Effective Laminate Elastic Engineering Constants

[zoltan117]

When I create an effective laminate for a quasi-iso tropic layup (-45,0,45,90) for tape I dont get the same values for the engineering constants E1 and E2 ie E1 does not equal E2.

Is there a theory manual that shows what assumptions Hypersizer is making when developing the smeared laminate properties?

When I use our internal in-house code E1= E2.

[Phil]

Please see the following link:

http://hypersizer.com/help/Content/Materials/EffLam/el-properties-stiffness.php


The engineering constants come from the inverse of the ABD matrix.  If the B terms are non-zero, it will throw off

Try making the laminate symmetric...  Instead of [-45/0/45/90], make it [-45/0/45/90]s instead.

[zoltan117]

Does hypersizer calculate the correct effective laminate properties for unsymmetric layups?

[mraedel]

I have problems to reproduce the elastic engineering constants in HyperSizer for single ply laminates with angles other than 0° and 90°.

I created a generic ply material and created effective laminates with (100% 0°, 0% 45°, 0% 90°); (0% 0°, 0% 45°, 100% 90°); (0% 0°, 100% 45°, 0% 90°). In the attached Excel spreadsheet I calculated the ABD-Matrix and from these values the elastic engineering constants according to http://hypersizer.com/help/#Materials/EffLam/el-properties-stiffness.php.

I checked the calculation with 2 composite analysis tools: eLamX² and alfalam. The calculations in my spreadsheet and the two composite analysis programs are identical.

However, for the (0% 0°, 100% 45°, 0% 90°) effective laminate, the engineering constants are different in HyperSizer than in all other calculations. They don't even match the values from the equations from the link.

What am I missing?

A second question: Why do effective laminates, defined as symmetric and balanced, create coupling stiffness terms in the B-matrix?

[August]

The reason for the discrepancy is rooted in the way that HS handles 45deg plies when deriving the effective laminate properties. Because HS doesn't distinguish between percent +45 and -45 in the effective laminate definition, it assumes that the laminate is balanced.

So in your case, HS is assuming that the effective laminate is 50% +45deg tape and 50% -45deg tape. The result is that the A13 and A23 terms are zero for the effective laminate. When the A matrix for the effective laminate (pic attached) is inverted to calculate E1 and E2, you get different results than a discrete laminate that is 100% +45deg.

It is good practice to not use effective laminates as small as one ply, because the smeared property assumptions begin to break down. If you are having this problem in a design application, I would recommend switching to discrete laminates for your 1-ply case.

[mraedel]

Hello August,

thanks for the explanation. I usually use effective Laminates with a minimum of 4 plies. This example is just a breakdown in the search for a model discrepancy.

My second question remains: I use an orthotropic laminae to create effective laminates. Here for example with (35% 0°, 35% 45°, 30% 90°). As you said, effective laminates are supposed to be symmetric and balanced. Using HyperFEA, the calculated ABD-matrix (attached pic) has a filled B-Matrix, indicating an unsymmetric laminate.

Why is that?

[August]

I can't re-create your non-zero B-matrix using those ply percentages with an effective laminate. Using your tape stiffness values from your previous post, I get a zero B-matrix every time.

Is the image of the ABD matrix coming from an unstiffened solid laminate concept?

HyperFEA would not have an impact on how the ABD calculation is done, so this is probably not causing the problem.

[mraedel]

The ABD matrix comes from a "One Stack Unstiffened" concept section. I thought that HyperFEA has no impact on the ABD-matrix calculation. I just wanted to illustrate the workflow.

The model is a curved shell panel in ANSYS using Shell181 elements as well as Link180- and Beam188 elements for the representation of an actuator.

I'll try to prepare a simple model.

Btw: the same happens for an isotropic material. Something is wrong.

[mraedel]

I created a generic model and can reproduce the behaviour. Despite isotropic material, the coupling stiffness matrix is populated. How is this possible?

I attached the model. Unfortunately, I can not attach the HyperSizer database (5MB zip) due to the size limit.

I basically created one assembly from the shell model and the components equivalent to the sections (11-22). I chose One Stack Unstiffened concept and isotropic material (Al 2024-T3). I use only buckling and isotropic strength criteria (longitudinal, transverse, shear, von-Mises).

I use version 7.0.53 of HyperSizer.

[August]

Based on the ABD matrix you're showing, it looks like you have the Reference Plane set to "Top" for the component (this is on the Options tab, far-right).

Setting this to Midplane yields a zero B-matrix for the un-stiffened plate in your example.

The default reference plane is Midplane. However, if you have set a reference plane in your FEM, HyperSizer will read it in and set this option for you. This is necessary so that the stiffness matrix in HyperSizer will match the stiffness in the FEM used to derive the loads for the elements in the component.

It is recommended to use a Midplane reference in your FEM for sizing with HyperSizer. Otherwise, you will need to use HyperFEA more frequently to keep the FEM loads in sync with your design.

-August

[mraedel]

Thanks for the answer. I already tried setting the element reference plane to MID. I changed my model and used "Reimport FEM" from the Project Setup windows. Unfortunately, it had no effect at the time.

Now, thanks to your suggestions, I tried it again. Still, no luck with "Reimport FEM". Only when I deleted the model using "Remove FEM" and than re-read the model with "Import FEM" I was successful.

Is it a bug or a feature, that the element reference plane is not update during "Reimport FEM"?

[August]

The fact that the reference plane did not change with "Reimport FEM" is likely not a bug. Reimport preserves more information in the database than using Remove and Import. This is to help reduce the number of corrections needed in HyperSizer if a small change is made to the FEM.