{"id":55408,"date":"2021-10-03T21:33:16","date_gmt":"2021-10-03T21:33:16","guid":{"rendered":"https:\/\/papersspot.com\/blog\/2021\/10\/03\/find-the-first-variation-of-the-following-functionals-the-strain-energy-of-the-beam-is-given-by\/"},"modified":"2021-10-03T21:33:16","modified_gmt":"2021-10-03T21:33:16","slug":"find-the-first-variation-of-the-following-functionals-the-strain-energy-of-the-beam-is-given-by","status":"publish","type":"post","link":"https:\/\/papersspot.com\/blog\/2021\/10\/03\/find-the-first-variation-of-the-following-functionals-the-strain-energy-of-the-beam-is-given-by\/","title":{"rendered":"Find the first variation of the following functionals, The strain energy of the beam is given by"},"content":{"rendered":"<p>For the applied loads:<br \/> distributed axial force f(x), distributed transverse load q(x), horizontal point load P at x=L,<br \/> transverse point load F at x=L, and bending moment Mo (counterclockwise) at x=L the potential<br \/> is given by<br \/> 00 0 0 0 ( ) 0<br \/> 0 ( ) () ()<br \/> L<br \/> x L<br \/> dw<br \/> V fu qw dx Pu L Fw L M dx =<br \/> \uf8ee \uf8f9 \u2212 =\u2212 \uf8ef \uf8fa<br \/> \uf8f0 \uf8fb \u222b<br \/> The total potential energy functional of the beam is given by 0 0 \u220f = (, ) uw U V<br \/> Determine the governing equations (Euler equations) and boundary conditions (35 points).<br \/> Problem #3: Determine the Euler equations and the natural boundary conditions associated with<br \/> the functional<br \/> 2 2 2 2 2 22 2<br \/> 2<br \/> 2 2 22<br \/> 1 ( ) 2 2(1 ) 2 2<br \/> D w w ww w<br \/> w dxdy kw dxdy qwdxdy <\/p>\n","protected":false},"excerpt":{"rendered":"<p>For the applied loads: distributed axial force f(x), distributed transverse load q(x), horizontal point load P at x=L, transverse point load F at x=L, and bending moment Mo (counterclockwise) at x=L the potential is given by 00 0 0 0 ( ) 0 0 ( ) () () L x L dw V fu qw [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[10],"class_list":["post-55408","post","type-post","status-publish","format-standard","hentry","category-research-paper-writing","tag-writing"],"_links":{"self":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/55408","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/comments?post=55408"}],"version-history":[{"count":0,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/55408\/revisions"}],"wp:attachment":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/media?parent=55408"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/categories?post=55408"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/tags?post=55408"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}