1 / 21

# Finite Element Analysis - PowerPoint PPT Presentation

Finite Element Analysis. Mathematical Background. http://www.kmitl.ac.th/~kpbumroo/12019801. Summary from Previous Lecture. Finite Element Computations Domain discretisation Element type and shape function Weak form and Galerkin WRM Element assemble Boundary conditions

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Finite Element Analysis' - blanca

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Finite Element Analysis

Mathematical Background

http://www.kmitl.ac.th/~kpbumroo/12019801

• Finite Element Computations

• Domain discretisation

• Element type and shape function

• Weak form and Galerkin WRM

• Element assemble

• Boundary conditions

• Solving algebraic equations

12019801 Finite Element Analysis

local

global

nodal values

local

• Finite Element Computations

• Domain discretisation

• Element type and shape function

12019801 Finite Element Analysis

local

• Finite Element Computations

• Weak form and Galerkin WRM

12019801 Finite Element Analysis

local

global

• Finite Element Computations

• Element assemble

12019801 Finite Element Analysis

global

• Finite Element Computations

• Boundary conditions

• Neuman boundary conditions

• Dirichlet boundary conditions

• Algebraic Equation Solvers

• Direct solver

• Gaussian elimination with pivoting

• LU decomposition

• Choleski decomposition

• Iterative solver

• Gauss-Siedel

• Jacobi

12019801 Finite Element Analysis

• Newton-Cotes formulas

• The Trapezoidal rule

• The first of Newton-Cotes formulas

12019801 Finite Element Analysis

The composite trapezoidal rule

12019801 Finite Element Analysis

The composite trapezoidal rule – MatLab M-file

12019801 Finite Element Analysis

• Simpson’s rules

• Simpson’s 1/3 rule

• Simpson’s 3/8 rule

12019801 Finite Element Analysis

• Romberg integration – based on Richardson’s extrapolation

• Combine two numerical integrations from trapezoidal rule (with different h) for improving accuracy

12019801 Finite Element Analysis

Romberg integration

12019801 Finite Element Analysis

Romberg integration – MatLab M-file

12019801 Finite Element Analysis

12019801 Finite Element Analysis

Gauss-Legendre

12019801 Finite Element Analysis

Change of interval

12019801 Finite Element Analysis

Two-dimensional integrals

12019801 Finite Element Analysis

Partial derivative

Partial differential equation = an equation involving partial derivatives of an unknown function of two or more independent variables

12019801 Finite Element Analysis

Linear

Non-Linear

Partial differential equation

Linear – if it is linear in the unknown function and all its derivatives

12019801 Finite Element Analysis

Linear second-order equations

Classification:

12019801 Finite Element Analysis

• Elliptic equations

• Laplace equation

• Parabolic equations

• Heat conduction equation

• Hyperbolic equations

• Wave equation

12019801 Finite Element Analysis