Modal decomposition and modal equations - II (16:01), 11.14. Strong form of the partial differential equation. Basis functions, and the matrix-vector weak form - I (19:52), 11.05. Functionals. The matrix-vector weak form - III - I (22:31), 03.06. Introduction. He's particularly interested in problems of mathematical biology, biophysics and the materials physics. Intro to C++ (C++ Classes) (16:43), 03.01. The strong form of linearized elasticity in three dimensions - II (15:44), 10.03. Linear elliptic partial differential equations - I (14:46), 01.02. 1. Using AWS on Linux and Mac OS (7:42), 03.07. The matrix-vector weak form - I (17:19), 07.14. Principle of virtual work and the Finite Element Method On this subject, there exist a large number of textbooks, many of which are on the shelves of the library. Time discretization; the Euler family - I (22:37), 11.08. From there to the video lectures that you are about to view took nearly a year. The finite dimensional weak form as a sum over element subdomains - I (16:08), 02.10. The formulation of the finite element analog of a model equation follows two main approaches, namely weighted-residual and weak formulation [116]. Particularly compelling was the fact that there already had been some successes reported with computer programming classes in the online format, especially as MOOCs. simultaneously to obtain a continuous solution in terms of its values at the nodes. The basis function is defined within the finite element using the values of the unknown variables at the nodes. 1. Elasticity; heat conduction; and mass diffusion. Lagrange basis functions in 1 through 3 dimensions - II (12:36), 08.02ct. The strong form of steady state heat conduction and mass diffusion - II (19:00), 07.03. The matrix-vector equations for quadratic basis functions - I - II (11:53), 04.09. The development itself focuses on the classical forms of partial differential equations (PDEs): elliptic, parabolic and hyperbolic. 1. Principles of FEA The finite element method (FEM), or finite element analysis (FEA), is a computational technique used to obtain approximate solutions of boundary value problems in engineering. The constitutive relations of linearized elasticity (21:09), 10.07. Heat conduction and mass diffusion at steady state. Free energy - I (17:38), 06.02. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - II (12:55), 11.12. Finite element error estimates (22:07), 06.01. The final finite element equations in matrix-vector form - II (18:23), 03.08ct. Coding Assignment 03 Template, 11.09ct. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - I (17:24), 11.11. system of equations. Dr. Garikipati's work draws from nonlinear mechanics, materials physics, applied mathematics and numerical methods. Equivalence between the strong and weak forms - 1 (25:10), 01.08ct. as illustrated in (4.1). Extremization of functionals (18:30), 06.04. The finite-dimensional weak form - Basis functions - I (18:23), 10.08. Each finite element is an independent geometric region of the domain over which equations with unknown variables of the given problem are defined using the governing equations of the mathematical Parabolic PDEs in three dimensions come next (unsteady heat conduction and mass diffusion), and the lectures end with hyperbolic PDEs in three dimensions (linear elastodynamics). The finite-dimensional weak form - II (15:56), 07.07. Free energy - II (13:20), 06.03. 1. Finite Element Method) 16.810 (16.682) 7 Fundamental Concepts (1) Elastic problems Thermal problems Fluid flow Electrostatics etc. In each finite element, these equations are solved by assuming basis functions which interpolate the unknown variables over the finite element, in order to approximate the solution of the Dirichlet boundary conditions - II (13:59), 11.02. Functionals. The matrix-vector equations for quadratic basis functions - II - I (19:09), 04.10. For clarity we begin with elliptic PDEs in one dimension (linearized elasticity, steady state heat conduction and mass diffusion). 4.1.2 Principles of Finite Element Method. Basis functions, and the matrix-vector weak form - II (12:03), 11.06. The finite-dimensional weak form - I (12:35), 07.06. The best approximation property (21:32), 05.06. Ann Arbor, December 2013. Coding Assignment 2 (3D Problem), 08.04. Higher polynomial order basis functions - II - I (13:38), 04.06. Assembly of the global matrix-vector equations - I (20:40), 10.14. Articles about Massively Open Online Classes (MOOCs) had been rocking the academic world (at least gently), and it seemed that your writer had scarcely experimented with teaching methods. The time-discretized equations (23:15), 12.07. Modal equations and stability of the time-exact single degree of freedom systems - I (10:49), 11.15. Boundary value problems are also called field problems. The pure Dirichlet problem - I (18:14), 04.02. The matrix-vector equations for quadratic basis functions - I - I (21:19), 04.08. Numerical integration -- Gaussian quadrature (13:57), 04.11ct. analogous to the original mathematical problem. Higher polynomial order basis functions - I - II (16:38), 04.05. The matrix-vector weak form - I - I (16:26), 03.02. Krishna Garikipati Quadrature rules in 1 through 3 dimensions (17:03), 08.03ct. It is hoped that these lectures on Finite Element Methods will complement the series on Continuum Physics to provide a point of departure from which the seasoned researcher or advanced graduate student can embark on work in (continuum) computational physics. Introduction. The idea for an online version of Finite Element … Coding Assignment 1 (Functions: Class Constructor to "basis_gradient") (14:40), 04.07. We then move on to three dimensional elliptic PDEs in scalar unknowns (heat conduction and mass diffusion), before ending the treatment of elliptic PDEs with three dimensional problems in vector unknowns (linearized elasticity). The integrals in terms of degrees of freedom - continued (20:55), 07.13. The matrix-vector equations for quadratic basis functions - II - II (24:08), 04.11. The strong form of linearized elasticity in three dimensions - I (09:58), 10.02. Aside: Insight to the basis functions by considering the two-dimensional case (16:43), 07.09.