{"id":357483,"date":"2024-03-17T13:35:26","date_gmt":"2024-03-17T13:35:26","guid":{"rendered":"\/forum\/forums\/topic\/purpose-of-using-pod-in-the-finite-element-method-and-how-should-i-use-it\/"},"modified":"2024-03-17T13:35:26","modified_gmt":"2024-03-17T13:35:26","slug":"purpose-of-using-pod-in-the-finite-element-method-and-how-should-i-use-it","status":"closed","type":"topic","link":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/purpose-of-using-pod-in-the-finite-element-method-and-how-should-i-use-it\/","title":{"rendered":"Purpose of  using POD in the finite element method, and how should i use it?"},"content":{"rendered":"<div>I performed a Finite Element Analysis using Proper Orthogonal Decomposition (POD) and obtained results, but I&#8217;m not sure what they signify.&nbsp;<\/div>\n<div>&nbsp;<\/div>\n<div>Let me first describe the process.<\/div>\n<div>&nbsp;<\/div>\n<div>1.I analyzed the deformation of a cantilever beam under a sinusoidal load using the transient structural analysis in ANSYS.&nbsp;<\/div>\n<div>2. I exported the nodal force and nodal displacement for each node.<\/div>\n<div>-The mesh had 828 nodes, but excluding the 28 nodes with fixed support, I extracted the forces in the xyz direction for 800 nodes(2400 total).<\/div>\n<div>-The F matrix is 2400&#215;1, and the K matrix is 2400&#215;2400.<\/div>\n<div>3. I stored the deformation every 0.05 seconds for 1 second into a snapshot matrix (2400&#215;20).<\/div>\n<div>I subtracted the mean from the data and performed 1\/N*(C*C&#8217;).<\/div>\n<div>&nbsp;<\/div>\n<div>4. I proceeded with singular value decomposition on the obtained snapshot matrix and extracted 2 modes that encompass 99.999% of the energy (2 basis).<\/div>\n<div>&nbsp;<\/div>\n<div>5. Using the Galerkin method, &empty;^T F= &empty;^T Kc&empty;(c is coefficient), I projected the governing equation F=KU onto the obtained basis &empty;, resulting in reduced dimension of&nbsp; F and K matrices.<\/div>\n<div>&nbsp;<\/div>\n<div>&nbsp;<\/div>\n<div>6. Consequently, in the equation F = KU, all values are constants except c, and U has been reduced from 2400 variables to just 2.<\/div>\n<div>While the original U matrix represented the deformation at each node, the reduced u_approx consists of only 2 values. What do these 2 values mean?<\/div>\n<div>&nbsp;<\/div>\n<div>I have completed all work related to POD, but I&#8217;m not quite sure what the results signify.<\/div>\n<div>If there were any mistakes in the process, please let me know.&nbsp;<\/div>\n<div>Thanks<\/div>\n<p>&nbsp;<\/p>\n","protected":false},"template":"","class_list":["post-357483","topic","type-topic","status-closed","hentry","topic-tag-apdl","topic-tag-mechanical","topic-tag-nodalcoordinates-1","topic-tag-reduced-order-model"],"aioseo_notices":[],"acf":[],"custom_fields":[{"0":{"_bbp_subscription":["77485","88"],"_bbp_author_ip":["96.7.218.215"]," _bbp_last_reply_id":["0"]," _bbp_likes_count":["0"],"_btv_view_count":["463"],"_bbp_topic_status":["unanswered"],"_edit_lock":["1710802187:291218"],"_bbp_topic_id":["357483"],"_bbp_forum_id":["27791"],"_bbp_engagement":["88","77485"],"_bbp_voice_count":["2"],"_bbp_reply_count":["1"],"_bbp_last_reply_id":["358470"],"_bbp_last_active_id":["358470"],"_bbp_last_active_time":["2024-03-22 11:12:38"]},"test":"dhjang4522hanyang-ac-kr"}],"_links":{"self":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/topics\/357483","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/topics"}],"about":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/types\/topic"}],"version-history":[{"count":0,"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/topics\/357483\/revisions"}],"wp:attachment":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/media?parent=357483"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}