{"id":10718,"date":"2018-12-25T10:41:08","date_gmt":"2018-12-25T02:41:08","guid":{"rendered":"http:\/\/www.jdcui.com\/?p=10718"},"modified":"2018-12-27T13:47:11","modified_gmt":"2018-12-27T05:47:11","slug":"femmatlab%e6%9c%89%e9%99%90%e5%85%83-modal-analysis-of-trusses-structure-%e6%a1%81%e6%9e%b6%e5%8d%95%e5%85%83%e6%a8%a1%e6%80%81%e5%88%86%e6%9e%90","status":"publish","type":"post","link":"http:\/\/www.jdcui.com\/?p=10718","title":{"rendered":"[FEM][MATLAB][\u6709\u9650\u5143] FEM Modal Analysis Programming with MATLAB (Truss Element)  (\u6841\u67b6\u5355\u5143\u6a21\u6001\u5206\u6790\u7f16\u7a0b)"},"content":{"rendered":"<p><span style=\"color: #ff00ff;\"><strong>\u575a\u6301\u5b9e\u5e72\u3001\u575a\u6301\u4e00\u7ebf\u3001\u575a\u6301\u79ef\u7d2f\u3001\u575a\u6301\u601d\u8003\uff0c\u575a\u6301\u521b\u65b0\u3002<\/strong><\/span><\/p>\n<p>\u63a5\u7740\u535a\u6587<strong><a href=\"http:\/\/www.jdcui.com\/?p=10716\" target=\"_blank\" rel=\"noopener\">\u300a[\u52a8\u529b\u5b66] \u6a21\u6001\u5206\u6790\u57fa\u7840 (Basics of modal analysis)\u300b<\/a><\/strong>\u7ee7\u7eed\u4ecb\u7ecd\u6841\u67b6\u5355\u5143\u7528\u4e8e\u6a21\u6001\u5206\u6790\u7684\u65b9\u6cd5\u3002\u8be5\u90e8\u5206\u5185\u5bb9\u4e5f\u662f \u4e66\u672c\u00a0<a href=\"http:\/\/www.jdcui.com\/?page_id=9731\" target=\"_blank\" rel=\"noopener\"><strong>\u300a\u6709\u9650\u5355\u5143\u6cd5\uff1a\u7f16\u7a0b\u4e0e\u8f6f\u4ef6\u5e94\u7528\u300b<\/strong><\/a>\u6a21\u6001\u5206\u6790\u7ae0\u8282\u7684\u90e8\u5206\u5185\u5bb9\u8282\u9009\u3002<\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong>10.2<\/strong> <strong>2D\u6841\u67b6\u7ed3\u6784\u6a21\u6001\u5206\u6790<\/strong><\/li>\n<\/ul>\n<p>\u6a21\u6001\u5206\u6790\u9700\u8981\u7684\u53c2\u6570\u4e3b\u8981\u6709\u7ed3\u6784\u7684\u521a\u5ea6\u77e9\u9635\u548c\u8d28\u91cf\u77e9\u9635\uff0c\u5176\u4e2d\u7684\u521a\u5ea6\u77e9\u9635\u4e0e\u9759\u529b\u5206\u6790\u4e2d\u7684\u521a\u5ea6\u77e9\u9635\u76f8\u540c\uff0c\u8fd9\u91cc\u4ec5\u7ed9\u51fa\u8fdb\u884c\u6a21\u6001\u5206\u6790\u6240\u9700\u7684\u8d28\u91cf\u77e9\u9635\u7b49\u5176\u4ed6\u6761\u4ef6\u3002<\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong>10.2.1 \u6841\u67b6\u5355\u5143\u8d28\u91cf\u77e9\u9635<\/strong><\/li>\n<\/ul>\n<p>\u96c6\u4e2d\u8d28\u91cf\u77e9\u9635\uff08\u5c40\u90e8\u5750\u6807\uff09<\/p>\n<p style=\"text-align: left;\">\u8bbe\u6746\u6750\u6599\u5bc6\u5ea6\u4e3a \uff0c\u5355\u5143\u957f\u5ea6\u4e3a \uff0c\u622a\u9762\u79ef\u4e3a \uff0c\u6bcf\u4e2a\u8282\u70b9\u5206\u62c5\u5355\u51431\/2\u8d28\u91cf\uff0c\u5219\u5355\u5143\u8d28\u91cf\u77e9\u9635<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-10775 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/TrussMassMatrix.gif\" alt=\"\" width=\"228\" height=\"108\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>(10.2\u20111)<\/strong><\/p>\n<p><strong>\u6574\u4f53\u5750\u6807\u4e0b\u7684\u8d28\u91cf\u77e9\u9635\u8f6c\u6362<\/strong><\/p>\n<p>\u6574\u4f53\u5750\u6807\u4e0b\u5355\u5143\u4e00\u81f4\u8d28\u91cf\u77e9\u9635\u4e3a<\/p>\n<p style=\"text-align: center;\">\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-10776 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/TrussMassMatrix2.gif\" alt=\"\" width=\"161\" height=\"35\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>\u00a0(10.2\u20112)<\/strong><\/p>\n<p>\u3010<strong>\u63a8\u5bfc<\/strong>\u3011\uff1a\u8d28\u70b9\u52a8\u80fd\u4e0e\u5750\u6807\u7cfb\u65e0\u5173\uff0c\u5219\u6709<\/p>\n<p style=\"text-align: center;\">\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-10777 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/TrussMatrix3.gif\" alt=\"\" width=\"283\" height=\"49\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>\u00a0 \u00a0(10.2\u20113)<\/strong><\/p>\n<p>\u5373<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-10778 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/TrussMatrix4.gif\" alt=\"\" width=\"533\" height=\"39\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<strong> (10.2\u20114)<\/strong><\/p>\n<p>\u4ece\u800c\u5f97\u5230\u5f0f(10.2\u20112)\u3002<\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong>10.2.2 \u7b97\u4f8b\uff1a2D\u6841\u67b6\u6a21\u6001\u5206\u6790<\/strong><\/li>\n<\/ul>\n<p>\u7b97\u4f8b\u91c7\u7528\u4e0e2D\u6841\u67b6\u9759\u529b\u5206\u6790\u4e2d\u76f8\u540c\u7684\u7ed3\u6784\uff0c\u5176\u4e2d\u6750\u6599\u5bc6\u5ea6\u4e3a7.85e-9t\/mm<sup>3<\/sup>\uff0c\u91c7\u7528\u96c6\u4e2d\u8d28\u91cf\u77e9\u9635\uff0c\u5c06\u5355\u5143\u8d28\u91cf\u96c6\u4e2d\u4e8e\u4e24\u7aef\u8282\u70b9\u3002\u7531\u4e8e\u7b97\u4f8b\u6a21\u6001\u5206\u6790\u7684Matlab\u4ee3\u7801\u4e0e\u524d\u9762\u7ae0\u8282\u4e2d\u9759\u529b\u5206\u6790\u7684Matlab\u4ee3\u7801\u5927\u4f53\u76f8\u540c\uff0c\u56e0\u6b64\u8fd9\u91cc\u4ec5\u7ed9\u8fdb\u884c\u6a21\u6001\u5206\u6790\u6240\u9700\u7684\u65b0\u589e\u7684 MATLAB \u4ee3\u7801\u3002<\/p>\n<p><code><span style=\"color: #008000;\"><em>% Truss 2D modal analysis<\/em><\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\"><em>% Author <\/em><em>\uff1a<\/em><em> JiDong Cui<\/em><em>\uff08\u5d14\u6d4e\u4e1c\uff09\uff0c<\/em><em>Xuelong Shen<\/em><em>\uff08\u6c88\u96ea\u9f99\uff09<\/em><\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\"><em>% Website : www.jdcui.com<\/em><\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\"><em>% 20151108<\/em><\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u2026\u2026<\/span><\/code><\/p>\n<p><em>\u6b64\u524d\u4ee3\u7801\u4e0e\u9759\u529b\u5206\u6790\u4ee3\u7801\u76f8\u540c\uff0c\u4e0d\u518d\u8d58\u8ff0\u3002<\/em><\/p>\n<p><em><code><strong><span style=\"color: #800000;\">% Properties definition<\/span><\/strong><\/code><\/em><\/p>\n<p><code><span style=\"color: #008000;\">\u2026\u2026<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">p=7.85E-9\u00a0\u00a0\u00a0\u00a0 % Density<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u2026\u2026<\/span><\/code><\/p>\n<p><em>\u5b9a\u4e49\u5355\u5143\u5c5e\u6027\u65f6\uff0c\u589e\u52a0\u5355\u5143\u6750\u6599\u5bc6\u5ea6\u03c1=7.85e-9\uff0c\u7528\u4e8e\u8ba1\u7b97\u5355\u5143\u8d28\u91cf\u3002<\/em><\/p>\n<p><code><em><strong><span style=\"color: #800000;\">% Global stiffness matrix and mass matrix<\/span><\/strong><\/em><\/code><\/p>\n<p><code><span style=\"color: #008000;\">stiffness = zeros(numDOF);<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">mass=zeros(numDOF);<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">for i=1:numEle;<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\"><em>\u00a0\u00a0\u00a0 % Index of the element nodes<\/em><\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 noindex = EleNode(i,:);<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\"><em>\u00a0\u00a0\u00a0 % Element length<\/em><\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 deltax = xx( noindex(2)) - xx( noindex(1));<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 deltay = yy( noindex(2)) - yy( noindex(1));<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 L = sqrt( deltax*deltax + deltay*deltay );<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\"><em>\u00a0\u00a0\u00a0 % Element stiffness matrix<\/em><\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 C = deltax \/ L;<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 S = deltay \/ L;<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 T=[ C,S, 0,0;<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -S,C, 0,0;<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0,0, C,S;<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0,0,-S,C<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ];<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 eleK = EA\/L*[ C*C C*S -C*C -C*S;<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 C*S S*S -C*S -S*S;<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -C*C -C*S C*C C*S;<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -C*S -S*S C*S S*S];<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 eleM0=p*A*L\/2*diag([1,1,1,1]);\u00a0\u00a0<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 eleM=T'*eleM0*T;<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\"><em>\u00a0\u00a0\u00a0 % Corresponding freedom of the element nodes<\/em><\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 eleDof = [noindex(1)*2-1 noindex(1)*2 noindex(2)*2-1 noindex(2)*2];<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\"><em>\u00a0\u00a0\u00a0 % Integration of element stiffness matrix and mass matrix<\/em><\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 stiffness( eleDof , eleDof) = stiffness( eleDof , eleDof) + eleK;<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u00a0\u00a0\u00a0 mass( eleDof , eleDof) = mass( eleDof , eleDof) + eleM;<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">end<\/span><\/code><\/p>\n<p><code>\u2026\u2026<\/code><\/p>\n<p><em>\u672c\u6bb5\u4ee3\u7801\u7684\u4f5c\u7528\u662f\u96c6\u6210\u7ed3\u6784\u6574\u4f53\u521a\u5ea6\u77e9\u9635\u548c\u6574\u4f53\u8d28\u91cf\u77e9\u9635\u3002\u672c\u7ed3\u6784\u5171\u6709numDOF\u4e2a\u81ea\u7531\u5ea6\uff0c\u56e0\u6b64\u9996\u5148\u91c7\u7528zeros()\u65b9\u6cd5\u5b9a\u4e49\u4e86\u4e00\u4e2anumDOF\u00d7numDOF\u7684\u96f6\u77e9\u9635mass\u3002\u5355\u5143\u7684\u8d28\u91cf\u77e9\u9635eleM0\u91c7\u7528\u96c6\u4e2d\u8d28\u91cf\u5f62\u5f0f\u6c42\u5f97\uff0c\u5e76\u91c7\u7528\u4e0e\u521a\u5ea6\u77e9\u9635\u76f8\u540c\u7684\u201c\u5bf9\u53f7\u5165\u5ea7\u6cd5\u201d\u5c06\u5355\u5143\u8d28\u91cf\u77e9\u9635\u7ec4\u88c5\u5230\u7ed3\u6784\u6574\u4f53\u8d28\u91cf\u77e9\u9635mass\u4e2d\u3002<\/em><\/p>\n<p><code><em><strong><span style=\"color: #800000;\">% Get the eigenvalues and eigenvectors<\/span><\/strong><\/em><\/code><\/p>\n<p><code><span style=\"color: #008000;\">A=mass(activeDof,activeDof)\\stiffness(activeDof,activeDof);<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">[Vo,Do] = eig(A);<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">fo=diag(sqrt(Do)\/(2*pi));<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">Vf=sortrows([Vo',fo],size(Vo,1)+1);<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">V=Vf(:,1:size(Vo,1))';<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">f=sort(fo)<\/span><\/code><\/p>\n<p><code><span style=\"color: #008000;\">\u2026\u2026<\/span><\/code><\/p>\n<p>\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<strong>eig([A])<\/strong>\u53ef\u76f4\u63a5\u6c42\u89e3\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff0c\u672c\u4f8b\u4e2d <strong>[A]=[K]<sup>-1<\/sup>[M]<\/strong>\uff0c\u6c42\u5f97\u7684\u7279\u5f81\u503c\u653e\u5728\u5411\u91cf<strong>{Do}<\/strong>\u4e2d\uff0c\u76f8\u5e94\u7684\u7279\u5f81\u5411\u91cf\u653e\u5728\u77e9\u9635<strong>[Vo]<\/strong>\u4e2d\u3002\u5176\u540e\u7684\u4ee3\u7801\u7528\u4e8e\u5904\u7406\u6c42\u89e3\u5f97\u5230\u7684\u6570\u636e\uff0c\u5176\u4e2d\u4ee3\u7801<strong>\u201cfo=\u201d<\/strong>\u7528\u4e8e\u6839\u636e\u7279\u5f81\u503c\u6c42\u5f97\u9891\u7387\uff0c\u4ee3\u7801<strong>\u201cV=\u201d<\/strong>\u7528\u4e8e\u5c06\u7279\u5f81\u5411\u91cf\u6392\u5e8f\uff0c\u4ee3\u7801<strong>\u201cf=\u201d<\/strong>\u7528\u4e8e\u5c06\u7ed3\u6784\u81ea\u632f\u9891\u7387\u8fdb\u884c\u6392\u5e8f\u3002\u56fe 10\u20111\u6240\u793a\u662f\u8be5\u6841\u67b6\u7ed3\u6784\u7684\u524d\u4e09\u9636\u632f\u578b\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10774\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/FEM_TrussModalAnalysis_Mode1.png\" alt=\"\" width=\"650\" height=\"325\" srcset=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/FEM_TrussModalAnalysis_Mode1.png 841w, http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/FEM_TrussModalAnalysis_Mode1-768x384.png 768w, http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/FEM_TrussModalAnalysis_Mode1-300x150.png 300w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/p>\n<p style=\"text-align: center;\">\uff08a\uff09\u7b2c\u4e00\u632f\u578b<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10771\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/FEM_TrussModalAnalysis_Mode2.gif\" alt=\"\" width=\"650\" height=\"325\" srcset=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/FEM_TrussModalAnalysis_Mode2.gif 839w, http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/FEM_TrussModalAnalysis_Mode2-768x384.gif 768w, http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/FEM_TrussModalAnalysis_Mode2-300x150.gif 300w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/p>\n<p style=\"text-align: center;\">\uff08b\uff09\u7b2c\u4e8c\u632f\u578b<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10772\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/FEM_TrussModalAnalysis_Mode3.gif\" alt=\"\" width=\"650\" height=\"325\" srcset=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/FEM_TrussModalAnalysis_Mode3.gif 839w, http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/FEM_TrussModalAnalysis_Mode3-768x384.gif 768w, http:\/\/www.jdcui.com\/wp-content\/uploads\/2018\/12\/FEM_TrussModalAnalysis_Mode3-300x150.gif 300w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/p>\n<p style=\"text-align: center;\">\uff08c\uff09\u7b2c\u4e09\u632f\u578b<\/p>\n<p style=\"text-align: center;\"><strong>\u56fe 10\u20111 \u6841\u67b6\u7ed3\u6784\u632f\u578b<\/strong><\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong><span style=\"color: #000000;\">\u76f8\u5173\u5185\u5bb9<\/span>\u00a0<span style=\"color: #0000ff;\">( Related Topics )<\/span><\/strong><\/li>\n<\/ul>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[00].<\/span><em><span style=\"color: #ff00ff;\">\u00a0<a style=\"color: #ff00ff;\" href=\"http:\/\/www.jdcui.com\/?page_id=9731\" target=\"_blank\" rel=\"noopener\">[Book][\u4e66] \u6709\u9650\u5355\u5143\u6cd5\uff1a\u7f16\u7a0b\u4e0e\u8f6f\u4ef6\u5e94\u7528<\/a><\/span><\/em><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[01].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=1927\">2D Truss by Matlab [Matlab 2D\u6841\u67b6\u6709\u9650\u5143] (code by myself)<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[02].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=1945\">3D Truss by MATLAB[MATLAB 3D \u6841\u67b6\u9759\u529b\u5206\u6790] (code by myself)<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[03].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8767\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] FEM Analysis: 2D Truss Element [\u6709\u9650\u5143\u5206\u6790: 2D\u6841\u67b6\u5355\u5143]<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[04].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8778\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] FEM Analysis: 2D Euler Beam Element [\u6709\u9650\u5143\u5206\u6790: 2D\u6b27\u62c9\u6881\u5355\u5143]<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[05].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8955\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] 2D\u526a\u5207\u6881\u5355\u5143<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[06].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8977\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] 2D Timoshenko\u6881\u5355\u5143<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[07].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8988\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] \u4e09\u89d2\u5f62\u5e38\u5e94\u53d8\u5355\u5143(CST)<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[08].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8991\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] \u5e73\u97624\u53d8\u5f62\u5355\u5143(Q4)<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[09].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=8999\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] 4\u8282\u70b9\u56db\u9762\u4f53\u5355\u5143(TET4)<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[10].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=9012\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] 8\u8282\u70b9\u516d\u9762\u4f53\u5355\u5143(C3D8)<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[11].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=9087\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] \u5e73\u97628\u8282\u70b9\u4e8c\u6b21\u201c\u5b8c\u5168\u79ef\u5206\u201d\u5355\u5143(CPS8)<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[12].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=9115\">[FEM][\u6709\u9650\u5143][\u7f16\u7a0b][Matlab][Code by myself] \u5e73\u97626\u8282\u70b9\u4e8c\u6b21\u201c\u5b8c\u5168\u79ef\u5206\u201d\u5355\u5143(CPS6)<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[13].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=10718\">[FEM][MATLAB][\u6709\u9650\u5143] FEM Modal Analysis Programming with MATLAB (Truss Element) (\u6841\u67b6\u5355\u5143\u6a21\u6001\u5206\u6790\u7f16\u7a0b)<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[14].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=10721\">[FEM][MATLAB][\u6709\u9650\u5143] FEM Modal Analysis Programming with MATLAB (Frame Elements) (\u6846\u67b6\u5355\u5143\u6a21\u6001\u5206\u6790\u7f16\u7a0b)<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[15].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=10724\">[\u529b\u5b66][\u6709\u9650\u5143]Basics of Linear Buckling Analysis [\u7ebf\u6027\u66f2\u5c48\u5206\u6790\u57fa\u7840]<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[16].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=10726\">[FEM][MATLAB][\u6709\u9650\u5143][\u7f16\u7a0b] FEM Buckling Analysis Programming with MATLAB (Truss Elements) (\u6841\u67b6\u5355\u5143\u66f2\u5c48\u5206\u6790\u7f16\u7a0b)<\/a><\/strong><\/p>\n<p style=\"padding-left: 30px;\"><strong><span style=\"color: #000000;\">[17].<\/span>\u00a0<a href=\"http:\/\/www.jdcui.com\/?p=10728\">[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)<\/a><\/strong><\/p>\n<hr \/>\n<p><center><strong><div  class=\"thumbs-rating-container\" id=\"thumbs-rating-10718\" data-content-id=\"10718\"><button class=\"thumbs-rating-up thumbs-rating-voted\" onclick=\"thumbs_rating_vote(10718, 1);\">Vote Up +9<\/button> <button class=\"thumbs-rating-down\" onclick=\"thumbs_rating_vote(10718, 2);\">Vote Down -0<\/button><span class=\"thumbs-rating-already-voted\">You already voted!<\/span><\/div><\/strong><\/center><\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong><span style=\"color: #000000;\">\u6ce8\u91ca<\/span>\u00a0<span style=\"color: #0000ff;\">( Comments\u00a0)<\/span><\/strong><\/li>\n<\/ul>\n<p style=\"padding-left: 30px;\">\u00a0\u00a0(<span style=\"color: #000000;\">\u00a0\u5982\u679c\u60a8\u53d1\u73b0\u6709\u9519\u8bef\uff0c\u6b22\u8fce\u6279\u8bc4\u6307\u6b63\u3002\u90ae\u7bb1\uff1a<span style=\"color: #0000ff;\">jidong_cui@163.com .\u00a0<strong>\u5982\u679c\u60a8\u559c\u6b22\u8fd9\u7bc7\u535a\u6587\uff0c\u8bf7\u5728\u4e0a\u9762\u7ed9\u6211\u00a0<span style=\"color: #ff0000;\">\u70b9\u4e2a\u8d5e\u00a0<\/span>\u5427\uff01<\/strong>\u00a0\ud83d\ude42 \u00a0 \ud83d\ude42 \u00a0\u00a0<\/span><\/span><\/p>\n<p style=\"padding-left: 30px;\">\u00a0\u00a0(<span style=\"color: #0000ff;\">\u00a0If you found any mistakes in the post, please let me know.\u00a0Email :\u00a0jidong_cui@163.com.\u00a0If you like this posts, please give me a\u00a0<span style=\"color: #ff0000;\">&#8220;<em><strong>thumbs up<\/strong><\/em>&#8220;<\/span>\u00a0rating on the above button!\u00a0<\/span>)<\/p>\n<ul style=\"list-style-type: square;\">\n<li style=\"text-align: left;\"><strong>\u5fae\u4fe1\u516c\u4f17\u53f7\u00a0(\u00a0<span style=\"color: #0000ff;\">Wechat\u00a0Subscription<\/span>)<\/strong><\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/01\/QRCODE.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3636\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/01\/QRCODE.jpg\" alt=\"WeChat_QRCode\" width=\"250\" height=\"255\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><strong>\u6b22\u8fce\u5173\u6ce8\u00a0\u201c<span style=\"color: #ff00ff;\">\u7ed3\u6784\u4e4b\u65c5<\/span>\u201d\u00a0\u5fae\u4fe1\u516c\u4f17\u53f7<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u575a\u6301\u5b9e\u5e72\u3001\u575a\u6301\u4e00\u7ebf\u3001\u575a\u6301\u79ef\u7d2f\u3001\u575a\u6301\u601d\u8003\uff0c\u575a\u6301\u521b\u65b0\u3002 \u63a5\u7740\u535a\u6587\u300a[\u52a8\u529b\u5b66] \u6a21\u6001\u5206\u6790\u57fa\u7840 (Basics of modal analysis)\u300b\u7ee7\u7eed\u4ecb\u7ecd\u6841\u67b6\u5355\u5143\u7528\u4e8e\u6a21\u6001\u5206\u6790\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\u6a21\u6001\u5206\u6790\u7ae0\u8282\u7684\u90e8\u5206\u5185\u5bb9\u8282\u9009\u3002 10.2 2D\u6841\u67b6\u7ed3\u6784\u6a21\u6001\u5206\u6790 \u6a21\u6001\u5206\u6790\u9700\u8981\u7684\u53c2\u6570\u4e3b\u8981\u6709\u7ed3\u6784\u7684\u521a\u5ea6\u77e9\u9635\u548c\u8d28\u91cf\u77e9\u9635\uff0c\u5176\u4e2d\u7684\u521a\u5ea6\u77e9\u9635\u4e0e\u9759\u529b\u5206\u6790\u4e2d\u7684\u521a\u5ea6\u77e9\u9635\u76f8\u540c\uff0c\u8fd9\u91cc\u4ec5\u7ed9\u51fa\u8fdb\u884c\u6a21\u6001\u5206\u6790\u6240\u9700\u7684\u8d28\u91cf\u77e9\u9635\u7b49\u5176\u4ed6\u6761\u4ef6\u3002 10.2.1 \u6841\u67b6\u5355\u5143\u8d28\u91cf\u77e9\u9635 \u96c6\u4e2d\u8d28\u91cf\u77e9\u9635\uff08\u5c40\u90e8\u5750\u6807\uff09 \u8bbe\u6746\u6750\u6599\u5bc6\u5ea6\u4e3a \uff0c\u5355\u5143\u957f\u5ea6\u4e3a \uff0c\u622a\u9762\u79ef\u4e3a \uff0c\u6bcf\u4e2a\u8282\u70b9\u5206\u62c5\u5355\u51431\/2\u8d28\u91cf\uff0c\u5219\u5355\u5143\u8d28\u91cf\u77e9\u9635 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (10.2\u20111) \u6574\u4f53\u5750\u6807\u4e0b\u7684\u8d28\u91cf\u77e9\u9635\u8f6c\u6362 \u6574\u4f53\u5750\u6807\u4e0b\u5355\u5143\u4e00\u81f4\u8d28\u91cf\u77e9\u9635\u4e3a \u00a0\u00a0 &#8230;<\/p>\n","protected":false},"author":1,"featured_media":10774,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[382,100,491,31,21,1087,5],"tags":[292,1660,28,139,1002,295,293,140,999],"class_list":["post-10718","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dynamics-","category-fem-","category-matlab","category-my-software-","category-programming","category-structural-analysis-","category-structural-engineering","tag-fem","tag-fem-programming","tag-matlab","tag-modal-analysis","tag-programming","tag-truss","tag-293","tag-140","tag-999"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.10 - aioseo.com -->\n\t<meta name=\"description\" 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