{"id":10728,"date":"2018-12-31T15:50:20","date_gmt":"2018-12-31T07:50:20","guid":{"rendered":"http:\/\/www.jdcui.com\/?p=10728"},"modified":"2026-02-18T21:01:03","modified_gmt":"2026-02-18T13:01:03","slug":"femmatlab%e6%9c%89%e9%99%90%e5%85%83%e7%bc%96%e7%a8%8b-programming-of-buckling-analysis-by-frame-elements-%e6%a1%86%e6%9e%b6%e5%8d%95%e5%85%83%e6%9b%b2%e5%b1%88%e5%88%86%e6%9e%90%e7%bc%96","status":"publish","type":"post","link":"http:\/\/www.jdcui.com\/?p=10728","title":{"rendered":"[FEM][MATLAB][\u6709\u9650\u5143][\u7f16\u7a0b] FEM Buckling Analysis Programming with MATLAB (Frame Elements) (\u6846\u67b6\u5355\u5143\u66f2\u5c48\u5206\u6790\u7f16\u7a0b)"},"content":{"rendered":"

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

\u4eca\u5929\u662f20181231,2018\u5e74\u7684\u6700\u540e\u4e00\u5929\uff0c\u5e0c\u671b\u65b0\u7684\u4e00\u5e74\u4f1a\u66f4\u597d\u3002<\/strong><\/p>\n

<\/p>\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\u6846\u67b6\u5355\u5143(Frame Element)\u7528\u4e8e\u5c48\u66f2\u5206\u6790<\/strong>\u7684\u65b9\u6cd5\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

11.4 <\/span>\u5c48\u66f2\u5206\u67902\uff1a2D\u6846\u67b6<\/strong><\/span><\/p>\n

\"\"<\/p>\n

\u56fe 11\u20117 \u7ed3\u6784\u6a21\u578b\u793a\u610f<\/strong><\/p>\n

\u56fe 11\u20117\u662f\u672c\u7ae0\u7684\u7b97\u4f8b\u7ed3\u6784\uff0c\u662f\u4e00\u6980\u5e73\u9762\u6846\u67b6\u7ed3\u6784\uff0c\u7ed3\u6784\u51e0\u4f55\u4fe1\u606f\u3001\u6784\u4ef6\u5c5e\u6027\u548c\u7ea6\u675f\u4fe1\u606f\u4e0e\u7b2c\u4e8c\u7ae0\u4e2d\u9759\u529b\u5206\u6790\u65f6\u76f8\u540c\uff0c\u8377\u8f7d\u6837\u5f0f\u4e3a\uff1a\u8282\u70b94\u5904\u53d7\u5230+x\u65b9\u541150kN\u7684\u96c6\u4e2d\u529b\u548c-z\u65b9\u5411\u7684100kN\u96c6\u4e2d\u529b\u4f5c\u7528\uff0c\u8282\u70b98\u53d7\u5230-z\u65b9\u5411\u7684100kN\u96c6\u4e2d\u529b\u4f5c\u7528\u3002\u672c\u7ae0\u5c06\u57fa\u4e8e\u6b27\u62c9\u6881\u5355\u5143\u5bf9\u8be5\u7ed3\u6784\u8fdb\u884c\u56fe\u4e2d\u8377\u8f7d\u6837\u5f0f\u4e0b\u7684\u5c48\u66f2\u5206\u6790\uff0c\u5e76\u5c06\u57fa\u4e8eMATLAB<\/strong>\u7f16\u7a0b\u8ba1\u7b97\u7684\u7ed3\u679c\u4e0eSAP2000\u3001midas Gen<\/strong>\u5206\u6790\u7ed3\u679c\u8fdb\u884c\u5bf9\u6bd4\u3002<\/p>\n

\u4ee5\u4e0b\u76f4\u63a5\u7ed9\u51fa\u6b27\u62c9\u6881\u5355\u5143\u7684\u51e0\u4f55\u521a\u5ea6\u77e9\u9635<\/p>\n

\"\"\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(11.4\u20111)<\/strong><\/p>\n

\u5176\u4e2dFx<\/sub><\/strong>\u4e3a\u5355\u5143\u8f74\u529b\u3002<\/p>\n

11.4.1 MATLAB\u4ee3\u7801\u4e0e\u6ce8\u91ca<\/strong><\/span><\/p>\n

\u5c48\u66f2\u5206\u6790\u7684Matlab\u4ee3\u7801\u4e0e\u524d\u9762\u7ae0\u8282\u4e2d\u9759\u529b\u5206\u6790\u7684Matlab\u4ee3\u7801\u7565\u6709\u4e0d\u540c\uff0c\u8fd9\u91cc\u7ed9\u51fa\u8fdb\u884c\u5c48\u66f2\u5206\u6790\u6240\u9700\u7684\u4e3b\u8981\u4ee3\u7801\u3002<\/p>\n

% Frame 2D Buckling Analysis<\/em><\/strong><\/span><\/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><\/strong><\/span><\/code><\/p>\n

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

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

\u2026\u2026<\/span><\/code><\/p>\n

\u6b64\u524d\u4ee3\u7801\u4e0e\u9759\u529b\u5206\u6790\u4ee3\u7801\u76f8\u540c\uff0c\u4e0d\u518d\u8d58\u8ff0\u3002<\/em><\/code><\/p>\n

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

force(10)=50;<\/span><\/code><\/p>\n

force(11)=-200;<\/span><\/code><\/p>\n

force(23)=-200;<\/span><\/code><\/p>\n

\u2026\u2026<\/span><\/code><\/p>\n

\u6839\u636e\u56fe 11\u20112\uff0c\u4e3a\u76f8\u5e94\u7684\u81ea\u7531\u5ea6\u65bd\u52a0\u8377\u8f7d\uff0c\u4f5c\u4e3a\u53c2\u8003\u8377\u8f7d\uff0c\u7528\u4e8e\u540e\u7eed\u6c42\u89e3\u5355\u5143\u7684\u51e0\u4f55\u521a\u5ea6\u77e9\u9635\u3002<\/em><\/code><\/p>\n

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

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

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

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

disp('Force')<\/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 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 E = EList(EleSect(i));<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 A = AList(EleSect(i));<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 I = IList(EleSect(i));<\/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 % Element stiffness matrix<\/em><\/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

\u8be5\u6bb5\u4ee3\u7801\u4e0e\u666e\u901a\u9759\u529b\u5206\u6790\u7684\u4ee3\u7801\u57fa\u672c\u76f8\u540c\uff0c\u4e3b\u8981\u7528\u4e8e\u8ba1\u7b97\u53c2\u8003\u8377\u8f7d\u4f5c\u7528\u4e0b\u5355\u5143\u7684\u5185\u529b\uff0c\u7528\u4e8e\u540e\u7eed\u8ba1\u7b97\u5355\u5143\u7684\u51e0\u4f55\u521a\u5ea6\u77e9\u9635\uff0c\u4ee5\u4e0b\u5c06\u4ecb\u7ecd\u5c48\u66f2\u5206\u6790\u90e8\u5206\u7684\u4e3b\u8981\u4ee3\u7801\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

% Traverse all elements<\/em><\/span><\/code><\/p>\n

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

\u00a0\u00a0\u00a0 % Index of the element nodes<\/em><\/span><\/code><\/p>\n

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

\u00a0\u00a0\u00a0 % Element length<\/em><\/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 g<\/em>eometric <\/em>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 % Section properties<\/em><\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 E = EList(EleSect(i));<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 A = AList(EleSect(i));<\/span><\/code><\/p>\n

\u00a0\u00a0\u00a0 I = IList(EleSect(i));<\/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 \u00a0EIL2;<\/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\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\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 % Corresponding freedom of the element nodes<\/em><\/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 g<\/em>eometric <\/em>stiffness matrix to the global g<\/em>eometric <\/em>stiffness matrix<\/em><\/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

\u672c\u6bb5\u4ee3\u7801\u4e3b\u8981\u4f5c\u7528\uff1a\u5229\u7528\u53c2\u8003\u8377\u8f7d\u4f5c\u7528\u4e0b\u7684\u5355\u5143\u5185\u529b\uff0c\u6c42\u89e3\u5355\u5143\u7684\u51e0\u4f55\u521a\u5ea6\u77e9\u9635\uff0c\u8fdb\u800c\u91c7\u7528\u201c\u5bf9\u53f7\u5165\u5ea7\u201d\u7684\u65b9\u5f0f\uff0c\u5c06\u5355\u5143\u7684\u51e0\u4f55\u521a\u5ea6\u77e9\u9635\u53e0\u52a0\uff0c\u83b7\u5f97\u7ed3\u6784\u6574\u4f53\u7684\u51e0\u4f55\u521a\u5ea6\u77e9\u9635\u00a0<\/em>[k\u03c3<\/sub>] <\/strong>\u3002<\/em><\/code><\/p>\n

% Solute<\/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><\/span><\/code><\/p>\n

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

posneg=1.\/fo.*abs(fo);\u00a0\u00a0\u00a0<\/span><\/code><\/p>\n

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

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

f=Vf(:,size(Vo,1)+1).*Vf(:,size(Vo,1)+2);<\/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

\"\"<\/p>\n

\uff08a\uff09\u7b2c\u4e00\u9636<\/p>\n

\"\"<\/p>\n

\uff08b\uff09\u7b2c\u4e8c\u9636<\/p>\n

\"\"<\/p>\n

\uff08c\uff09\u7b2c\u4e09\u9636<\/p>\n

\u56fe 11\u20118 \u6846\u67b6\u7ed3\u6784\u5c48\u66f2\u6a21\u6001<\/strong><\/p>\n

11.4.2 SAP2000\u5206\u6790\u7ed3\u679c\u5bf9\u6bd4<\/strong><\/p>\n

\u8868 11\u20112\u00a0<\/strong>\u7ed9\u51fa\u4e86MATLAB\u5206<\/strong>\u6790\u7684\u7ed3\u6784\u524d6\u9636\u5c48\u66f2\u56e0\u5b50\u4e0eSAP2000\u5206\u6790\u7ed3\u679c\u7684\u5bf9\u6bd4\uff0c\u53ef\u4ee5\u770b\u51fa\uff0c\u4e24\u8005\u543b\u5408\u5f88\u597d\u3002<\/p>\n

\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t
\u5c48\u66f2\u6a21\u6001<\/th>SAP2000\u7ed3\u679c<\/th>MATLAB\u7ed3\u679c<\/th>\u76f8\u5bf9\u504f\u5dee\uff08%\uff09<\/th>\n<\/tr>\n<\/thead>\n
1<\/td>74.696<\/td>74.696<\/td>0<\/td>\n<\/tr>\n
2<\/td>154.931<\/td>154.931<\/td>0<\/td>\n<\/tr>\n
3<\/td>302.256<\/td>302.256<\/td>0<\/td>\n<\/tr>\n
4<\/td>520.888<\/td>520.888<\/td>0<\/td>\n<\/tr>\n
5<\/td>786.546<\/td>786.546<\/td>0<\/td>\n<\/tr>\n
6<\/td>997.026<\/td>997.026<\/td>0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n2D Frame Buckling SAP2000 vs. Matlab<\/span>\n\n

\u8868 11\u20112 2D\u6846\u67b6\u67b6\u5c48\u66f2\u5206\u6790\u7ed3\u679c\u5bf9\u6bd4<\/strong><\/p>\n

11.4.3 midas Gen\u5206\u6790\u7ed3\u679c\u5bf9\u6bd4<\/strong><\/p>\n

midas Gen\u6a21\u6001\u5206\u6790\u8fc7\u7a0b\u4e0e\u4e0a\u8282\u4e2d\u6841\u67b6\u7ed3\u6784\u7c7b\u4f3c\uff0c\u6b64\u5904\u4e0d\u518d\u8d58\u8ff0\u3002midas Gen\u6a21\u6001\u5206\u6790\u7ed3\u679c\u5982\u56fe 11\u20119\u6240\u793a\uff0c\u5bf9\u6bd4\u4e0a\u8ff0MATLAB\u5206\u6790\u7ed3\u679c\u4e0eSAP2000\u5206\u6790\u7ed3\u679c\uff0c\u53ef\u89c1\u5206\u6790\u7ed3\u679c\u543b\u5408\u5f88\u597d\u3002<\/p>\n

\"\"<\/p>\n

\u56fe 11\u20119 midas Gen\u5c48\u66f2\u5206\u6790\u7ed3\u679c<\/strong><\/p>\n

\n