{"id":357656,"date":"2024-03-18T14:45:54","date_gmt":"2024-03-18T14:45:54","guid":{"rendered":"\/forum\/forums\/topic\/how-can-i-use-proper-orthogonal-decomposition-on-finite-element-analysis\/"},"modified":"2024-03-18T14:45:54","modified_gmt":"2024-03-18T14:45:54","slug":"how-can-i-use-proper-orthogonal-decomposition-on-finite-element-analysis","status":"closed","type":"topic","link":"https:\/\/innovationspace.ansys.com\/forum\/forums\/topic\/how-can-i-use-proper-orthogonal-decomposition-on-finite-element-analysis\/","title":{"rendered":"How can I use Proper Orthogonal Decomposition on finite element analysis"},"content":{"rendered":"<div>Im trying to do&nbsp; Finite Element Analysis using Proper Orthogonal Decomposition (POD), but i cant get force matrix and dont know what result mean.&nbsp;<\/div>\n<div>&nbsp;<\/div>\n<div>Let me first describe the process.<\/div>\n<div>&nbsp;<\/div>\n<div>1.I analyzed a cantilever beam under a sinusoidal load using the transient structural analysis in ANSYS.&nbsp;<\/div>\n<div>&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 should be 2400&#215;1. But exported txt file only contain force of 28 nodes which are fixed.&nbsp;&nbsp;<\/div>\n<div>-K matrix is 2400&#215;2400( I used APDL code to export it)<\/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 contain 99.999% of the energy (2 basis).<\/div>\n<div>-I manually extracted results at 0.05-second intervals, obtaining 20 data points. Is there a method to acquire the results for all time steps at once?<\/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. ( if F matirx is 2400&#215;1)<\/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>&nbsp;<\/div>\n<div>Theres two main question.&nbsp;<\/div>\n<div>&nbsp;<\/div>\n<div>First, are there any method that i can export nodal force of every nodes(800)?<\/div>\n<div>obtained nodal forces are useless since they are force of Fixed nodes.<\/div>\n<div>&nbsp;<\/div>\n<div>Second, 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? I know those values represent the most important feature of original system but what are they?<\/div>\n<div>&nbsp;<\/div>\n<div>If there were any mistakes in the process, please let me know.<\/div>\n<div>&nbsp;<\/div>\n<div>Thanks<\/div>\n","protected":false},"template":"","class_list":["post-357656","topic","type-topic","status-closed","hentry","topic-tag-reduced-order-model"],"aioseo_notices":[],"acf":[],"custom_fields":[{"0":{"_bbp_subscription":["77485","88"],"_bbp_author_ip":["168.143.243.24"]," _bbp_last_reply_id":["0"]," _bbp_likes_count":["0"],"_btv_view_count":["799"],"_bbp_topic_status":["unanswered"],"_bbp_topic_id":["357656"],"_bbp_forum_id":["27791"],"_bbp_engagement":["88","77485"],"_bbp_voice_count":["2"],"_bbp_reply_count":["1"],"_bbp_last_reply_id":["358474"],"_bbp_last_active_id":["358474"],"_bbp_last_active_time":["2024-03-22 11:34:37"]},"test":"dhjang4522hanyang-ac-kr"}],"_links":{"self":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/topics\/357656","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\/357656\/revisions"}],"wp:attachment":[{"href":"https:\/\/innovationspace.ansys.com\/forum\/wp-json\/wp\/v2\/media?parent=357656"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}