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4.43.63.41.00.51. 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：1example2-1 fig.2-4 9,18,10,2,0,61,2,3,0.0,0.0,4,5,6,4.4,0.0,7,8,9,8.8,0.010,11,12,0.0,-3.6,13,14,15,4.4,-3.6,16,17,18,8.8,-3.60,0,0,0.0,-7.2,0,0,0,4.4,-7.2,0,0,0,8.8,-7.21,2,1,2,3,1,4,5,1,5,6,1,1,4,2,4,7,2,2,5,2,5,8,2,3,6,2,6,9,22.8e7,0.3,0.52.8e7,0.4,0.81,1,1.0,1.0,2,1,1.0,1.0,3,1,3.4,3.4,4,1,3.4,3.4,5,1,-0.5,-0.5,6,1,-0.5,-0.503. 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7 / 7