Finite element plate with triangular mesh

[GiorgioBurbanelli89]

I managed to make the mesh

Malla traingular de placa rectangular.txt
I would continue with the shape functions of stiffness and displacement matrices, as in Nedelcho's Slab FEA example.
Could someone help me or guide me which steps to follow to make an example similar to ned but with the traingular mesh please?

[Proektsoftbg]

The simple triangular element is not suitable for plate bending. You should use higher order elements and it is not an easy task to answer in 2-3 lines. You need to dive deeper in the topic.

[GiorgioBurbanelli89]

@Proektsoftbg You're right, I've looked into it, but it could be used for a circuit board based on Mindlin's theory.

[GiorgioBurbanelli89]

The simple triangular element is not suitable for plate bending. You should use higher order elements and it is not an easy task to answer in 2-3 lines. You need to dive deeper in the topic.

Ned,

In 2018, Rama, Marinkovic & Zehn (TU Berlin) published
a breakthrough combining DSG + cell smoothing with ANDES
for triangular shell elements.

Paper: DOI 10.1007/s40430-018-1276-4

Result: 3-node triangles now converge to exact solutions
for plate bending. Your statement was correct for 1971-2017.
Technology changed in 2018.

The paper demonstrates convergence on Raasch hook, twisted
beam, pinched hemisphere, and Cook's membrane tests.

Simple triangles ARE now suitable for plate bending.

[Proektsoftbg]

Hi!

My statment is still valid because the simple 3-node (constant strain) triangle element still exists. Also higher order elements exist, as I mentioned. I adviced you to search for such as you obviously did. The element you found is actually of higher order. It internally subdivides into 3 sub-elements using the element center as an additional node. See section 2.1. "Plate behavior".

The ANDES formulation concerns the membrane behaviour (see Section 2.2) which is not needed in your case - for creating a plate analysis program. This element is way too complicated for your job - it is for layered shells (composite laminates).

Higher order triangular elements exit long ago 2018. Adding one centeral (fake) node or side nodes is comonly used for improving the element behaviour. As you can probably see already, the problem is not so simple and requires a lot of reading. You have to dive deep in the topic, as I mentioned.

Instead, you choose to question the correctness of answer above in such a shallow andaggressive way taking some randomg publication. This is not constructive and helpful for anyone. I do not like this manner because I have to answer in some way and waste valuable time. I do not have time now to work on triangular plate element in Calcpad and it is not a priority for the project. If you want to do it, you will have to do it yourself.