Triangular thick plate stiffness matrix transformation

In summary, the original writer of a book on thick triangular plates uses the shape function Ni = ai + bi*x + ci*y for the stiffness matrix, but does not mention the need to transform it into global coordinates. The illustrations in the book show the local 1-2 edge of the triangle aligned to the global X-axis, raising the question of whether this is necessary or just a coincidence. If transformation is required, the base point for rotation is unclear, and any comment or suggestion would be appreciated.
  • #1
Ronankeating
63
0
Hi community member,

Regarding the book that I'm reading original writer has used Ni = ai + bi*x + ci*y shape function for the formulation of stiffness matrix for thick triangular plates.

The writer has not mentioned in the article that the resulting stiffness matrix is required to be transformed to global coordinates. What arised my suspicion was, in the illustrations local 1-2 edge of triangle is always aligned to global X-axis. Is it coincidental or "must" to perform the transformation to that specific shape function?

If transformation is required at all to match the exact illustrations, how should be performed, I mean how to choose the base point for rotation, rotation around any arbitrary vertex will work ?


Best Regards,
 
Engineering news on Phys.org
  • #2
Any comment will be appreciated!
 

Related to Triangular thick plate stiffness matrix transformation

1. What is a triangular thick plate stiffness matrix transformation?

A triangular thick plate stiffness matrix transformation is a mathematical method used in structural engineering to analyze the stiffness and deflection of triangular-shaped plates. It involves converting the original rectangular-shaped stiffness matrix into a triangular-shaped one to simplify the calculation process.

2. Why is a triangular thick plate stiffness matrix transformation necessary?

A triangular thick plate stiffness matrix transformation is necessary because it allows for a more efficient and accurate analysis of triangular plates. The original rectangular-shaped stiffness matrix can be difficult to work with and may result in errors, whereas the triangular-shaped matrix simplifies the calculation process and reduces the chances of mistakes.

3. What factors affect the triangular thick plate stiffness matrix transformation?

The factors that affect the triangular thick plate stiffness matrix transformation include the thickness of the plate, the material properties of the plate, and the boundary conditions. These factors can influence the stiffness and deflection of the triangular plate and must be taken into account during the transformation process.

4. How is the triangular thick plate stiffness matrix transformation performed?

The triangular thick plate stiffness matrix transformation is performed by adjusting the original rectangular-shaped stiffness matrix to fit the triangular plate geometry. This is done by rearranging and deleting certain terms in the matrix, resulting in a simplified and more accurate representation of the plate's stiffness and deflection.

5. What are the applications of a triangular thick plate stiffness matrix transformation?

A triangular thick plate stiffness matrix transformation is commonly used in the analysis and design of triangular-shaped structural elements, such as triangular roof trusses, bridges, and towers. It is also used in finite element analysis to model and simulate the behavior of triangular plates under different loading conditions.

Similar threads

  • Materials and Chemical Engineering
Replies
4
Views
5K
  • General Engineering
Replies
4
Views
4K
Replies
16
Views
2K
Replies
1
Views
2K
  • Beyond the Standard Models
Replies
2
Views
2K
Replies
12
Views
6K
Replies
4
Views
8K
Replies
24
Views
7K
  • Beyond the Standard Models
Replies
6
Views
3K
  • General Discussion
Replies
1
Views
8K
Back
Top