1 / 44

finite difference andfinite element

discretisation

- by
- Christian Maier

table of contents

- introduction
- method of FDM
- method of FEM
- lattice
- technical applications

Arbour with torque transfer

D40mm

1

2

T250Nm

Arbour with torque transfer

- calculation of the mechanical stress and safety
- drag torsional moment
- shering stress

Arbour with torque transfer

- definition of safety
- determination of the material stress
- safety number

Arbour with torque transfer

- not considered details
- dynamic influences
- surface quality (roughness)
- notch sensifity

Complex problem

from www.i-deus.hu/tablo/tablo7/fem.gif

How can this problem be solved analytically in

about one hour?

table of contents

- introduction
- method of FDM
- method of FEM
- lattice
- technical applications

The Dirichlet problem for the Poisson equation

- Example Poisson equation
- Conditions
- Solve within a rectangle
- Area is
- Open
- Not empty
- contiguous

The Dirichlet problem for the Poisson equation

- given functions
- searched function
- conditions

The finite-difference-method

- the idea
- searching for an approximate function
- to get a solution
- for the marginal problem
- for a number of finite points

The finite-difference-method

- what is to do
- derivative in first condition is replaced by

quotients of differences - second condition must be valid only on latice

points

The finite-difference-method

from Numerik partieller DGL, Knabner/Angermann

- characteristics
- two dimensions in space
- Constant mesh size (hgt0)
- h truncation parameter

The finite-difference-method

- definition of the latice points
- a lh, b mh
- short writing
- all points in the rectangle

The finite-difference-method

- form the system of equations part one
- given
- given

The finite-difference-method

- form the system of equations part two
- given
- given

The finite-difference-method

- latice points within the rectangle
- latice points on the boundary of the rectangle

The finite-difference-method

- linear equation for approximate value
- definitions

The finite-difference-method

from Numerik partieller DGL, Knabner/Angermann

- the 5 points star of the difference method

The finite-difference-method

- dimension of the boundary equation
- form of the equation system
- dimensions

The finite-difference-method

- shape of the right side of the equation

The finite-difference-method

- form of

0

0

The finite-difference-method

- form of identity matrix
- form of matrix

0

0

table of contents

- introduction
- method of FDM
- method of FEM
- lattice
- technical applications

The finite-element-method

- short example for the calculating operations
- given equations
- testing function

The finite-element-method

- next step integration over the area

The finite-element-method

- next step discretisation

The finite-element-method

- next step use of a base

The finite-element-method

- next step use of a base

table of contents

- introduction
- method of FDM
- method of FEM
- lattice
- technical applications

Lattice points

from Skriptum zur Vorlesung Leichtbau, Prof.

Baier

Lattice points

from Skriptum zur Vorlesung Leichtbau, Prof.

Baier

Lattice points

table of contents

- introduction
- method of FDM
- method of FEM
- lattice points
- technical applications
- bend guider
- parts of a robot arm

the technical application

- two examples
- bend guider
- analytical
- numerical
- parts of a robot arm

the technical application

x

z

the technical application

- equation of motion

the technical application

- solution for this problem

the technical application

- Human robot

the technical application

- arm

the technical application

- elbow joint

the technical application

- elbow joint

the technical application

the technical application