asdeasoft.net

Dear STKo
in my thesis I have to describe the theoretical part about the asdshellq4 element.

I have already described the part about membrane behaviour (element QACM-I), the bending part MITC4.
According to the attached articles, I have derived the stiffness matrices for these.

I wanted to ask how to formulate the stiffness matrix for the asdshellq4 element?

Will it be the sum of the stiffness matrix mitc4 and qacm-i taking into account the additional degree of freedom associated with drilling ??

I initially wrote this down with the following equation
K asdsheel4=K Mitc4 + K Qacm-I

How can I describe how the stiffness matrix for ASDSHELLQ4 is built, when there are different shape functions for mitc4 and for QACM-I?

Does it depend on the load applied to the element? If it is perpendicular to the element causing bending so the matrix K ASDSHELL Q4 will be equal to K MITC4?

Each node has 6 DOFs in global coordinates.
First, you have to build the stiffness matrix in the local coordinates (1,2,3 are local translations ULx, ULy, ULz) (3,4,5 are local rotations, RLx, RLy, RLz)
The AGQ6-I is the membrane part that acts on the first 3 DOFs in local coordinates (1,2,3).
The MITC4 is the plate part that acts on the last 3 DOFs in local coordinates (4,5,6).
So they are not summed (as they act on different DOFs), but assembled in the local total stiffness matrix.

Then the local stiffness matrix (membrane + bending) is transformed in global coordinates using a transformation matrix, that can be a simple rotation matrix (for linear kinematics) or a more involved procedure (for corotational kinematics)

STKO Team wrote: ↑

Mon Aug 26, 2024 8:57 am

Each node has 6 DOFs in global coordinates.
First, you have to build the stiffness matrix in the local coordinates (1,2,3 are local translations ULx, ULy, ULz) (3,4,5 are local rotations, RLx, RLy, RLz)
The AGQ6-I is the membrane part that acts on the first 3 DOFs in local coordinates (1,2,3).
The MITC4 is the plate part that acts on the last 3 DOFs in local coordinates (4,5,6).
So they are not summed (as they act on different DOFs), but assembled in the local total stiffness matrix.

Then the local stiffness matrix (membrane + bending) is transformed in global coordinates using a transformation matrix, that can be a simple rotation matrix (for linear kinematics) or a more involved procedure (for corotational kinematics)

Hi. Sorry to get back on the topic, but there is one thing I wanted to ask you.

Is it correct that the membrane part of the AGQ6-I acts on 3 translations? (1,23,)? and not 2 translations in plane ULX, ULY (1,2) and the rotation RLZ?

Summary AGQ6-I acts on (1,2,6) DOFs
and MITC4 ULZ and RLX,RLY (3,4,5) DOFs ?

I found something like this in one reference: I have written that the local stiffness matrix of ASDSHELLQ4 can be represented as: but I have assigned driling deegre to mitC4

Is this notation in this case correct?

The AGQ6-I is the membrane part that acts on the first 3 DOFs in local coordinates (1,2,3).
The MITC4 is the plate part that acts on the last 3 DOFs in local coordinates (4,5,6).

Yes sorry, there was a typo here.
Membrane = Ux(1) Uy(2) and optionally Rz(6, the drilling DOF)
Bending = Uz(3) Rx(4) Ry(5)

Dear Sylwester

May I ask whether you have finished your thesis? I am particularly interested in the theoretical part concerning the asdShellQ4 element, but I have not been able to locate any complete material. Would you be so kind as to share the relevant theoretical documentation for the asdShellQ4 shell element? I would be extremely grateful.