矩阵位移法
有限元平面刚架内力计算报告
（FORTRAN 77 语言）
（一）结构设计例题：
已知条件：
跨度：4m 高度：3m
结点集中荷载：集中力 F =F 2=F 3=15KN 集中力矩 M=8KN·m 非结点荷载：水平方向：均布力Q 1=13KN／m 集中力：F =F 2=F 3=13KN 竖直方向：均布力 Q 2=20KN／m 构件材料性质：
单元（1）～（29）EA=400 EI=15
（二） RPF.DAT输入数据
29,22,52,52,5,14 0,0,1,2,3 4,0,4,5,6 6,0,7,8,9 6,0,7,8,10 8,0,11,12,13 12,0,14,15,16 0,3,17,18,19 4,3,20,21,22 8,3,23,24,25 12,3,26,27,28 0,6,29,30,31 4,6,32,33,34 8,6,35,36,37 12,6,38,39,40 0,9,41,42,43 4,9,44,45,46 8,9,47,48,49 12,9,50,51,52 0,12,0,0,0 4,12,0,0,0 8,12,0,0,0
1,7,400,15 7,11,400,15 11,15,400,15 15,19,400,15 2,8,400,15 8,12,400,15 12,16,400,15 16,20,400,15 5,9,400,15 9,13,400,15 13,17,400,15 17,21,400,15 6,10,400,15 10,14,400,15 14,18,400,15 18,22,400,15 1,2,400,15 2,3,400,15 4,5,400,15 7,8,400,15 8,9,400,15 9,10,400,15 11,12,400,15 12,13,400,15 13,14,400,15 15,16,400,15 16,17,400,15 17,18,400,15 22,8 25,8 26,-15 38,-15 50,-15 17,1,4,13 18,1,2,13 19,1,2,13 20,1,4,13 24,1,4,13 25,1,4,13 26,1,4,13
28,2,2,13 29,2,2,13 1,1,3,-15 2,1,3,-15 3,1,3,-15 4,1,3,-15
（三）RPF.DAT 输出数据
NE= 29 NJ= 22 N= 52 NW= 52 NPJ= 5 NPF= NODE X Y XX YY 1 0.0000 0.0000 1 2 3 2 4.0000 0.0000 4 5 6 3 6.0000 0.0000 7 8 9 4 6.0000 0.0000 7 8 10 5 8.0000 0.0000 11 12 13 6 12.0000 0.0000 14 15 16 7 0.0000 3.0000 17 18 19 8 4.0000 3.0000 20 21 22 9 8.0000 3.0000 23 24 25 10 12.0000 3.0000 26 27 28 11 0.0000 6.0000 29 30 31 12 4.0000 6.0000 32 33 34 13 8.0000 6.0000 35 36 37 14 12.0000 6.0000 38 39 40 15 0.0000 9.0000 41 42 43 16 4.0000 9.0000 44 45 46 17 8.0000 9.0000 47 48 49 18 12.0000 9.0000 50 51 52 19 0.0000 12.0000 0 0 0 20 4.0000 12.0000 0 0 0 21 8.0000 12.0000 0 0 0 22 12.0000 12.0000 0 0 0
ELEMENT NODE-I NODE-J EA EI 1 1 7 0.400000E+03 0.150000E+02 2 7 11 0.400000E+03 0.150000E+02 3 11 15 0.400000E+03 0.150000E+02 4 15 19 0.400000E+03 0.150000E+02
14 ZZ
5 2 8 0.400000E+03 0.150000E+02 6 8 12 0.400000E+03 0.150000E+02 7 12 16 0.400000E+03 0.150000E+02 8 16 20 0.400000E+03 0.150000E+02 9 5 9 0.400000E+03 0.150000E+02 10 9 13 0.400000E+03 0.150000E+02 11 13 17 0.400000E+03 0.150000E+02 12 17 21 0.400000E+03 0.150000E+02 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
CODE 22. 25. 26. 38. 50.
ELEMENT 17. 18. 19. 20. 24. 25. 26. 6 10 0.400000E+03 0.150000E+02 10 14 0.400000E+03 0.150000E+02 14 18 0.400000E+03 0.150000E+02 18 22 0.400000E+03 0.150000E+02 1 2 0.400000E+03 0.150000E+02 2 3 0.400000E+03 0.150000E+02 4 5 0.400000E+03 0.150000E+02 5 6 0.400000E+03 0.150000E+02 7 8 0.400000E+03 0.150000E+02 8 9 0.400000E+03 0.150000E+02 9 10 0.400000E+03 0.150000E+02 11 12 0.400000E+03 0.150000E+02 12 13 0.400000E+03 0.150000E+02 13 14 0.400000E+03 0.150000E+02 15 16 0.400000E+03 0.150000E+02 16 17 0.400000E+03 0.150000E+02 17 18 0.400000E+03 0.150000E+02 PX-PY-PM 8.0000 8.0000 -15.0000 -15.0000 -15.0000 IND A Q 1. 4.0000 13.0000 1. 2.0000 13.0000 1. 2.0000 13.0000 1. 4.0000 13.0000 1. 4.0000 13.0000 1. 4.0000 13.0000 1. 4.0000 13.0000
27. 2. 2.0000 13.0000 28. 2. 2.0000 13.0000 29. 2. 2.0000 13.0000 1. 1. 3.0000 -15.0000 2. 1. 3.0000 -15.0000 3. 1. 3.0000 -15.0000 4. 1. 3.0000 -15.0000
NODE U V CETA 1 0.251899E+02 0.536529E+00 0.831988E+00 2 0.249658E+02 0.237100E+01 0.703423E+00 3 0.248687E+02 0.477721E+01 0.130850E+01 4 0.248687E+02 0.477721E+01 -0.164476E+01 5 0.247715E+02 0.243246E+01 0.612781E-01 6 0.246820E+02 0.197250E+01 -0.305744E-01 7 0.223159E+02 0.367608E+00 0.107471E+01 8 0.219297E+02 0.198589E+01 0.102294E+01 9 0.216723E+02 0.202250E+01 0.956543E+00 10 0.214814E+02 0.176651E+01 0.126965E+01 11 0.163065E+02 0.253047E+00 0.228357E+01 12 0.158914E+02 0.162915E+01 0.141780E+01 13 0.155793E+02 0.162911E+01 0.139229E+01 14 0.153627E+02 0.146119E+01 0.150539E+01 15 0.760580E+01 0.706096E-01 0.251975E+01 16 0.731117E+01 0.873842E+00 0.168815E+01 17 0.707370E+01 0.852961E+00 0.160915E+01 18 0.688001E+01 0.835088E+00 0.218008E+01 19 0.000000E+00 0.000000E+00 0.000000E+00 20 0.000000E+00 0.000000E+00 0.000000E+00 21 0.000000E+00 0.000000E+00 0.000000E+00 22 0.000000E+00 0.000000E+00 0.000000E+00
ELEMENT N Q
1 N1= 22.5228 Q1= 22.4069 M1= N2= -22.5228 Q2= 22.5931 M2= 2 N1= 15.2749 Q1= 16.0204 M1= N2= -15.2749 Q2= 28.9796 M2= 3 N1= 24.3250 Q1= 12.5286 M1= N2= -24.3250 Q2= 32.4714 M2= 4 N1= 9.4146 Q1= -3.0078 M1= M 9.8967 -10.1761 -4.5138 -14.9251 -4.8881 -25.0263 -14.4130
N2= -9.4146 Q2= 48.0078 M2= -62.1105 5 N1= 51.3486 Q1= -2.9768 M1= -6.0629 N2= -51.3486 Q2= 2.9768 M2= -2.8677 6 N1= 47.5649 Q1= -15.8480 M1= -25.7462 N2= -47.5649 Q2= 15.8480 M2= -21.7976 7 N1= 100.7079 Q1= -26.1423 M1= -40.5651 N2= -100.7079 Q2= 26.1423 M2= -37.8617 8 N1= 116.5123 Q1= -31.8597 M1= -39.3487 N2= 9 N1= N2= 10 N1= N2= 11 N1= N2= 12 N1= N2= 13 N1= N2= 14 N1= N2= 15 N1= N2= 16 N1= N2= 17 N1= N2= 18 N1= N2= 19 N1= N2= 20 N1= N2= 21 N1= N2= 22 N1= N2= 23 N1= N2= 24 N1= N2= -116.5123 54.6622 -54.6622 52.4515 -52.4515 103.4867 -103.4867 113.7281 -113.7281 27.4663 -27.4663 40.7087 -40.7087 83.4804 -83.4804 111.3451 -111.3451 22.4069 -22.4069 19.4301 -19.4301 19.4301 -19.4301 8.9470 -8.9470 38.6135 -38.6135 25.7424 -25.7424 19.0936 -19.0936 41.5082 -41.5082 Q2= 31.8597 Q1= -10.4831 Q2= 10.4831 Q1= -17.1318 Q2= 17.1318 Q1= -26.6895 Q2= 26.6895 Q1= -31.0666 Q2= 31.0666 Q1= -8.9470 Q2= 8.9470 Q1= -13.0406 Q2= 13.0406 Q1= -19.6968 Q2= 19.6968 Q1= -24.0660 Q2= 24.0660 Q1= -22.5228 Q2= -29.4772 Q1= -21.8714 Q2= -4.1286 Q1= 4.1286 Q2= -30.1286 Q1= -24.5337 Q2= -27.4663 Q1= 7.2479 Q2= -7.2479 Q1= 11.0316 Q2= -11.0316 Q1= 13.2423 Q2= -13.2423 Q1= -9.0501 Q2= -42.9499 M2= -56.2302 M1= -20.2010 M2= -11.2483 M1= -27.8765 M2= -23.5190 M1= -41.1185 M2= -38.9500 M1= -38.5541 M2= -54.6456 M1= -19.9216 M2= -6.9193 M1= -20.7396 M2= -18.3822 M1= -32.9186 M2= -26.1717 M1= -25.1986 M2= -46.9993 M1= -9.8967 M2= 23.8057 M1= -17.7428 M2= 0.0000 M1= 0.0000 M2= 34.2572 M1= -14.0562 M2= 19.9216 M1= 14.6898 M2= 14.3016 M1= 22.3123 M2= 21.8143 M1= 25.3105 M2= 27.6588 M1= 19.8132 M2= 47.9866
25 N1= 31.2139 Q1= -10.1931 M1= 14.3761 N2= -31.2139 Q2= -41.8069 M2= 48.8515 26 N1= 21.6562 Q1= -9.2283 M1= 15.7860 N2= -21.6562 Q2= -42.7717 M2= 51.3009 27 N1= 29.4636 Q1= 14.9103 M1= 39.4392 N2= -29.4636 Q2= -27.9103 M2= 46.2022 28 N1= 23.7462 Q1= 12.1060 M1= 31.0083 N2= -23.7462 Q2= -25.1060 M2= 43.4158 29 N1= 19.3692 Q1= 14.8647 M1= 34.0883
N2= -19.3692 Q2= -27.8647 M2= 51.3703
（四）内力图（弯矩、剪力、轴力）绘制
M图(KN.M)
Fs 图（KN.m ）
Fn(KN)
(五) 结构力学求解器输出数据 杆端 1 杆端 2
---------------------------------------- ------------------------------------------ 单元码 轴力 剪力 弯矩 轴力 剪力 弯矩
----------------------------------------------------------------------------------------------- 1 -22.5227667 -22.4068938 9.89674839 -22.5227667 22.5931062 10.1760669 2 -15.2749013 -16.0203676 -4.51377994 -15.2749013 28.9796323 14.9251172 3 -24.3249550 -12.5285507 -4.88807889 -24.3249550 32.4714492 25.0262689 4 -9.41460837 3.00781576 -14.4129539 -9.41460837 48.0078157 62.1104933 5 -51.3486485 2.97683693 -6.06285082 -51.3486485 2.97683693 2.86765998 6 -47.5648721 15.8479544 -25.7462352 -47.5648721 15.8479544 21.7976281 7 -100.707913 26.1422563 -40.5650995 -100.707913 26.1422563 37.8616695 8 -116.512256 31.8596520 -39.3487475 -116.512256 31.8596520 56.2302085 9 -54.6622378 10.4831008 -20.2009767 -54.6622378 10.4831008 11.2483256 10 -52.4515405 17.1318140 -27.8764708 -52.4515405 17.1318140 23.5189713 11 -103.486721 26.6895021 -41.1185233 -103.486721 26.6895021 38.9499831 12 -113.728068 31.0665587 -38.5541022 -113.728068 31.0665587 54.6455739 13 -27.4663468 8.94695608 -19.9215801 -27.4663468 8.94695608 6.91928809 14 -40.7086859 13.0405990 -20.7395584 -40.7086859 13.0405990 18.3822387 15 -83.4804099 19.6967922 -32.9186436 -83.4804099 19.6967922 26.1717329 16 -111.345067 24.0659734 -25.1985710 -111.345067 24.0659734 46.9993493 17 -22.4068938 22.5227667 -9.89674839 -22.4068938 -29.4772332 -23.8056814 18 -19.4300568 21.8714153 -17.7428306 -19.4300568 -4.12858469 -0.00000000
19 -19.4300568 -4.12858469 0.00000000 -19.4300568 -30.1285846 -34.2571693 20 -8.94695608 24.5336531 -14.0561926 -8.94695608 -27.4663468 -19.9215801 21 -38.6134738 -7.24786541 14.6898469 -38.6134738 -7.24786541 -14.3016147 22 -25.7423562 -11.0316418 22.3122805 -25.7423562 -11.0316418 -21.8142867 23 -19.0936429 -13.2423390 25.3105097 -19.0936429 -13.2423390 -27.6588465 24 -41.5081831 9.05005375 19.8131961 -41.5081831 -42.9499462 -47.9865888 25 -31.2138812 10.1930950 14.3761388 -31.2138812 -41.8069049 -48.8514809 26 -21.6561931 9.22827596 15.7860137 -21.6561931 -42.7717240 -51.3008823 27 -29.4636335 -14.9103467 39.4392228 -29.4636335 -27.9103467 -46.2021639 28 -23.7462378 -12.1060036 31.0082531 -23.7462378 -25.1060036 -43.4157612 29 -19.3691812 -14.8646570 34.0883241 -19.3691812 -27.8646570 -51.3703040
(六) 学习小结
在大一就学过C++语言，如今学起fortran 语言相对简单很多，fortran 语言是专门处理数据的计算机编程语言，我们主要是用其源程序利用矩阵位移法的思路解决问题。通过对源程序数据的输入，加深了对矩阵位移法的理解，同时也体会到了此方法的重要性。在输入调试运行过程中收入颇多:
(1)矩阵位移法与传统的位移法思路基本相同，其中的区别就是离散化，从而便于计算机解决问题。由手算到电算，只是思路上进步了一小步，可是对于解决计算问题是进步了一大步。
（2）fortran 语言源程序求解力学问题，为我们提供了新的求解方法，既可用于我们的基础力学的求解问题，也可用于本专业所遇到的具体工程力学问题求解。期间通过结构力学求解器求解问题，也为日后学习本专业软件如（pkpm,sub2000）奠定了基础。
（3）由于对此程序陌生，导致操作中错误频出，可是经过反复的调试运行，最终得到了正确的结构。诸如节点荷载，非节点荷载，坐标系规定，铰节点的处理，不同支座。这些不懂的知识点都由不懂到掌握。