32_LST example

In this post, I'll solve an example of the LST element which was explained in previous post.

 

 

The triangle has a six nodes, with a height of $h$ and a width of $b$

Displacement can be calculated as follows using the coordinates of the six nodes.

 

 

 

Upon rearranging for ${a_i}$

 

 

By substituting the two equations into the displacement function, it can be expressed as follows.

 

 

 

This can be represented in the form of a shape function as follows.

 

 

Additionally, each shape function is as follows.

 

 

Performing the necessary differentiation to calculate the element displacement results in $\beta $ and $\gamma $ being as follows.

 

 

Therefore, It can be represented as follows.

 

 

Therefore,the stiffness matrix for an element with a constant thickness can be obtained.