{"id":3155,"date":"2016-06-13T00:39:45","date_gmt":"2016-06-12T16:39:45","guid":{"rendered":"http:\/\/www.jdcui.com\/?p=3155"},"modified":"2025-09-06T11:25:04","modified_gmt":"2025-09-06T03:25:04","slug":"torsion-analysis-by-thermal-analogy-with-abaqusabaqus%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=3155","title":{"rendered":"Torsion analysis by thermal analogy with Abaqus (Abaqus\u70ed\u6bd4\u62df\u626d\u8f6c\u5e94\u529b\u5206\u6790)"},"content":{"rendered":"<p>\u4e0a\u4e00\u7bc7\u535a\u6587<strong>\u300a<a href=\"http:\/\/www.jdcui.com\/?p=3112\">Torsion analysis by thermal analogy with ANSYS(ANSYS\u70ed\u6bd4\u62df\u626d\u8f6c\u5e94\u529b\u5206\u6790)<\/a>\u300b<\/strong>\u7528ANSYS\u8f6f\u4ef6\u5229\u7528\u7a33\u6001\u70ed\u4f20\u5bfc\u5206\u6790\u529f\u80fd\u5bf9\u622a\u9762\u7684\u626d\u8f6c\u5e94\u529b\u8fdb\u884c\u4e86\u5206\u6790\uff0c\u672c\u6587\u5229\u7528Abaqus\u5b9e\u73b0\u76f8\u540c\u7684\u5206\u6790\u3002<\/p>\n<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\u5408Abaqus\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 Abaqus.<\/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 style=\"padding-left: 20px;\">2D\u60c5\u51b5\u4e0b\u7684\u7a33\u6001\u70ed\u4f20\u5bfc\u63a7\u5236\u65b9\u7a0b<\/p>\n<p><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><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\u7528Abaqus\u8fdb\u884c\u5206\u6790\uff0c\u5177\u4f53\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n<p>\uff081\uff09\u8bbe\u7f6e\u5de5\u4f5c\u8def\u5f84\u5e76\u521b\u5efa\u6570\u636e\u5e93\uff08<span style=\"color: #0000ff;\">Set Work Directory and Create Model Database<\/span>\uff09<\/p>\n<p>\uff082\uff09\u521b\u5efa\u90e8\u4ef6\uff08<span style=\"color: #0000ff;\">Create Part<\/span>\uff09<\/p>\n<p style=\"padding-left: 20px;\">\u7531\u4e8e\u5206\u6790\u95ee\u9898\u4e3a2D\uff0c\u6a21\u578b\u7a7a\u95f4\u9009\u4e3a 2D Planar\uff1b\u7c7b\u578b\u4e3a Deformable\uff1b\u57fa\u672c\u7279\u6027\u4e3a Shell\u3002\uff08<span style=\"color: #0000ff;\">As the problem is 2D, set 2D Planar as the Modeling Space, Deformable as the Type and Shell\u00a0as the Base Feature.<\/span>\uff09<\/p>\n<p style=\"padding-left: 20px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-3164\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/CreatePart.png\" alt=\"CreatePart\" width=\"249\" height=\"505\" \/><\/p>\n<p>\uff083\uff09\u521b\u5efa\u6750\u6599 \uff08<span style=\"color: #0000ff;\">Create\u00a0Material<\/span>\uff09<\/p>\n<p style=\"padding-left: 20px;\">\u5728\u5c5e\u6027\u6a21\u5757\u4e0b\uff08<span style=\"color: #0000ff;\"> Property<\/span>\uff09\u5b9a\u4e49\u6750\u6599\uff0c\u8bbe\u7f6e\u70ed\u4f20\u5bfc\u7cfb\u6570\u4e3a1\u3002<span style=\"color: #0000ff;\">Under the Property,\u00a0create a material and enter 1 for Thermal Conductivity.\uff09<\/span><\/p>\n<p style=\"padding-left: 20px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3165\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/CreateMat.png\" alt=\"CreateMat\" width=\"500\" height=\"652\" \/><\/p>\n<p>\uff084\uff09\u521b\u5efa\u622a\u9762\u5e76\u8d4b\u4e88\u622a\u9762\u00a0\uff08<span style=\"color: #0000ff;\">Create\u00a0Section and Assign Section in Property Module<\/span>\uff09<\/p>\n<p>\uff085\uff09\u521b\u5efa\u7ec4\u4ef6\u00a0\uff08<span style=\"color: #0000ff;\">Create Assembly\u00a0<\/span>\uff09<\/p>\n<p>\uff086\uff09\u521b\u5efa\u7528\u4e8e\u7a33\u6001\u70ed\u5206\u6790\u7684\u5206\u6790\u6b65\uff08<span style=\"color: #0000ff;\">Create Step for Steady-Thermal Analysis\u00a0<\/span>\uff09<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3168\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/CreateStep.png\" alt=\"CreateStep\" width=\"600\" height=\"334\" srcset=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/CreateStep.png 829w, http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/CreateStep-768x428.png 768w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>\uff086\uff09\u5b9a\u4e49\u8377\u8f7d\u548c\u8fb9\u754c\u6761\u4ef6\uff08<span style=\"color: #0000ff;\">Define load and boundary condition<\/span>\uff09<\/p>\n<p style=\"padding-left: 20px;\">\u5b9a\u4e49\u96f6\u6e29\u5ea6\u6761\u4ef6\u548c2G\u03b8\u4f53\u70ed\u6d41\u7b49\u6548\u8377\u8f7d\u3002<\/p>\n<p style=\"padding-left: 20px;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-3178\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/CreateLoad_BodyHeatflux2.png\" alt=\"CreateLoad_BodyHeatflux2\" width=\"598\" height=\"356\" \/><\/p>\n<p>\uff087\uff09\u5e03\u7f6e\u79cd\u5b50\u548c\u5212\u5206\u7f51\u683c\uff08<span style=\"color: #0000ff;\">Seed Part Mesh<\/span>\uff09<\/p>\n<p style=\"padding-left: 20px;\">\u9009\u62e9\u70ed\u4f20\u5bfc\u5355\u5143\u3002(<span style=\"color: #0000ff;\">Assign Heat Transfer Element)<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-3170\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/AssignElement.png\" alt=\"AssignElement\" width=\"459\" height=\"449\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-3169\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/MeshPart.png\" alt=\"MeshPart\" width=\"600\" height=\"481\" \/><\/p>\n<p>\uff088\uff09\u521b\u5efa\u4efb\u52a1\u5e76\u63d0\u4ea4\u5206\u6790\uff08<span style=\"color: #0000ff;\">Create Job and submit to run analysis<\/span>\uff09<\/p>\n<p>\uff089\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;\">Check\u00a0Results<\/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><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3171\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/NodalTemperature-1.png\" alt=\"NodalTemperature\" width=\"600\" height=\"402\" \/><\/p>\n<p>\uff082\uff09\u67e5\u770b\u70ed\u6d41\u91cf\u00a0(<span style=\"color: #0000ff;\">Thermal Flux\u00a0<\/span>)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3172\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/HFL1.png\" alt=\"HFL1\" width=\"600\" height=\"412\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3173\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/HFL2.png\" alt=\"HFL2\" width=\"600\" height=\"406\" \/><\/p>\n<p>\uff083\uff09\u67e5\u770b\u70ed\u6d41\u91cf\u5411\u91cf\u00a0(<span style=\"color: #0000ff;\">Thermal Flux\u00a0Vector<\/span>)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3175\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2016\/06\/HFLVector.png\" alt=\"HFLVector\" width=\"600\" height=\"398\" \/><\/p>\n<ul style=\"list-style-type: square;\">\n<li><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 500.6Mpa\u76f8\u8fd1\u3002<\/p>\n<hr \/>\n<p><center style=\"line-height: 1.5;\"><div  class=\"thumbs-rating-container\" id=\"thumbs-rating-3155\" data-content-id=\"3155\"><button class=\"thumbs-rating-up thumbs-rating-voted\" onclick=\"thumbs_rating_vote(3155, 1);\">Vote Up +11<\/button> <button class=\"thumbs-rating-down thumbs-rating-voted\" onclick=\"thumbs_rating_vote(3155, 2);\">Vote Down -1<\/button><span class=\"thumbs-rating-already-voted\">You already voted!<\/span><\/div><\/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\u5408Abaqus\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 fuction in general finite element program. This post gives an example on how to do torsion analysis as thermal analogy with Abaqus.)<\/p>\n","protected":false},"author":1,"featured_media":7982,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[336,100,5],"tags":[395,418,430,292,294,428,421,427,429,422,425,293,423,424,426],"class_list":["post-3155","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-abaqus","category-fem-","category-structural-engineering","tag-abaqus","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":[],"views":2191,"_links":{"self":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts\/3155","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3155"}],"version-history":[{"count":0,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts\/3155\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/media\/7982"}],"wp:attachment":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3155"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}