Learn · Finite Element Method: Variational Methods to Computer Programming
Lecture 32 of 35Week 11:Eigen value problems and Transient problem in 1D & 2D Scalar Valued Problems
Lec 32: Solving eigenvalue problem of membrane, writing FEM code in MATLAB
Prof. Atanu Banerjee and Prof. Arup Nandy · IIT Guwahati
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- Finite Element Method: Variational Methods to Computer Programming, IIT Guwahati (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures
- Lec 1: Functional, First variation, Euler Lagrange equation; Several Dependent variables
- Lec 2: Functional with higher order derivatives; Variational statement
- Lec 3: Differential equation, Variational statement and Minimization problem; Rayleigh-Ritz method
- Lec 4: FEM steps: Explained with discrete linear springs; Gaussian Quadrature rule for integration
- Lec 5: Solving one Ordinary Differential Equation using Linear Finite Element
- Lec 6: Solving one Ordinary Differential Equation using Quadratic Finite Element
- Lec 7: Bar Element: Elemental equation; Matlab Implementation with Example
- Lec 8: Bar Element: Postprocessing; Comparison with Analytical Solution; Bar with linear springs
- Lec 9: Truss Element: Elemental equation; Matlab Implementation with Example
- Lec 10: Beam Element: Variational statement; Hermite shape function
- Lec 11: Beam Element: Elemental equation; Matlab implementation with Example
- Lec 12: Beam Element: Matlab implementation for the example with Non-uniform distributed load
- Lec 13: Frame Element: Derivation of elemental equation in global reference frame
- Lec 14: Frame Element: Matlab implementation with one Example
- Lec 15: Generalization of Geometry data; Stiffness matrix, Load vector formation at element level
- Lec 16: Generalization of Assembly, Imposition of Boundary condition and Load information
- Lec 17: Indicial Notation: Summation convention, Kronecker delta, Permutation symbol
- Lec 18: Second order tensor; Gradient, Divergence, Curl and Laplacian in Indicial notation
- Lec 19: Gauss Divergence theorem and its application in Heat transfer and Structural analysis
- Lec 20: Derivation of weak form of 2D steady-state heat conduction problem
- Lec 21: Triangular element, calculating element stiffness and element force vector
- Lec 22: Numerical example, assembly, mapping
- Lec 23: Numerical integration, Neumann boundary, and higher order shape functions
- Lec 24: Quadrilateral element, Lagrange shape functions, Serendipity elements
- Lec 25: Development of a MATLAB code for solving 2D steady-state heat conduction problem
- Lec 26: Demonstration of the MATLAB code
- Lec 27: Elasticity problems in two dimension and obtaining the weak form
- Lec 28: Deriving element stiffness matrix and element force vector, numerical example
- Lec 29: Development of a MATLAB code for solving planar elasticity problems
- Lec 30: Superconvergent Patch Recovery, error estimator, adaptive refinement
- Lec 31: Solving eigenvalue problem in bar and beam, writing FEM code in MATLAB
- Lec 32: Solving eigenvalue problem of membrane, writing FEM code in MATLAB
- Lec 33: Solving transient problems (parabolic type)
- Lec 34: Solving transient problems (hyperbolic type)
- Lec 35: Solving elasticity problems in 3D using FEM, Solvers