{"id":417,"date":"2014-10-18T13:59:01","date_gmt":"2014-10-18T17:59:01","guid":{"rendered":"https:\/\/coefs.charlotte.edu\/atabarra\/?page_id=417"},"modified":"2015-02-12T01:08:29","modified_gmt":"2015-02-12T06:08:29","slug":"fem","status":"publish","type":"page","link":"https:\/\/coefs.charlotte.edu\/atabarra\/fem\/","title":{"rendered":"Finite Elements"},"content":{"rendered":"<p><strong>Topics covered in the Finite Element Analysis and Applications:<\/strong><\/p>\n<ul>\n<ul>\n<li>Variational Boundary Value Problems in 1-D\n<ul>\n<li>Model problem\n<ul>\n<li>Longitudinal Deformation of a bar<\/li>\n<li>Steady State Heat conduction in a bar<\/li>\n<\/ul>\n<\/li>\n<li>Strong and weak formulation<\/li>\n<li>Functional space<\/li>\n<li>Equivalence of weak and strong form<\/li>\n<\/ul>\n<p>&nbsp;<\/li>\n<li>Galerkin Finite Element Method in 1-D\n<ul>\n<li>Finite element discretization<\/li>\n<li>Trial and test function<\/li>\n<li>Discrete weak form<\/li>\n<li>Numerical integration<\/li>\n<li>Stiffness matrix<\/li>\n<li>External load work<\/li>\n<li>Higher order finite elements<\/li>\n<li>Error measure and convergence<\/li>\n<\/ul>\n<p>&nbsp;<\/li>\n<li>Galerkin Finite Element Method in 2-D (Heat Conduction)\n<ul>\n<li>Notations\n<ul>\n<li>Gradient<\/li>\n<li>Divergence<\/li>\n<\/ul>\n<\/li>\n<li>Conservation of Energy<\/li>\n<li>Weak form<\/li>\n<li>Finite elements\n<ul>\n<li>Trial and test functions<\/li>\n<li>Weak form discretization<\/li>\n<li>Linear triangular elements<\/li>\n<li>Bilinear quadrilateral elements<\/li>\n<li>Pascal&#8217;s triangle<\/li>\n<li>Higher order triangular and quadrilateral elements<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/li>\n<li>Continuum Finite Elements\n<ul>\n<li>Linearized theory of elasticity\n<ul>\n<li>Cauchy&#8217;s law<\/li>\n<li>Equilibrium equations<\/li>\n<li>Small strain tensor<\/li>\n<li>Hooke&#8217;s law<\/li>\n<li>Weak form of the equilibrium equation<\/li>\n<li>Finite elements\n<ul>\n<li>Triangular elements<\/li>\n<li>Quadrilateral elements<\/li>\n<li>Tetrahedron elements<\/li>\n<li>Eight node brick elements<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul>\n<ul>\n<li>Structural Elements\n<ul>\n<li>Space truss<\/li>\n<li>Euler-Bernoulli beams<\/li>\n<li>Plate theory<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul>\n<li>Solution method and stability\n<ul>\n<li>Explicit time integration method<\/li>\n<li>Lagrange multiplier method<\/li>\n<li>Augmented Lagrange multiplier method<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Topics covered in the Finite Element Analysis and Applications: Variational Boundary Value Problems in 1-D Model problem Longitudinal Deformation of a bar Steady State Heat conduction in a bar Strong and weak formulation Functional space Equivalence of weak and strong &hellip; <a href=\"https:\/\/coefs.charlotte.edu\/atabarra\/fem\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":120,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-417","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/coefs.charlotte.edu\/atabarra\/wp-json\/wp\/v2\/pages\/417","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/coefs.charlotte.edu\/atabarra\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/coefs.charlotte.edu\/atabarra\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/coefs.charlotte.edu\/atabarra\/wp-json\/wp\/v2\/users\/120"}],"replies":[{"embeddable":true,"href":"https:\/\/coefs.charlotte.edu\/atabarra\/wp-json\/wp\/v2\/comments?post=417"}],"version-history":[{"count":5,"href":"https:\/\/coefs.charlotte.edu\/atabarra\/wp-json\/wp\/v2\/pages\/417\/revisions"}],"predecessor-version":[{"id":496,"href":"https:\/\/coefs.charlotte.edu\/atabarra\/wp-json\/wp\/v2\/pages\/417\/revisions\/496"}],"wp:attachment":[{"href":"https:\/\/coefs.charlotte.edu\/atabarra\/wp-json\/wp\/v2\/media?parent=417"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}