Introduction to variational methods - Raleigh-Ritz method - Lagrange method - Hamilton Method

HW#01

229/9/2016

One Dimensional 2nd Order Problems
- Domain discretization
- Selection to trial functions
- Top-down approach
- Interpolation functions
- Element Equations
- Bottom-Up approach
- Global equations

HW#02

36/10/2016

HW#03

413/10/2016

One Dimensional 2nd Order Problems
- Applying boundary conditions
- Solving system of equations
- The secondary equations
- Examples
- Bar problem - Heat transfer problem - Fluid mechanics problem

Analysis of trusses
- Bar Element in 2-D
- Element-Node connectivity
- Applying boundary conditions and setting external loads
- Solving truss problems

HW#04

520/10/2016

Euler-Bernoulli Beams
- Governing equations
- Element Equations
- Assembling the global equations
- Applying boundary conditions
- Solving equations

HW#05

627/10/2016

Euler-Bernoulli Beams
- Frame problems in 2-D

HW#06

73/11/2016

Higher order Elements
- Extra nodes in 1-D elements
- Using non-polynomial functions
- Using numerical integration to obtain element matrices

HW#07 Midterm #1

810/11/2016

Eigenvalue problems
- Formulation of the problem
- Solving the problem
- Post processing

HW#08

917/11/2016

Time dependent problems
- Examples of time dependent problems
- Formulating the problem
- solving the problem

HW#09

1024/11/2016

Nonlinear problems - Examples of nonlinear problems - Formulating the problem - Solving the problem

HW#10

111/12/2016

Two dimensional problems
- The logistic problem
- Trial functions
- Deriving the element equations
- Applying boundary conditions

HW#11 Midterm #2

128/12/2016

Two dimensional problems
- Thermal conduction in 2-D
- Potential flow in 2-D

HW#12

1315/12/2016

Two dimensional problems
- Plane elasticity in 2-D

## Fall 2016 Schedule

- Course outline and objectives

- Course assessment

Review of Galerkin Method

- Weighted residual methods

- Galerkin Method

- The weak form

Introduction to variational methods

- Raleigh-Ritz method

- Lagrange method

- Hamilton Method

- Domain discretization

- Selection to trial functions

- Top-down approach

- Interpolation functions

- Element Equations

- Bottom-Up approach

- Global equations

- Applying boundary conditions

- Solving system of equations

- The secondary equations

- Examples

- Bar problem

- Heat transfer problem

- Fluid mechanics problem

Analysis of trusses

- Bar Element in 2-D

- Element-Node connectivity

- Applying boundary conditions and setting external loads

- Solving truss problems

- Governing equations

- Element Equations

- Assembling the global equations

- Applying boundary conditions

- Solving equations

- Frame problems in 2-D

- Extra nodes in 1-D elements

- Using non-polynomial functions

- Using numerical integration to obtain element matrices

Midterm #1- Formulation of the problem

- Solving the problem

- Post processing

- Examples of time dependent problems

- Formulating the problem

- solving the problem

- Examples of nonlinear problems

- Formulating the problem

- Solving the problem

- The logistic problem

- Trial functions

- Deriving the element equations

- Applying boundary conditions

Midterm #2- Thermal conduction in 2-D

- Potential flow in 2-D

- Plane elasticity in 2-D

- Composite materials

- Smart materials

## Introduction to the FEM (Book Draft)

Introduction to the Finite Element MethodfromMohammad Tawfik.