{"id":10890,"date":"2019-01-03T23:24:49","date_gmt":"2019-01-03T15:24:49","guid":{"rendered":"http:\/\/www.jdcui.com\/?p=10890"},"modified":"2023-08-08T15:04:39","modified_gmt":"2023-08-08T07:04:39","slug":"femmatlab%e6%9c%89%e9%99%90%e5%85%83%e7%bc%96%e7%a8%8b-%e5%8e%8b%e6%9d%86%e7%a8%b3%e5%ae%9a%e9%97%ae%e9%a2%98matlab%e6%9c%89%e9%99%90%e5%85%83%e7%bc%96%e7%a8%8b-%e3%80%8a%e6%9c%89%e9%99%90","status":"publish","type":"post","link":"http:\/\/www.jdcui.com\/?p=10890","title":{"rendered":"[FEM][MATLAB][\u6709\u9650\u5143][\u7f16\u7a0b] \u538b\u6746\u7a33\u5b9a\u95ee\u9898MATLAB\u6709\u9650\u5143\u7f16\u7a0b (\u300a\u6709\u9650\u5355\u5143\u6cd5-\u7f16\u7a0b\u4e0e\u8f6f\u4ef6\u5e94\u7528\u300b\u7ae0\u8282\u8282\u9009)"},"content":{"rendered":"

\u5b9e\u5e72\u3001\u5b9e\u8df5\u3001\u79ef\u7d2f\u3001\u601d\u8003\u3001\u521b\u65b0\u3002<\/strong><\/span><\/p>\n

\n

\u63a5\u7740\u535a\u6587\u300a[\u529b\u5b66][\u6709\u9650\u5143][FEM]Basics of Buckling Analysis [\u66f2\u5c48\u5206\u6790\u57fa\u7840]<\/strong><\/a>\u300b\u7ee7\u7eed\u4ecb\u7ecd\u7ecf\u5178\u6750\u6599\u529b\u5b66\u6216\u7ed3\u6784\u529b\u5b66\u8bfe\u672c\u4e0a\u4ecb\u7ecd\u7684\u538b\u6746\u7a33\u5b9a\u95ee\u9898\u3002\u8be5\u90e8\u5206\u5185\u5bb9\u4e5f\u662f \u4e66\u672c\u00a0\u300a\u6709\u9650\u5355\u5143\u6cd5\uff1a\u7f16\u7a0b\u4e0e\u8f6f\u4ef6\u5e94\u7528\u300b<\/strong><\/a>\u5c48\u66f2\u5206\u6790<\/strong>\u7ae0\u8282\u7684\u90e8\u5206\u5185\u5bb9\u8282\u9009\u3002<\/p>\n

11.5 \u5c48\u66f2\u5206\u67903\uff1a\u538b\u6746\u7a33\u5b9a<\/span> <\/strong><\/p>\n

\u4f5c\u4e3a\u5c48\u66f2\u5206\u6790\u7684\u8865\u5145\uff0c\u672c\u8282\u8ba8\u8bba\u4e00\u4e0b\u538b\u6746\u7a33\u5b9a\u95ee\u9898\u3002<\/p>\n

\"\"<\/p>\n

\u56fe 11\u201110 \u538b\u6746\u652f\u5ea7\u60c5\u51b5<\/strong><\/p>\n

\u7b97\u4f8b\u7ed3\u6784\u4e3a\u4e00\u6839\u7b49\u622a\u9762\u8f74\u5fc3\u53d7\u538b\u76f4\u6746\uff0c\u76f4\u6746\u6750\u6599\u4e3a\u94a2\u7ba1\uff0c\u94a2\u7ba1\u5916\u5f84100mm\uff0c\u7ba1\u539a5mm\uff0c\u9ad85m\u3002\u4e00\u5171\u8003\u8651\u4e865\u79cd\u7ea6\u675f\u60c5\u51b5\uff0c\u5206\u522b\u4e3a\uff1a1.\u4e24\u7aef\u94f0\u63a5\uff1b2.\u4e00\u7aef\u94f0\u63a5\u3001\u4e00\u7aef\u5d4c\u56fa\uff1b3.\u4e24\u7aef\u5d4c\u56fa\uff1b4.\u4e00\u7aef\u5d4c\u56fa\u3001\u4e00\u7aef\u6ed1\u52a8\uff1b5.\u4e00\u7aef\u5d4c\u56fa\u3001\u4e00\u7aef\u81ea\u7531\u3002\u9488\u5bf9\u6bcf\u79cd\u7ea6\u675f\u60c5\u51b5\uff0c\u5206\u522b\u5c06\u538b\u6746\u5212\u5206\u4e3a1\u4e2a\u30012\u4e2a\u30015\u4e2a\u300110\u4e2a\u300120\u4e2a\u6881\u5355\u5143\uff0c\u8fdb\u884c\u5c48\u66f2\u5206\u6790\u3002<\/p>\n

11.5.1\u00a0MATLAB\u4ee3\u7801\u4e0e\u6ce8\u91ca<\/span><\/strong><\/p>\n

\u672c\u8282\u4ee5\u5e95\u7aef\u5d4c\u56fa\u3001\u4e0a\u7aef\u81ea\u7531\u3001\u5212\u520620\u4e2a\u5355\u5143\u7684\u60c5\u51b5\u4e3a\u4f8b\uff0c\u7ed9\u51fa\u8fdb\u884c\u5c48\u66f2\u5206\u6790\u6240\u9700\u7684\u4e3b\u8981\u4ee3\u7801\u3002<\/p>\n

% Pressed Bar Buckling Analysis<\/em><\/span><\/strong><\/code><\/p>\n

% Author <\/em>\uff1a<\/em> JiDong Cui<\/em>\uff08\u5d14\u6d4e\u4e1c\uff09\uff0c<\/em>Xuelong Shen<\/em>\uff08\u6c88\u96ea\u9f99\uff09<\/em><\/span><\/strong><\/code><\/p>\n

% Website : www.jdcui.com<\/em><\/span><\/strong><\/code><\/p>\n

% 20170609<\/em><\/span><\/strong><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u4ee3\u7801\u8bf4\u660e\u3002<\/em><\/code><\/p>\n

% Clear all parameters<\/em><\/strong><\/span><\/code><\/p>\n

clear all<\/span><\/code><\/p>\n

clc<\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u5220\u9664MATLAB\u5de5\u4f5c\u7a7a\u95f4\u4e2d\u7684\u6240\u6709\u53d8\u91cf\uff0c\u5e76\u91ca\u653e\u7cfb\u7edf\u5185\u5b58\u3002\u201cclc\u201d\u7684\u4f5c\u7528\u662f\u6e05\u9664\u547d\u4ee4\u884c\u7684\u5386\u53f2\u6587\u4ef6\u3002<\/em><\/code><\/p>\n

% Format of data output<\/em><\/strong><\/span><\/code><\/p>\n

format shortEng<\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u8be5\u6bb5\u4ee3\u7801\u5bf9\u6570\u636e\u8f93\u51fa\u663e\u793a\u683c\u5f0f\u8fdb\u884c\u8bbe\u7f6e\uff0c\u6307\u5b9a\u683c\u5f0f\u4e3a\u201cshortEng\u201d\uff0c\u5728\u8be5\u683c\u5f0f\u4e0b\uff0c\u7ed3\u679c\u6570\u636e\u4ee5\u5de5\u7a0b\u8ba1\u6570\u6cd5\u7684\u5f62\u5f0f\u8f93\u51fa\uff0c\u5373\u5c06\u6570\u5b57\u8868\u793a\u621010\u7684\u5e42\u7684\u500d\u6570\uff0c\u4e14\u5c0610\u7684\u5e42\u9650\u5236\u4e3a3\u7684\u500d\u6570\uff0c\u5982a\u00d7103i<\/sup>\uff0ci\u4e3a\u6574\u6570\u3002<\/em><\/code><\/p>\n

% Properties definition<\/em><\/strong><\/span><\/code><\/p>\n

E = 2.0E+05;<\/span><\/code><\/p>\n

A = 1492.2565;<\/span><\/code><\/p>\n

I = 1688115.2;<\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u8be5\u6bb5\u4ee3\u7801\u5b9a\u4e49\u4e86\u82e5\u5e72\u53d8\u91cf\uff0c\u5305\u62ec\u6750\u6599\u7684\u5f39\u6027\u6a21\u91cfE\u3001\u622a\u9762\u9762\u79efA\u548c\u622a\u9762\u60ef\u6027\u77e9\u00a0I<\/strong>\u3002<\/em><\/code><\/p>\n

% Node coordinates<\/em><\/strong><\/span><\/code><\/p>\n

nodeCoord = [0 0;0 250;0 500;0 750;0 1000;0 1250;0 1500;0 1750;0 2000;0 2250;0 2500;0 2750;0 3000;0 3250;0 3500;0 3750;0 4000;0 4250;0 4500;0 4750;0 5000];<\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u672c\u7b97\u4f8b\u53ea\u8fdb\u884cXY\u5e73\u9762\u5185\u5206\u6790\uff0c\u538b\u6746\u5206\u4e3a20\u4e2a\u5355\u5143\uff0c\u4e00\u5171\u670921\u4e2a\u8282\u70b9\uff0c\u6bcf\u4e2a\u8282\u70b9\u6709x\u3001y\u4e24\u4e2a\u5750\u6807\uff0c\u56e0\u6b64\u8be5\u6bb5\u4ee3\u7801\u5b9a\u4e49\u4e86\u4e00\u4e2a21\u00d72\u77e9\u9635NodeCoord\uff0c\u7528\u4e8e\u5b58\u50a8\u7ed3\u6784\u4e2d21\u4e2a\u8282\u70b9\u7684x\u3001y\u5750\u6807\u3002<\/em><\/code><\/p>\n

% Element nodes<\/em><\/strong><\/span><\/code><\/p>\n

EleNode = [1 2;2 3;3 4;4 5;5 6;6 7;7 8;8 9;9 10;10 11;11 12;12 13;13 14;14 15;15 16;16 17;17 18;18 19;19 20;20 21];<\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u672c\u7b97\u4f8b\u5171\u670920\u4e2a\u5355\u5143\uff0c\u6bcf\u4e2a\u5355\u5143\u67092\u4e2a\u8282\u70b9\uff0c\u56e0\u6b64\u8be5\u6bb5\u4ee3\u7801\u5b9a\u4e49\u4e86\u4e00\u4e2a20\u00d72\u7684\u77e9\u9635EleNode\uff0c\u7528\u4e8e\u5b58\u50a820\u4e2a\u5355\u5143\u7684\u8282\u70b9\u7f16\u53f7\u3002<\/em><\/code><\/p>\n

restrainedDof = [1 2 3];\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u672c\u7b97\u4f8b\u4e2d\uff0c\u8282\u70b91\u7684x\u5e73\u52a8\u3001y\u5e73\u52a8\u3001\u7ed5z\u8f6c\u52a8\u81ea\u7531\u5ea6\u88ab\u7ea6\u675f\uff0c\u5bf9\u5e94\u7684\u6574\u4f53\u81ea\u7531\u5ea6\u7684\u7f16\u53f7\u5206\u522b\u662f1\u30012\u30013\uff0c\u56e0\u6b64\u8be5\u6bb5\u4ee3\u7801\u5b9a\u4e49\u4e86\u4e00\u4e2a1\u00d73\u7684\u884c\u5411\u91cfrestrainedDof\uff0c\u7528\u4e8e\u5b58\u50a8\u7ea6\u675f\u81ea\u7531\u5ea6\u7f16\u53f7\u3002<\/em><\/code><\/p>\n

% Number of elements and nodes<\/em><\/strong><\/span><\/code><\/p>\n

numEle = size(EleNode,1)<\/span><\/code><\/p>\n

numNode = size(nodeCoord,1)<\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u8be5\u6bb5\u4ee3\u7801\u5b9a\u4e49\u4e86\u4e24\u4e2a\u53d8\u91cfnumEle\u548cnumNode\uff0c\u5206\u522b\u7528\u4e8e\u5b58\u50a8\u7ed3\u6784\u4e2d\u7684\u5355\u5143\u6570\u91cf\uff08\u5373\u77e9\u9635EleNode\u7684\u884c\u6570\uff09\u548c\u8282\u70b9\u6570\u91cf\uff08\u5373\u77e9\u9635NodeCoord\u7684\u884c\u6570\uff09\u3002\u672c\u4f8b\u4e2dnumEle=20\uff0cnumNode=21\u3002<\/em><\/code><\/p>\n

% X coordination and Y coordination of all nodes<\/em><\/strong><\/span><\/code><\/p>\n

xx = nodeCoord(:,1)<\/span><\/code><\/p>\n

yy = nodeCoord(:,2)<\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u8be5\u6bb5\u4ee3\u7801\u5b9a\u4e49\u4e86\u4e24\u4e2a21\u00d71\u7684\u5217\u5411\u91cfxx\u548cyy\uff0c\u5206\u522b\u7528\u4e8e\u5b58\u50a8\u6240\u6709\u8282\u70b9\u7684x\u5750\u6807\u548c\u6240\u6709\u8282\u70b9\u7684y\u5750\u6807\u3002<\/em><\/code><\/p>\n

% Total number of freedom<\/em><\/strong><\/span><\/code><\/p>\n

numDOF = numNode*3;<\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u8be5\u6bb5\u4ee3\u7801\u5b9a\u4e49\u4e86\u4e00\u4e2a\u53d8\u91cfnumDOF\uff0c\u7528\u4e8e\u5b58\u50a8\u81ea\u7531\u5ea6\u7684\u603b\u6570\u3002\u672c\u7b97\u4f8b\u5171\u670921\u4e2a\u8282\u70b9\uff08numNode=21\uff09\uff0c\u6bcf\u4e2a\u8282\u70b9\u67093\u4e2a\u81ea\u7531\u5ea6\uff0c\u56e0\u6b64numDOF\u7684\u503c\u4e3a21\u00d73=63\u3002<\/em><\/code><\/p>\n

% Loading<\/em><\/strong><\/span><\/code><\/p>\n

force(62)=-1;\u00a0 %20 element<\/span><\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u672c\u7b97\u4f8b\u5728\u8282\u70b921\u5904\u65bd\u52a0\u4e86-z\u65b9\u5411\u7684\u5355\u4f4d\u96c6\u4e2d\u529b\uff0c\u8282\u70b921\u7684-z\u65b9\u5411\u5e73\u52a8\u81ea\u7531\u5ea6\u5bf9\u5e94\u6574\u4f53\u81ea\u7531\u5ea6\u7684\u7f16\u53f7\u4e3a62\uff0c\u56e0\u6b64\u8be5\u6bb5\u4ee3\u7801\u4e3a\u6574\u4f53\u8282\u70b9\u529b\u5411\u91cfforce\u7684\u76f8\u5e94\u5143\u7d20\u8d4b\u503c\uff0c\u6307\u5b9aforce(62)\u7684\u503c\u4e3a-1\uff0c\u5176\u4f59\u5143\u7d20\u7684\u503c\u4ecd\u4e3a0\u3002<\/em><\/code><\/p>\n

% Global stiffness matrix<\/em><\/strong><\/span><\/code><\/p>\n

stiffness = zeros(numDOF);<\/span><\/code><\/p>\n

for i=1:numEle;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 noindex = EleNode(i,:);<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 deltax = xx( noindex(2)) - xx( noindex(1));<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 deltay = yy( noindex(2)) - yy( noindex(1));<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 L = sqrt( deltax*deltax + deltay*deltay );<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 C = deltax \/ L;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 S = deltay \/ L;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 % Element stiffness matrix<\/em><\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 T = [ C S 0 0 0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -S C 0 0 0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 0 -1 0 0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 0 0 C S 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 0 0 -S C 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 0 0 0 0 -1<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 ];<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 EAL = E*A\/L;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 EIL1 = E*I\/L;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 EIL2 = 6.0*E*I\/(L*L);<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 EIL3 = 12.0*E*I\/(L*L*L);<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 eleK = [ EAL\u00a0\u00a0 0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0 -EAL\u00a0\u00a0 0\u00a0\u00a0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 EIL3\u00a0 EIL2\u00a0\u00a0\u00a0 0\u00a0 -EIL3\u00a0 EIL2;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 EIL2\u00a0 4*EIL1\u00a0 0\u00a0 -EIL2\u00a0 2*EIL1;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -EAL\u00a0\u00a0 0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0 EAL\u00a0 0\u00a0\u00a0\u00a0\u00a0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a00\u00a0\u00a0 -EIL3 -EIL2\u00a0\u00a0\u00a0 0\u00a0\u00a0 EIL3\u00a0 -EIL2;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 EIL2\u00a0 2*EIL1\u00a0 0\u00a0 -EIL2 4*EIL1<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ];\u00a0\u00a0\u00a0<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 eleDof = [noindex(1)*3-2 noindex(1)*3-1 noindex(1)*3 noindex(2)*3-2 noindex(2)*3-1 noindex(2)*3];<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 % Integrate element stiffness matrix to the global stiffness matrix<\/em><\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 stiffness( eleDof , eleDof) = stiffness( eleDof,eleDof) + T'*eleK*T;\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/code><\/p>\n

end<\/span><\/code><\/p>\n

% Unrestrained freedom<\/em><\/strong><\/span><\/code><\/p>\n

activeDof = setdiff( [1:numDOF]',restrainedDof);<\/span><\/code><\/p>\n

% Solute balance function<\/em><\/span><\/strong><\/code><\/p>\n

disp('Displacement');<\/span><\/code><\/p>\n

displacement(activeDof) = stiffness( activeDof , activeDof)\\force(activeDof);<\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u4e0a\u8ff0\u4ee3\u7801\u5efa\u7acb\u5e73\u8861\u65b9\u7a0b\u5e76\u6c42\u89e3\u3002<\/em><\/code><\/p>\n

% Element axial force<\/em><\/strong><\/span><\/code><\/p>\n

AxialForce=zeros(numEle,1);<\/span><\/code><\/p>\n

for i=1:numEle<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 noindex = EleNode(i,:);<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 deltax = xx( noindex(2)) - xx( noindex(1));<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 deltay = yy( noindex(2)) - yy( noindex(1));<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 L = sqrt( deltax*deltax + deltay*deltay );<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 % Element stiffness matrix<\/em><\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 C = deltax \/ L;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 S = deltay \/ L;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 T = [ C S 0 0 0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0-S C 0 0 0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 0 1 0 0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 0 0 C S 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 0 0 -S C 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 0 0 0 0 1<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 ];<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 EAL = E*A\/L;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 EIL1 = E*I\/L;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 EIL2 = 6.0*E*I\/(L*L);<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 EIL3 = 12.0*E*I\/(L*L*L);<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 eleK = [ EAL\u00a0\u00a0 0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0 -EAL\u00a0\u00a0 0\u00a0\u00a0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 EIL3\u00a0 EIL2\u00a0\u00a0\u00a0 0\u00a0 -EIL3\u00a0 EIL2;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 EIL2\u00a0 4*EIL1\u00a0 0\u00a0 -EIL2\u00a0 2*EIL1;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -EAL\u00a0\u00a0 0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0 EAL\u00a0 0\u00a0\u00a0\u00a0\u00a0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 -EIL3 -EIL2\u00a0\u00a0\u00a0 0\u00a0\u00a0 EIL3\u00a0 -EIL2;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 EIL2\u00a0 2*EIL1\u00a0 0\u00a0 -EIL2 4*EIL1<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ];<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 eleDof = [noindex(1)*3-2 noindex(1)*3-1 noindex(1)*3 noindex(2)*3-2 noindex(2)*3-1 noindex(2)*3];<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 ue=displacement(eleDof,:);<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 uep=T*ue;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 fp=eleK*uep;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 AxialForce(i)=fp(4);<\/span><\/code><\/p>\n

end<\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u4e0a\u8ff0\u4ee3\u7801\u7528\u4e8e\u6c42\u89e3\u5404\u4e2a\u5355\u5143\u7684\u8f74\u529b\uff0c\u5b58\u653e\u5728\u6570\u7ec4AxialForce\u4e2d\uff0c\u7528\u4e8e\u540e\u7eed\u6c42\u89e3\u5355\u5143\u51e0\u4f55\u521a\u5ea6\u77e9\u9635\u3002<\/em><\/code><\/p>\n

% Geometric Stiffness Matrix<\/em><\/strong><\/span><\/code><\/p>\n

stiffnessM = zeros(numDOF);<\/span><\/code><\/p>\n

stiffnessG = zeros(numDOF);<\/span><\/code><\/p>\n

for i=1:numEle;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 noindex = EleNode(i,:);<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 deltax = xx( noindex(2)) - xx( noindex(1));<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 deltay = yy( noindex(2)) - yy( noindex(1));<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 L = sqrt( deltax*deltax + deltay*deltay );<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 C = deltax \/ L;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 S = deltay \/ L;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 T = [ C S 0 0 0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -S C 0 0 0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 0 -1 0 0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 0 0 C S 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 0 0 -S C 0;<\/span><\/code><\/p>\n

\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a00 0 0 0 0 -1<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 ];<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 EAL = E*A\/L;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 EIL1 = E*I\/L;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 EIL2 = 6.0*E*I\/(L*L);<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 EIL3 = 12.0*E*I\/(L*L*L);<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 eleKm = [ EAL\u00a0\u00a0 0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0 -EAL\u00a0\u00a0 0\u00a0\u00a0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 EIL3\u00a0 EIL2\u00a0\u00a0\u00a0 0\u00a0 -EIL3\u00a0 EIL2;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 EIL2\u00a0 4*EIL1\u00a0 0\u00a0 -EIL2\u00a0 2*EIL1;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -EAL\u00a0\u00a0 0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0 EAL\u00a0 0\u00a0\u00a0\u00a0\u00a0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 -EIL3 -EIL2\u00a0\u00a0\u00a0 0\u00a0\u00a0 EIL3\u00a0 -EIL2;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 EIL2\u00a0 2*EIL1\u00a0 0\u00a0 -EIL2 4*EIL1<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ];<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 eleKgu=AxialForce(i)\/L*[0,\u00a0\u00a0 0,\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a00,0,\u00a0\u00a0\u00a0 0,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0, 6\/5,\u00a0\u00a0\u00a0 L\/10,0, -6\/5,\u00a0\u00a0\u00a0 L\/10;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0,L\/10,2*L^2\/15,0,-L\/10, -L^2\/30;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0,\u00a0\u00a0 0,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0,0,\u00a0\u00a0\u00a0 0,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0,-6\/5,\u00a0\u00a0 -L\/10,0,\u00a0 6\/5,\u00a0\u00a0 -L\/10;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0,L\/10, -L^2\/30,0,-L\/10,2*L^2\/15<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ];<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 eleKg=T'*eleKgu*T;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 eleDof = [noindex(1)*3-2 noindex(1)*3-1 noindex(1)*3 noindex(2)*3-2 noindex(2)*3-1 noindex(2)*3];<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 stiffnessM( eleDof , eleDof) = stiffnessM( eleDof,eleDof) + T'*eleKm*T;<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 stiffnessG( eleDof , eleDof) = stiffnessG( eleDof , eleDof) + eleKg;<\/span><\/code><\/p>\n

end<\/span><\/code><\/p>\n

\u6ce8\u91ca\uff1a\u672c\u6bb5\u4ee3\u7801\u4e3b\u8981\u7528\u4e8e\u6839\u636e\u5355\u5143\u51e0\u4f55\u521a\u5ea6\u77e9\u9635\u548c\u5355\u5143\u5185\u529b\u6c42\u5f97\u7ed3\u6784\u6574\u4f53\u51e0\u4f55\u521a\u5ea6\u77e9\u9635\u3002<\/em><\/code><\/p>\n

% Solution<\/em><\/strong><\/span><\/code><\/p>\n

A=-stiffnessM(activeDof,activeDof)\\stiffnessG(activeDof,activeDof);<\/span><\/code><\/p>\n

[Vo,Do] = eig(A);\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % Get the eigenvalues and eigenvectors<\/em><\/span><\/code><\/p>\n

fo=diag(Do);<\/span><\/code><\/p>\n

Vf=sortrows([Vo',fo],size(Vo,1)+1);<\/span><\/code><\/p>\n

V=Vf(:,1:size(Vo,1))';\u00a0\u00a0\u00a0<\/span><\/code><\/p>\n

f=sort(fo);\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/code><\/p>\n

fac=1.\/f<\/span><\/code><\/p>\n

fac=1.\/f<\/span><\/code><\/p>\n

\u672c\u6bb5\u4ee3\u7801\u901a\u8fc7\u6c42\u89e3\u6807\u51c6\u7279\u5f81\u503c\u95ee\u9898\uff0c\u6c42\u5f97\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u3002Matlab\u5185\u7f6e\u51fd\u6570\u00a0eig([A])\u00a0<\/strong>\u53ef\u76f4\u63a5\u6c42\u89e3\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff0c\u6c42\u5f97\u7684\u7279\u5f81\u503c\u653e\u5728\u5411\u91cf\u00a0{Do}\u00a0<\/strong>\u4e2d\uff0c\u76f8\u5e94\u7684\u7279\u5f81\u5411\u91cf\u653e\u5728\u77e9\u9635\u00a0[Vo]\u00a0<\/strong>\u4e2d\u3002\u5176\u540e\u7684\u4ee3\u7801\u7528\u4e8e\u5904\u7406\u6c42\u89e3\u5f97\u5230\u7684\u6570\u636e\uff0c\u5176\u4e2d\u4ee3\u7801\u201cV=\u201d\u7528\u4e8e\u5c06\u7279\u5f81\u5411\u91cf\u6392\u5e8f\uff0c\u4ee3\u7801\u201cf=\u201d\u7528\u4e8e\u5c06\u7ed3\u6784\u81ea\u632f\u9891\u7387\u8fdb\u884c\u6392\u5e8f\uff0c\u4ee3\u7801\u00a0\u201cfac=\u201d\u00a0<\/strong>\u7528\u4e8e\u6c42\u5f97\u5c48\u66f2\u56e0\u5b50<\/strong>\uff0c\u5373\u7279\u5f81\u503c\u7684\u5012\u6570\u3002\u56fe 11\u20113\u6240\u793a\u662f\u8be5\u6841\u67b6\u7ed3\u6784\u7684\u524d\u4e09\u9636\u5c48\u66f2\u6a21\u6001\u3002<\/p>\n

11.5.2 SAP2000\u5206\u6790<\/span><\/strong><\/p>\n

\u7531\u4e8e\u538b\u6746\u6a21\u578b\u8f83\u4e3a\u7b80\u5355\uff0c\u6b64\u5904\u4e0d\u518d\u8d58\u8ff0\u5efa\u6a21\u8fc7\u7a0b\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u91cc\u5728\u538b\u6746\u9876\u7aef\u65bd\u52a0\u7684\u8377\u8f7d\u4e3a1\uff0c\u5982\u6b64\u7b97\u51fa\u6765\u7684\u5c48\u66f2\u56e0\u5b50\u4e5f\u5c31\u7b49\u4e8e\u538b\u6746\u7684\u4e34\u754c\u627f\u8f7d\u529b\u3002<\/p>\n

\u5404\u7ea6\u675f\u60c5\u51b5\u4e0b\u538b\u6746\u4e34\u754c\u627f\u8f7d\u529b\u7684MATLAB\u5206\u6790\u7ed3\u679c\u4e0eSAP2000\u5206\u6790\u7ed3\u679c\u53ca\u5176\u4e0e\u7406\u8bba\u89e3\u7684\u5bf9\u6bd4\u5217\u8868\u5982\u4e0b\u3002<\/p>\n

\u8868 11\u20113 \u7ea6\u675f\u60c5\u51b51\uff1a\u4e24\u7aef\u94f0\u63a5\uff08\u5355\u4f4d\uff1aN\uff09<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n
\u7ea6\u675f\u60c5\u51b5<\/td>\n\u4e24\u7aef\u94f0\u63a5<\/td>\n<\/tr>\n
\u5355\u5143\u5212\u5206<\/td>\n\u7406\u8bba\u89e3<\/td>\nSAP2000<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\nMATLAB<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\n<\/tr>\n
1<\/td>\n133288<\/td>\n162059<\/td>\n21.585<\/td>\n162059<\/td>\n21.585<\/td>\n<\/tr>\n
2<\/td>\n133288<\/td>\n134290<\/td>\n0.752<\/td>\n134291<\/td>\n0.752<\/td>\n<\/tr>\n
5<\/td>\n133288<\/td>\n133317<\/td>\n0.022<\/td>\n133317<\/td>\n0.022<\/td>\n<\/tr>\n
10<\/td>\n133288<\/td>\n133290<\/td>\n0.001<\/td>\n133290<\/td>\n0.001<\/td>\n<\/tr>\n
20<\/td>\n133288<\/td>\n133288<\/td>\n0.000<\/td>\n133288<\/td>\n0.000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u6ce8\uff1a\u538b\u6746\u4e34\u754c\u627f\u8f7d\u529b\u7406\u8bba\u503c\uff1a\u03c02<\/sup>EI\/(\u03bcl)2<\/sup>=133288N\uff0c\u5176\u4e2d\u03bc=1.0\u3002<\/em><\/span><\/p>\n

\u8868 11\u20114 \u7ea6\u675f\u60c5\u51b52\uff1a\u4e00\u7aef\u94f0\u63a5\u3001\u4e00\u7aef\u56fa\u5b9a\uff08\u5355\u4f4d\uff1aN\uff09<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n
\u7ea6\u675f\u60c5\u51b5<\/td>\n\u4e00\u7aef\u94f0\u63a5\u4e00\u7aef\u56fa\u5b9a<\/td>\n<\/tr>\n
\u5355\u5143\u5212\u5206<\/td>\n\u7406\u8bba\u89e3<\/td>\nSAP2000<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\nMATLAB<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\n<\/tr>\n
1<\/td>\n266657<\/td>\n405148<\/td>\n51.936<\/td>\n405148<\/td>\n51.936<\/td>\n<\/tr>\n
2<\/td>\n266657<\/td>\n279671<\/td>\n4.880<\/td>\n279671<\/td>\n4.880<\/td>\n<\/tr>\n
5<\/td>\n266657<\/td>\n272910<\/td>\n2.345<\/td>\n272910<\/td>\n2.345<\/td>\n<\/tr>\n
10<\/td>\n266657<\/td>\n272689<\/td>\n2.262<\/td>\n272690<\/td>\n2.262<\/td>\n<\/tr>\n
20<\/td>\n266657<\/td>\n272675<\/td>\n2.257<\/td>\n272675<\/td>\n2.257<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u6ce8\uff1a\u538b\u6746\u4e34\u754c\u627f\u8f7d\u529b\u7406\u8bba\u503c\uff1a\u03c02<\/sup>EI\/(\u03bcl)2<\/sup>=266657N\uff0c\u5176\u4e2d\u03bc=0.707\u3002<\/em><\/span><\/p>\n

\u8868 11\u20115 \u7ea6\u675f\u60c5\u51b53\uff1a\u4e24\u7aef\u5d4c\u56fa\uff08\u5355\u4f4d\uff1aN\uff09<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n
\u7ea6\u675f\u60c5\u51b5<\/td>\n\u4e24\u7aef\u5d4c\u56fa<\/td>\n<\/tr>\n
\u5355\u5143\u5212\u5206<\/td>\n\u7406\u8bba\u89e3<\/td>\nSAP2000<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\nMATLAB<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\n<\/tr>\n
1<\/td>\n533153<\/td>\n–<\/td>\n–<\/td>\n–<\/td>\n–<\/td>\n<\/tr>\n
2<\/td>\n533153<\/td>\n540197<\/td>\n1.321<\/td>\n540197<\/td>\n1.321<\/td>\n<\/tr>\n
5<\/td>\n533153<\/td>\n534862<\/td>\n0.321<\/td>\n534862<\/td>\n0.321<\/td>\n<\/tr>\n
10<\/td>\n533153<\/td>\n533266<\/td>\n0.021<\/td>\n533266<\/td>\n0.021<\/td>\n<\/tr>\n
20<\/td>\n533153<\/td>\n533160<\/td>\n0.001<\/td>\n533160<\/td>\n0.001<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u6ce8\uff1a\u538b\u6746\u4e34\u754c\u627f\u8f7d\u529b\u7406\u8bba\u503c\uff1a\u03c02<\/sup>EI\/(\u03bcl)2<\/sup>=533153N\uff0c\u5176\u4e2d\u03bc=0.5\u3002<\/span><\/em><\/p>\n

\u8868 11\u20116 \u7ea6\u675f\u60c5\u51b54\uff1a\u4e00\u7aef\u5d4c\u56fa\u3001\u4e00\u7aef\u6ed1\u52a8\uff08\u5355\u4f4d\uff1aN\uff09<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n
\u7ea6\u675f\u60c5\u51b5<\/td>\n\u4e00\u7aef\u5d4c\u56fa\u3001\u4e00\u7aef\u6ed1\u52a8<\/td>\n<\/tr>\n
\u5355\u5143\u5212\u5206<\/td>\n\u7406\u8bba\u89e3<\/td>\nSAP2000<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\nMATLAB<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\n<\/tr>\n
1<\/td>\n133288<\/td>\n135049<\/td>\n1.321<\/td>\n135049<\/td>\n1.321<\/td>\n<\/tr>\n
2<\/td>\n133288<\/td>\n134291<\/td>\n0.752<\/td>\n134291<\/td>\n0.752<\/td>\n<\/tr>\n
5<\/td>\n133288<\/td>\n133317<\/td>\n0.022<\/td>\n133317<\/td>\n0.022<\/td>\n<\/tr>\n
10<\/td>\n133288<\/td>\n133290<\/td>\n0.001<\/td>\n133290<\/td>\n0.001<\/td>\n<\/tr>\n
20<\/td>\n133288<\/td>\n133288<\/td>\n0.000<\/td>\n133288<\/td>\n0.000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u6ce8\uff1a\u538b\u6746\u4e34\u754c\u627f\u8f7d\u529b\u7406\u8bba\u503c\uff1a\u03c02<\/sup>EI\/(\u03bcl)2<\/sup>=133288N\uff0c\u5176\u4e2d\u03bc=1.0\u3002<\/span><\/em><\/p>\n

\u8868 11\u20117 \uff1a\u7ea6\u675f\u60c5\u51b55\uff1a\u4e00\u7aef\u5d4c\u56fa\u3001\u4e00\u7aef\u81ea\u7531\uff08\u5355\u4f4d\uff1aN\uff09<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n
\u7ea6\u675f\u60c5\u51b5<\/td>\n\u4e00\u7aef\u5d4c\u56fa\u3001\u4e00\u7aef\u81ea\u7531<\/td>\n<\/tr>\n
\u5355\u5143\u5212\u5206<\/td>\n\u7406\u8bba\u89e3<\/td>\nSAP2000<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\nMATLAB<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\n<\/tr>\n
1<\/td>\n33322<\/td>\n33573<\/td>\n0.753<\/td>\n33573<\/td>\n0.753<\/td>\n<\/tr>\n
2<\/td>\n33322<\/td>\n33339<\/td>\n0.051<\/td>\n33339<\/td>\n0.051<\/td>\n<\/tr>\n
5<\/td>\n33322<\/td>\n33323<\/td>\n0.003<\/td>\n33323<\/td>\n0.003<\/td>\n<\/tr>\n
10<\/td>\n33322<\/td>\n33322<\/td>\n0.000<\/td>\n33322<\/td>\n0.000<\/td>\n<\/tr>\n
20<\/td>\n33322<\/td>\n33322<\/td>\n0.000<\/td>\n33322<\/td>\n0.000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u6ce8\uff1a\u538b\u6746\u4e34\u754c\u627f\u8f7d\u529b\u7406\u8bba\u503c\uff1a\u03c02<\/sup>EI\/(\u03bcl)2<\/sup>=33322N\uff0c\u5176\u4e2d\u03bc=2.0\u3002<\/span><\/em><\/p>\n

11.5.3 midas Gen\u5206\u6790<\/span><\/strong><\/p>\n

\u538b\u6746\u6a21\u578b\u7684midas Gen\u5efa\u6a21\u601d\u8def\u4e0eSAP2000\u7c7b\u4f3c\uff0c\u6b64\u5904\u4e0d\u518d\u8d58\u8ff0\u3002<\/p>\n

\u5404\u7ea6\u675f\u60c5\u51b5\u4e0b\u538b\u6746\u4e34\u754c\u627f\u8f7d\u529b\u7684MATLAB\u5206\u6790\u7ed3\u679c\u4e0emidas Gen\u5206\u6790\u7ed3\u679c\u53ca\u5176\u4e0e\u7406\u8bba\u89e3\u7684\u5bf9\u6bd4\u5217\u8868\u5982\u4e0b\u3002<\/p>\n

\u8868 11\u20118 \u7ea6\u675f\u60c5\u51b51\uff1a\u4e24\u7aef\u94f0\u63a5\uff08\u5355\u4f4d\uff1aN\uff09<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n
\u7ea6\u675f\u60c5\u51b5<\/td>\n\u4e24\u7aef\u94f0\u63a5<\/td>\n<\/tr>\n
\u5355\u5143\u5212\u5206<\/td>\n\u7406\u8bba\u89e3<\/td>\nmidas Gen<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\nMATLAB<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\n<\/tr>\n
1<\/td>\n133288<\/td>\n162059<\/td>\n21.585<\/td>\n162059<\/td>\n21.585<\/td>\n<\/tr>\n
2<\/td>\n133288<\/td>\n134290<\/td>\n0.752<\/td>\n134291<\/td>\n0.752<\/td>\n<\/tr>\n
5<\/td>\n133288<\/td>\n133317<\/td>\n0.022<\/td>\n133317<\/td>\n0.022<\/td>\n<\/tr>\n
10<\/td>\n133288<\/td>\n133290<\/td>\n0.001<\/td>\n133290<\/td>\n0.001<\/td>\n<\/tr>\n
20<\/td>\n133288<\/td>\n133288<\/td>\n0.000<\/td>\n133288<\/td>\n0.000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u6ce8\uff1a\u538b\u6746\u4e34\u754c\u627f\u8f7d\u529b\u7406\u8bba\u503c\uff1a\u03c02<\/sup>EI\/(\u03bcl)2<\/sup>=133288N\uff0c\u5176\u4e2d\u03bc=1.0\u3002<\/em><\/span><\/p>\n

\u8868 11\u20119 \u7ea6\u675f\u60c5\u51b52\uff1a\u4e00\u7aef\u94f0\u63a5\u3001\u4e00\u7aef\u56fa\u5b9a\uff08\u5355\u4f4d\uff1aN\uff09<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n
\u7ea6\u675f\u60c5\u51b5<\/td>\n\u4e00\u7aef\u94f0\u63a5\u4e00\u7aef\u56fa\u5b9a<\/td>\n<\/tr>\n
\u5355\u5143\u5212\u5206<\/td>\n\u7406\u8bba\u89e3<\/td>\nmidas Gen<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\nMATLAB<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\n<\/tr>\n
1<\/td>\n266657<\/td>\n405148<\/td>\n51.936<\/td>\n405148<\/td>\n51.936<\/td>\n<\/tr>\n
2<\/td>\n266657<\/td>\n279671<\/td>\n4.880<\/td>\n279671<\/td>\n4.880<\/td>\n<\/tr>\n
5<\/td>\n266657<\/td>\n272910<\/td>\n2.345<\/td>\n272910<\/td>\n2.345<\/td>\n<\/tr>\n
10<\/td>\n266657<\/td>\n272689<\/td>\n2.262<\/td>\n272690<\/td>\n2.262<\/td>\n<\/tr>\n
20<\/td>\n266657<\/td>\n272675<\/td>\n2.257<\/td>\n272675<\/td>\n2.257<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u6ce8\uff1a\u538b\u6746\u4e34\u754c\u627f\u8f7d\u529b\u7406\u8bba\u503c\uff1a\u03c02<\/sup>EI\/(\u03bcl)2<\/sup>=266657N\uff0c\u5176\u4e2d\u03bc=0.707\u3002<\/em><\/span><\/p>\n

\u8868 11\u201110 \u7ea6\u675f\u60c5\u51b53\uff1a\u4e24\u7aef\u5d4c\u56fa\uff08\u5355\u4f4d\uff1aN\uff09<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n
\u7ea6\u675f\u60c5\u51b5<\/td>\n\u4e24\u7aef\u5d4c\u56fa<\/td>\n<\/tr>\n
\u5355\u5143\u5212\u5206<\/td>\n\u7406\u8bba\u89e3<\/td>\nmidas Gen<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\nMATLAB<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\n<\/tr>\n
1<\/td>\n533153<\/td>\n–<\/td>\n–<\/td>\n–<\/td>\n–<\/td>\n<\/tr>\n
2<\/td>\n533153<\/td>\n540197<\/td>\n1.321<\/td>\n540197<\/td>\n1.321<\/td>\n<\/tr>\n
5<\/td>\n533153<\/td>\n534862<\/td>\n0.321<\/td>\n534862<\/td>\n0.321<\/td>\n<\/tr>\n
10<\/td>\n533153<\/td>\n533266<\/td>\n0.021<\/td>\n533266<\/td>\n0.021<\/td>\n<\/tr>\n
20<\/td>\n533153<\/td>\n533160<\/td>\n0.001<\/td>\n533160<\/td>\n0.001<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u6ce8\uff1a\u538b\u6746\u4e34\u754c\u627f\u8f7d\u529b\u7406\u8bba\u503c\uff1a\u03c02<\/sup>EI\/(\u03bcl)2<\/sup>=533153N\uff0c\u5176\u4e2d\u03bc=0.5\u3002<\/span><\/em><\/p>\n

\u8868 11\u201111 \u7ea6\u675f\u60c5\u51b54\uff1a\u4e00\u7aef\u5d4c\u56fa\u3001\u4e00\u7aef\u6ed1\u52a8\uff08\u5355\u4f4d\uff1aN\uff09<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n
\u7ea6\u675f\u60c5\u51b5<\/td>\n\u4e00\u7aef\u5d4c\u56fa\u3001\u4e00\u7aef\u6ed1\u52a8<\/td>\n<\/tr>\n
\u5355\u5143\u5212\u5206<\/td>\n\u7406\u8bba\u89e3<\/td>\nmidas Gen<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\nMATLAB<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\n<\/tr>\n
1<\/td>\n133288<\/td>\n135049<\/td>\n1.321<\/td>\n135049<\/td>\n1.321<\/td>\n<\/tr>\n
2<\/td>\n133288<\/td>\n134291<\/td>\n0.752<\/td>\n134291<\/td>\n0.752<\/td>\n<\/tr>\n
5<\/td>\n133288<\/td>\n133317<\/td>\n0.022<\/td>\n133317<\/td>\n0.022<\/td>\n<\/tr>\n
10<\/td>\n133288<\/td>\n133290<\/td>\n0.001<\/td>\n133290<\/td>\n0.001<\/td>\n<\/tr>\n
20<\/td>\n133288<\/td>\n133288<\/td>\n0.000<\/td>\n133288<\/td>\n0.000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u6ce8\uff1a\u538b\u6746\u4e34\u754c\u627f\u8f7d\u529b\u7406\u8bba\u503c\uff1a\u03c02<\/sup>EI\/(\u03bcl)2<\/sup>=133288N\uff0c\u5176\u4e2d\u03bc=1.0\u3002<\/em><\/span><\/p>\n

\u8868 11\u201112 \uff1a\u7ea6\u675f\u60c5\u51b55\uff1a\u4e00\u7aef\u5d4c\u56fa\u3001\u4e00\u7aef\u81ea\u7531\uff08\u5355\u4f4d\uff1aN\uff09<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n
\u7ea6\u675f\u60c5\u51b5<\/td>\n\u4e00\u7aef\u5d4c\u56fa\u3001\u4e00\u7aef\u81ea\u7531<\/td>\n<\/tr>\n
\u5355\u5143\u5212\u5206<\/td>\n\u7406\u8bba\u89e3<\/td>\nmidas Gen<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\nMATLAB<\/td>\n\u76f8\u5bf9\u8bef\u5dee\uff08%\uff09<\/td>\n<\/tr>\n
1<\/td>\n33322<\/td>\n33573<\/td>\n0.753<\/td>\n33573<\/td>\n0.753<\/td>\n<\/tr>\n
2<\/td>\n33322<\/td>\n33339<\/td>\n0.051<\/td>\n33339<\/td>\n0.051<\/td>\n<\/tr>\n
5<\/td>\n33322<\/td>\n33323<\/td>\n0.003<\/td>\n33323<\/td>\n0.003<\/td>\n<\/tr>\n
10<\/td>\n33322<\/td>\n33322<\/td>\n0.000<\/td>\n33322<\/td>\n0.000<\/td>\n<\/tr>\n
20<\/td>\n33322<\/td>\n33322<\/td>\n0.000<\/td>\n33322<\/td>\n0.000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u6ce8\uff1a\u538b\u6746\u4e34\u754c\u627f\u8f7d\u529b\u7406\u8bba\u503c\uff1a\u03c02<\/sup>EI\/(\u03bcl)2<\/sup>=33322N\uff0c\u5176\u4e2d\u03bc=2.0\u3002<\/em><\/span><\/p>\n

\u3010\u5bf9\u6bd4\u53ef\u77e5\uff0cMATLAB\u3001SAP2000\u4e0emidas Gen\u5206\u6790\u7ed3\u679c\u543b\u5408\u5f88\u597d\uff0c\u4e14\u968f\u7740\u5355\u5143\u7ec6\u5316\uff0c\u6570\u503c\u5206\u6790\u7ed3\u679c\u9010\u6e10\u63a5\u8fd1\u7406\u8bba\u503c\u3002\u3011<\/strong><\/span><\/em><\/h4>\n
\n