剪力 弯矩
--------------------------------------------------------------------------------------------
1 -2.19554203 2.92851225 -2.41020485 -2.19554203 -1.47148775 0.79524905
2 -1.74586139 1.11557122 1.59652304 -1.74586139 -3.28442878 -3.17496359
3 -0.77367253 8.10865160 -5.82221041 -0.77367253 -6.85134840 -3.05614339
4 -0.41768687 5.93657507 -1.28642850 -0.41768687 -9.02342493 -8.07749820

5 -2.92851225 -2.19554203 2.41020485 -2.92851225 -0.39554203 -2.25374645
6 -11.0371638 -1.16921455 3.56846396 -11.0371638 0.63078545 2.59929157
7 -2.58705897 0.44968063 -0.80127399 -2.58705897 0.44968063 0.81757630
8 -15.3749824 0.80566629 -0.95213859 -15.3749824 0.80566629 1.94826005
9 -3.28442878 1.74586139 -3.17496359 -3.28442878 1.74586139 3.11013742
10 -12.3078537 2.16354826 -4.96736078 -12.3078537 2.16354826 2.82141297
--------------------------------------------------------------------------------------------
反力计算
约束反力值 ( 乘子 = 1)
--------------------------------------------------------------------------------------------
结点约束反力 合力
支 座 ---------------------------------------- ------------------------------------------
结 点 水平 竖直 力矩 大小 角度 力矩
--------------------------------------------------------------------------------------------
9 -2.16354826 12.3078537 2.82141297 12.4965676 99.9699354 2.82141297
8 -0.80566629 15.3749824 1.94826005 15.3960768 92.9996194 1.94826005
7 -0.63078545 11.0371638 2.59929157 11.0551741 93.2709555 2.59929157
---------------------------------------------------------------------------------------

5.结果分析和讨论：
(1) 静力平衡条件：输出节点约束反力之和与相应的总荷载平衡，探讨计算结果的正确性；
水平方向：求解器：2.164 +0.806+0.631=3.601
外荷载：0.5*2*3.6=3.6
竖直方向：求解器：12.308+15.375+11.037=38.72
外荷载：2*4.4*1+2*4.4*3.6=38.7
所以计算结果正确
（2）比较有限元与结构力学求解器的计算结果：符合
a) 绘出内力（M、Q、N）图、位移图（用结构力学求解器的结果）

弯矩图（M）

剪力图（Q）

轴力图

位移图

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