What size is the Global Stiffness Matrix in this Example?

In summary, the conversation discusses the construction of a Beam composed of three elements and 4 nodes, taking into consideration lateral deflections and slopes. The question is whether the same method is used to calculate the global stiffness matrix for this beam as for a 6x6 stiffness matrix for a beam with two elements and 3 nodes. There is a lot of information available on the internet about global stiffness matrices, but the size of the matrix is determined by the number of nodes multiplied by the number of degrees of freedom per node. However, many sources do not provide a straightforward approach and may be confusing or missing key details.
  • #1
ihebmtir
3
0
TL;DR Summary
4 nodes global stifness matrix
does this Beam, composed of three elements and 4 nodes(considering lateral deflections and slopes) has an 8x8 global stifness matrix
and if so is the global matrix calculated the same way as a 6x6 stifness matrix for the same kind of beam but only with two elements and 3 nodes
 

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  • #3
The size of global stiffness matrix is the number of nodes multiplied by the number of degrees of freedom per node.
 
  • #4
Arjan82 said:
There is tons of info on the web about this:

https://www.google.com/search?q=global+stiffness+matrix
Yes, all bad. I looked at many sources and none of them follow a straightforward problem without shortcuts that obscure the method or missing key details or not explaining where things go or mixing numbers and matrices or whatever.
 

FAQ: What size is the Global Stiffness Matrix in this Example?

What is the Global Stiffness Matrix?

The Global Stiffness Matrix is a mathematical representation of the stiffness of a structure or system. It is used in engineering and physics to analyze the behavior and stability of a structure under different loads and conditions.

How is the Global Stiffness Matrix calculated?

The Global Stiffness Matrix is calculated by combining the individual stiffness matrices of each element in the structure. The individual stiffness matrices take into account the material properties, geometry, and boundary conditions of each element.

Why is the size of the Global Stiffness Matrix important?

The size of the Global Stiffness Matrix is important because it determines the number of equations that need to be solved to analyze the behavior of a structure. The larger the matrix, the more complex the structure and the more computations are required.

What factors affect the size of the Global Stiffness Matrix?

The size of the Global Stiffness Matrix is affected by the number of elements in the structure, the number of degrees of freedom, and the type of analysis being performed. For example, a 3D structure will have a larger matrix than a 2D structure.

Can the size of the Global Stiffness Matrix be reduced?

Yes, the size of the Global Stiffness Matrix can be reduced by using techniques such as symmetry and substructuring. These methods help to simplify the structure and reduce the number of equations that need to be solved, making the analysis more efficient.

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