Finite Element: Collection Test with solution

These post is specially for undergraduate study for Finite Element.
The topic for the question and solution including:

1. One dimensional
2. Plane truss
3. Bending of beam


please click here for collection

Sample 1
Sample 2
Sample 3
Sample 4

Finite Element: Bending of Prismatic Beams

What is a Beam?
A beam is a structural element that primarily carries bending (flexure or
transverse) loading.
Beams generally carry vertical forces but they can also sustain horizontal
loads (e.g. due to an earthquake).
Beams are characterized by: a) shape of cross-section, b) length, c)
material, and d) type of supports
Beams are used in the construction sectors are typically made of steel,
reinforced concrete, or wood

Types of Beam
The most common types of steel beam is the
I-beam or wide-flange beam or a universal
beam. They are commonly used in steelframed
buildings and bridges
Other common beam profiles are the C-channel, the hollow structural
beam, and the angled-beams

For Further reading please Click here >>>>>>Beam

Finite Element: One Dimensional & truss example to solution

This is example to solution the basic concept of the Finite element.
1. The example of the matrix
2. Gaussian Elimination Method
3. One dimensional problem
4. Truss Element problem

Click Full Example for further reading

Finite Element: One Dimensional Problem example to solution

The manual step to solve the One Dimensional in Finite Element Method:

1. Transform into finite Element Model
2. Calculate the stiffness matrix
3. Assemble the stiffness matrix [K]
4. Write the element force vector
5. Write the global system linear equation
6. apply the boundary conditions and reduced global system of linear equation
7. Solve the unknown nodal displacements
8. Find the reaction force

Clicks One Dimensional to download a question
and Clicks One Dimension for Solution

Finite Elements: Matrix Algebra & Gaussian Elimination

The important Mathematics method for solving problem in Finite Elements Method. Normally the methods using Gaussian Elimination. This method using a matrix method.

Click Gaussian Elimination To read a full notes and Example

Finite Element: Introduction to Finite Element Method

Finite element method is a numerical method that can be used
for solving engineering problems.
It is particularly useful for problems involving complex geometries, combined
loading and material properties, in which the analytical solutions are not available.
FAQ: Is this method accurate?... Yes, for simple problems and if material properties
and loading condition are modeled very close to the actual conditions. No,
especially when the problems to be solved are too complex.
Among the sources of error involved in this method are…
Geometrical simplification;
Interpolation function;
Material properties;
Round‐off, etc.

Click here for a full notes