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# FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING

Duration: 32:08:00
Lectures: 36
Level: Beginner Finite Element Method (FEM) is one of the most popular numerical method to boundary and initial value
problems. One distinct feature of FEM is that it can be generalized to the domains of any arbitrary geometry. Theory of FEM is developed on Variational methods.

1
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Intro video
5:53
2
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 1: Functional, First variation, Euler Lagrange equation; Several Dependent variables
50:04
3
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 2: Functional with higher order derivatives; Variational statement
47:34
4
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 3: Differential equation, Variational statement and Minimization problem; Rayleigh-Ritz method
56:28
5
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 4: FEM steps: Explained with discrete linear springs; Gaussian Quadrature rule for integration
54:58
6
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 5: Solving one Ordinary Differential Equation using Linear Finite Element
59:20
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 6: Solving one Ordinary Differential Equation using Quadratic Finite Element
59:01
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 7: Bar Element: Elemental equation; Matlab Implementation with Example
45:19
9
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 8: Bar Element: Postprocessing; Comparison with Analytical Solution; Bar with linear springs
37:22
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 9: Truss Element: Elemental equation; Matlab Implementation with Example
1:02:40
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 10: Beam Element: Variational statement; Hermite shape function
45:32
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 11: Beam Element: Elemental equation; Matlab implementation with Example
52:44
13
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 12: Beam Element: Matlab implementation for the example with Non-uniform distributed load
35:37
14
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 13: Frame Element: Derivation of elemental equation in global reference frame
43:19
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 14: Frame Element: Matlab implementation with one Example
37:33
16
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 15: Generalization of Geometry data; Stiffness matrix, Load vector formation at element level
34:19
17
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 16: Generalization of Assembly, Imposition of Boundary condition and Load information
44:07
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 17: Indicial Notation: Summation convention, Kronecker delta, Permutation symbol
37:54
19
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 18: Second order tensor; Gradient, Divergence, Curl and Laplacian in Indicial notation
48:29
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 19: Gauss Divergence theorem and its application in Heat transfer and Structural analysis
33:36
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 20: Derivation of weak form of 2D steady-state heat conduction problem
49:57
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 21: Triangular element, calculating element stiffness and element force vector
56:56
23
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 22: Numerical example, assembly, mapping
53:36
24
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 23: Numerical integration, Neumann boundary, and higher order shape functions
56:03
25
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 24: Quadrilateral element, Lagrange shape functions, Serendipity elements
1:13:16
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 25: Development of a MATLAB code for solving 2D steady-state heat conduction problem
1:10:38
27
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 26: Demonstration of the MATLAB code
1:01:28
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 27: Elasticity problems in two dimension and obtaining the weak form
1:00:45
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 28: Deriving element stiffness matrix and element force vector, numerical example
1:01:14
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 29: Development of a MATLAB code for solving planar elasticity problems
46:23
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 30: Superconvergent Patch Recovery, error estimator, adaptive refinement
1:08:37
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 31: Solving eigenvalue problem in bar and beam, writing FEM code in MATLAB
55:19
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 32: Solving eigenvalue problem of membrane, writing FEM code in MATLAB
47:35
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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 33: Solving transient problems (parabolic type)
1:!2:32
35
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 34: Solving transient problems (hyperbolic type)
1:03:28
36
FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING-Lec 35: Solving elasticity problems in 3D using FEM, Solvers
1:07:09

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FINITE ELEMENT METHOD: VARIATIONAL METHODS TO COMPUTER PROGRAMMING
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