{"id":3112,"date":"2016-06-11T23:05:23","date_gmt":"2016-06-11T15:05:23","guid":{"rendered":"http:\/\/www.jdcui.com\/?p=3112"},"modified":"2026-02-15T19:59:28","modified_gmt":"2026-02-15T11:59:28","slug":"torsion-analysis-by-thermal-analogy-with-ansysansys%e7%83%ad%e6%af%94%e6%8b%9f%e6%89%ad%e8%bd%ac%e5%ba%94%e5%8a%9b%e5%88%86%e6%9e%90","status":"publish","type":"post","link":"http:\/\/www.jdcui.com\/?p=3112","title":{"rendered":"Torsion analysis by thermal analogy with ANSYS (ANSYS\u70ed\u6bd4\u62df\u626d\u8f6c\u5e94\u529b\u5206\u6790)"},"content":{"rendered":"<p>\u7a33\u6001\u70ed\u4f20\u5bfc\u7684\u63a7\u5236\u65b9\u7a0b\u4e0e\u7ecf\u5178\u626d\u8f6c\u7406\u8bba\u7684\u63a7\u5236\u65b9\u7a0b\u5177\u6709\u76f8\u4f3c\u6027\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6bd4\u62df\uff0c\u5728\u901a\u7528\u6709\u9650\u5143\u8f6f\u4ef6\u4e2d\u5229\u7528\u7a33\u6001\u70ed\u4f20\u5bfc\u5206\u6790\u7684\u529f\u80fd\u8fdb\u884c\u626d\u8f6c\u95ee\u9898\u7684\u5206\u6790\u3002\u672c\u6587\u7ed3\u5408ANSYS\u8f6f\u4ef6\uff0c\u901a\u8fc7\u4e00\u4e2a\u5b9e\u4f8b\u8bf4\u660e\u8fd9\u4e2a\u6bd4\u62df\u7684\u5177\u4f53\u8fc7\u7a0b\u3002(<span style=\"color: #0000ff;\">The steady heat conduction problem and the classic torsion theory have analogy in their control partial differential equations. We can conduct a torsional analysis making use of the steady analysis fuction in general finite element program. This post gives an example on how to do torsion analysis as thermal analogy with ANSYS.<\/span>)<\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong>\u7a33\u6001\u70ed\u4f20\u5bfc\u63a7\u5236\u65b9\u7a0b\u4e0e\u626d\u8f6c\u63a7\u5236\u65b9\u7a0b \uff08<span style=\"color: #0000ff;\">\u00a0Control partial differential equations of\u00a0steady heat conduction problem and classic torsion theory<\/span>\uff09<\/strong><\/li>\n<\/ul>\n<p>\uff081\uff09\u7a33\u6001\u70ed\u4f20\u5bfc\u63a7\u5236\u65b9\u7a0b<\/p>\n<p>2D\u60c5\u51b5\u4e0b\u7684\u7a33\u6001\u70ed\u4f20\u5bfc\u63a7\u5236\u65b9\u7a0b<\/p>\n<p style=\"padding-left: 30px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3117\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/SteadyHeatConduction.png\" alt=\"SteadyHeatConduction\" width=\"220\" height=\"56\" \/><\/p>\n<p>\uff082\uff09St. Venant \u626d\u8f6c\u504f\u5fae\u5206\u65b9\u7a0b<\/p>\n<p style=\"padding-left: 30px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3116\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/Torsion.png\" alt=\"Torsion\" width=\"200\" height=\"174\" \/><\/p>\n<p>\u4e24\u8005\u7684\u504f\u5fae\u5206\u65b9\u7a0b\u5747\u4e3aHelmholtz\u65b9\u7a0b\u7684\u7279\u6b8a\u5f62\u5f0f\u3002\u56e0\u6b64\u53ef\u4ee5\u5229\u7528\u901a\u7528\u6709\u9650\u5143\u8f6f\u4ef6\u4e2d\u7684\u7a33\u6001\u70ed\u4f20\u5bfc\u5206\u6790\u529f\u80fd\u901a\u8fc7\u6bd4\u62df\u8fdb\u884c\u622a\u9762\u7684\u626d\u8f6c\u5e94\u529b\u5206\u6790\u3002<\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong>\u7b97\u4f8b\uff08<span style=\"color: #0000ff;\">Example<\/span>\uff09<\/strong><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3152\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/TorsionProblem.png\" alt=\"TorsionProblem\" width=\"600\" height=\"211\" srcset=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/TorsionProblem.png 969w, http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/TorsionProblem-768x269.png 768w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong>\u6709\u9650\u5143\u6a21\u62df\uff08<span style=\"color: #0000ff;\">FEM Analysis<\/span>\uff09<\/strong><\/li>\n<\/ul>\n<p>\u5229\u7528ANSYS APDL\u8fdb\u884c\u5206\u6790\uff0c\u5177\u4f53\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n<p>\uff081\uff09\u5728\u524d\u5904\u7406\u6a21\u5757\u4e2d\u65b0\u5efa\u5355\u5143\u7c7b\u578b\uff08<span style=\"color: #0000ff;\">Create Element Type in Preprocessor\u00a0Module<\/span>\uff09<\/p>\n<p style=\"padding-left: 20px;\">\u91c7\u752877\u53f7\u5355\u5143<\/p>\n<p style=\"padding-left: 60px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3148\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/ElementType-1.png\" alt=\"ElementType\" width=\"400\" height=\"349\" \/><\/p>\n<p>\uff082\uff09\u5728\u524d\u5904\u7406\u6a21\u5757\u4e2d\u65b0\u5efa\u6750\u6599\uff08<span style=\"color: #0000ff;\">Create Material in Preprocessor\u00a0Module<\/span>\uff09<\/p>\n<p style=\"padding-left: 20px;\">\u6750\u6599\u4e3b\u8981\u5b9a\u4e49\u70ed\u4f20\u5bfc\u7cfb\u6570<\/p>\n<p style=\"padding-left: 60px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3129\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/Material.png\" alt=\"Material\" width=\"500\" height=\"265\" \/><\/p>\n<p>\uff083\uff09\u5728\u524d\u5904\u7406\u6a21\u5757\u521b\u5efa\u9762\u5e76\u5212\u5206\u7f51\u683c\uff08<span style=\"color: #0000ff;\">Create Area\u00a0and Mesh in Preprocessor\u00a0Module<\/span>\uff09<\/p>\n<p style=\"padding-left: 30px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3130\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/Mesh.png\" alt=\"Mesh\" width=\"500\" height=\"491\" \/><\/p>\n<p>\uff084\uff09\u65bd\u52a0\u96f6\u6e29\u5ea6\u8fb9\u754c\u6761\u4ef6\uff08<span style=\"color: #0000ff;\">Apply Zero Temperature Boundary Condition<\/span>\uff09<\/p>\n<p>\uff085\uff09\u65bd\u52a0\u70ed\u6e90\uff08<span style=\"color: #0000ff;\">Apply Heat on Area<\/span>\uff09<\/p>\n<p style=\"padding-left: 20px;\">\u7b49\u6548\u70ed\u6e90\uff1a2G\u03b8 = 2*76923*0.0005 = 76.923<\/p>\n<p style=\"padding-left: 60px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3131\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/HEATGenera.png\" alt=\"HEATGenera\" width=\"600\" height=\"301\" srcset=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/HEATGenera.png 881w, http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/HEATGenera-768x385.png 768w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>\uff086\uff09\u6c42\u89e3\u6709\u9650\u5143\u6a21\u578b\uff08<span style=\"color: #0000ff;\">Solve FEM model in Solution Module<\/span>\uff09<\/p>\n<p style=\"padding-left: 20px;\">\u8fdb\u884c\u7a33\u6001\u70ed\u4f20\u5bfc\u5206\u6790<\/p>\n<p>\uff087\uff09\u67e5\u770b\u7ed3\u679c\uff08<span style=\"color: #0000ff;\">Check Results<\/span>\uff09<\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong>\u67e5\u770b\u5206\u6790\u7ed3\u679c\uff08<span style=\"color: #0000ff;\">Results<\/span>\uff09<\/strong><\/li>\n<\/ul>\n<p>\uff081\uff09\u67e5\u770b\u8282\u70b9\u6e29\u5ea6 (<span style=\"color: #0000ff;\">Nodal Temperature<\/span>)<\/p>\n<p style=\"padding-left: 30px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3126\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/NodalTemperature.png\" alt=\"NodalTemperature\" width=\"600\" height=\"483\" \/><\/p>\n<p style=\"padding-left: 20px;\">\u53ef\u4ee5\u770b\u51fa\u626d\u8f6c\u5e94\u529b\u51fd\u6570\u7684\u5f62\u72b6\u3002<\/p>\n<p>\uff082\uff09\u67e5\u770b\u6e29\u5ea6\u68af\u5ea6 (<span style=\"color: #0000ff;\">Nodal Temperature Gradient<\/span>)<\/p>\n<p style=\"padding-left: 40px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3127\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/NodalTemperatureGraintX.png\" alt=\"NodalTemperatureGraintX\" width=\"600\" height=\"489\" \/><\/p>\n<p style=\"padding-left: 30px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3128\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/NodalTemperatureGraintY.png\" alt=\"NodalTemperatureGraintY\" width=\"600\" height=\"484\" \/><\/p>\n<p>\uff083\uff09\u67e5\u770b\u70ed\u6d41\u91cf\u5411\u91cf\u00a0(<span style=\"color: #0000ff;\">Thermal Flux\u00a0Vector<\/span>)<\/p>\n<p style=\"padding-left: 30px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3136\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/ThermalFluxVector.png\" alt=\"ThermalFluxVector\" width=\"600\" height=\"451\" \/><\/p>\n<p style=\"padding-left: 20px;\">\u4ece\u70ed\u6d41\u91cf\u5411\u91cf\u56fe\u4e5f\u53ef\u4ee5\u770b\u51fa\uff0c\u77e9\u5f62\u622a\u9762\u626d\u8f6c\u526a\u5207\u5e94\u529b\u7684\u5206\u5e03\uff1a\u8fb9\u7684\u4e2d\u95f4\u6700\u5927\uff0c\u89d2\u70b9\u4e3a0\u3002<\/p>\n<ul style=\"list-style-type: square;\">\n<li>\u00a0<strong>\u4e0e\u7406\u8bba\u7ed3\u679c\u5bf9\u6bd4\uff08<span style=\"color: #0000ff;\">Comparison with Theory\u00a0<\/span>\uff09<\/strong><\/li>\n<\/ul>\n<p style=\"padding-left: 20px;\">\u6839\u636e\u5f39\u6027\u7406\u8bba\uff0c<em>\u03b8<\/em> = T\/ (<em>ab<\/em><sup>3<\/sup><em>G\u03b2<\/em><sub>1<\/sub>) ,\u00a0<em>\u03c4<\/em><sub>max\u00a0<\/sub>=\u00a0T\/ (<em>ab<\/em><sup>2<\/sup><em>\u03b2<\/em>).<\/p>\n<p style=\"padding-left: 20px;\"><em>\u03c4<\/em><sub>max\u00a0<\/sub>=\u00a0<em>\u03b8(<em>ab<\/em><sup>3<\/sup><em>G\u03b2<\/em><sub>1<\/sub>) \/\u00a0(<em>ab<\/em><sup>2<\/sup><em>\u03b2<\/em>) =\u00a0\u03b8bG\u03b2<sub>1<\/sub>\u00a0\/\u00a0\u03b2 = 0.0005*20*76923*0.141\/0.208 =\u00a0521.4492<\/em>Mpa<\/p>\n<p style=\"padding-left: 20px;\">\u4e0e\u5206\u6790\u7ed3\u679c 519.165Mpa\u76f8\u8fd1\u3002<\/p>\n<hr \/>\n<p><center style=\"line-height: 1.5;\"><strong><div  class=\"thumbs-rating-container\" id=\"thumbs-rating-3112\" data-content-id=\"3112\"><button class=\"thumbs-rating-up thumbs-rating-voted\" onclick=\"thumbs_rating_vote(3112, 1);\">Vote Up +12<\/button> <button class=\"thumbs-rating-down thumbs-rating-voted\" onclick=\"thumbs_rating_vote(3112, 2);\">Vote Down -1<\/button><span class=\"thumbs-rating-already-voted\">You already voted!<\/span><\/div><\/strong><\/center><\/p>\n<ul style=\"list-style-type: square;\">\n<li style=\"text-align: left;\"><strong>\u5fae\u4fe1\u516c\u4f17\u53f7\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>\u7a33\u6001\u70ed\u4f20\u5bfc\u7684\u63a7\u5236\u65b9\u7a0b\u4e0e\u7ecf\u5178\u626d\u8f6c\u7406\u8bba\u7684\u63a7\u5236\u65b9\u7a0b\u5177\u6709\u76f8\u4f3c\u6027\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6bd4\u62df\uff0c\u5728\u901a\u7528\u6709\u9650\u5143\u8f6f\u4ef6\u4e2d\u5229\u7528\u7a33\u6001\u70ed\u4f20\u5bfc\u5206\u6790\u7684\u529f\u80fd\u8fdb\u884c\u626d\u8f6c\u95ee\u9898\u7684\u5206\u6790\u3002\u672c\u6587\u7ed3\u5408ANSYS\u8f6f\u4ef6\uff0c\u901a\u8fc7\u4e00\u4e2a\u5b9e\u4f8b\u8bf4\u660e\u8fd9\u4e2a\u6bd4\u62df\u7684\u5177\u4f53\u8fc7\u7a0b\u3002(The steady heat conduction problem and the classic torsion theory have analogy in their control partial differential equations. We can conduct a torsional analysis making use of the steady analysis &#8230;<\/p>\n","protected":false},"author":1,"featured_media":7982,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[417,100,1087],"tags":[418,430,292,294,428,421,427,429,422,425,293,423,424,426],"class_list":["post-3112","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ansys","category-fem-","category-structural-analysis-","tag-ansys","tag-elasticity","tag-fem","tag-finite-element-method","tag-thermal","tag-torsion","tag-427","tag-429","tag-422","tag-425","tag-293","tag-423","tag-424","tag-426"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.10 - aioseo.com -->\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"CJD\"\/>\n\t<meta name=\"keywords\" content=\"ansys,elasticity,fem,finite element 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