## Stiffness matrix for a 4 node plate in bending (12x12)

## Stiffness matrix for a 4 node plate in bending (12x12)

(OP)

I have looked long and hard for this stiffness matrix and I know it's out there. I know there is a general matrix (just like the ones they give for beams) where the values are functions of L, E, and I and A etc. I can't find anything on the internet that gives these values, I only find mind bogeling ways to derive this matrix which is over my head.

This is the closest I could find in these posts...

I wish I had read your post a long time ago, but for the curious . . .

The stiffness matrix for a rectangular plate in bending (12DOF) is given on pp.116-120 of "Theory of Matrix Structural Analysis" by J.S. Przemieniecki, published by Dover Publications, Inc., 1968 & 1985.

Good Luck. - Ed

Ahhhh, I don't want to buy this book, can someone please point me to a page that has this 12 x 12 matrix or please put these values in this post. I know how to derive this using a program by doing the unit displacement stuff but I need a general one that considers all E's I's and L's.

Thanks you!

This is the closest I could find in these posts...

I wish I had read your post a long time ago, but for the curious . . .

The stiffness matrix for a rectangular plate in bending (12DOF) is given on pp.116-120 of "Theory of Matrix Structural Analysis" by J.S. Przemieniecki, published by Dover Publications, Inc., 1968 & 1985.

Good Luck. - Ed

Ahhhh, I don't want to buy this book, can someone please point me to a page that has this 12 x 12 matrix or please put these values in this post. I know how to derive this using a program by doing the unit displacement stuff but I need a general one that considers all E's I's and L's.

Thanks you!

## RE: Stiffness matrix for a 4 node plate in bending (12x12)

Note that the formula is good for rectangular elements only. For arbitrary quadrilaterals, the kinematic matrix B need to be modified (not included, don't want to discourage you with complicated stuff.)

Hope this helps!

## RE: Stiffness matrix for a 4 node plate in bending (12x12)

## RE: Stiffness matrix for a 4 node plate in bending (12x12)

The formula is in local plane. You only need to transform the resulted stiffness matrix (not the formula) if you want to plug in 3D structures.

Enjoy the FEA!

LHC

http://cgFEA.com