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### Author Topic: Simple plate in biaxial tensile stress fails primarily by buckling?  (Read 1171 times)

#### Neergaard

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##### Simple plate in biaxial tensile stress fails primarily by buckling?
« on: February 03, 2016, 06:22:36 PM »
All

To verify that HyperSizer handles materials failure at different temperatures properly, I made a simple FEM of a square plate under equibiaxial tensile stress (see picture).  The material failure calculations where correct (giving me confidence for more complex geometries), but the primary failure mode for a uniform sheet was buckling.

I cannot understand that result.  Am I missing something here?

#### James

• Posts: 235
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##### Re: Simple plate in biaxial tensile stress fails primarily by buckling?
« Reply #1 on: February 03, 2016, 07:01:47 PM »
Can you post the margin-analysis details for the buckling analysis? See: http://hypersizer.com/help_7.1/#ReportMS/report-msdetail-create.php?Highlight=analysis detail

When you apply a temperature to a plate in HyperSizer, it will compute the thermal strain based on the alpha*deltaT. Depending on the assumed boundary conditions, if the thermal strain is not equivalent to the actual strain, then the design-to strain will induce a stress.

This is explained in the stiffness HME document (see section 4): http://hypersizer.com/download.php?type=analysis&file=HyperSizer_Stiffness_Method_-_Thermoelastic_In-Plane_Stiffness_Formulation.HME.pdf

-James

#### Neergaard

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##### Re: Simple plate in biaxial tensile stress fails primarily by buckling?
« Reply #2 on: February 04, 2016, 05:24:43 PM »
James

Good to hear from you.

Here you go.  I attach both the detailed Excel spreadsheet and a screenshot of the sizing window (failure tab) after analysis.

On the subject of temperature, I set the initial temperature to 293.2 or 593.2 K for the hot and cold load sets, then set the temperature boundary condition to equal the initial temperature.  The change in temperature (delta T) from initial to the load set will be zero if I did everything right.

In addition, the edges of the plate are constrained at the mid-node not to slide along the edge, or to translate perpendicular to the plane of the plate.  The center node of the plate is pinned.  If there were thermal expansion strains, the plate would expand, but being isothermal, there would be no thermal stresses.

-Neergaard

#### rendoc

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##### Re: Simple plate in biaxial tensile stress fails primarily by buckling?
« Reply #3 on: May 09, 2016, 11:34:56 AM »
Was a solution to this problem ever posted?  I'm having a similar issue, and from what I can tell, it seems to be related to the method HS uses to pull FEM loads and average them for panel buckling.

In my case, I have a panel that is tension dominated except for about 5% of elements in the corners (similar to the posted example).  HS appears to be filtering out the tension elements, averaging the remaining compression elements, and reporting a buckling margin, which is not correct.

Is there an way for HS to determine when panels are tension-dominated, causing it to ignore a very small percentage of compression-loaded elements, and not perform a buckling check?

#### James

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##### Re: Simple plate in biaxial tensile stress fails primarily by buckling?
« Reply #4 on: May 10, 2016, 08:03:25 AM »
For a single load case, HyperSizer will perform separate area-weighted averages for elements in tension and elements in compression. Using a std deviation approach, HyperSizer averages the elements and adds a multiple of the standard deviation to calculate a set of tension design-to loads and repeats the process for the elements in compression to calculate the compression design-to loads (average compression loads always used for buckling analysis). This prevents a positive and negative load from canceling each other out. This is desirable if you have a load reversal in your component.

For components with many elements there is potentially an issue with the statistical methods in that they could combine worst-case membrane loads, moments and transverse shear loads from different areas of your panel creating conservative design-to loads. For strength, local buckling, crippling, etc. we recommend using the peak element method for load processing. This approach will create case-consistent and element-consistent load cases.

The panel buckling analyses will always use the element area-weighted average compression load. This is because panel buckling is based on an average load state throughout the panel. However, I don't think it's accurate to allow the tension load to cancel out the compression load because part of the panel could be in compression and it could buckle. To account for the load reversal in the panel, HyperSizer will adjust the x-span and y-span (a and b) based on how much of the plate is actually in compression.

-James

#### James

• Posts: 235
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##### Re: Simple plate in biaxial tensile stress fails primarily by buckling?
« Reply #5 on: May 10, 2016, 08:27:31 AM »
Here is another forum post that discusses how HyperSizer adjusts the buckling spans for plates in biaxial load states, with load reversals.

http://hypersizer.com/forum/index.php/topic,88.0.html

-James

#### rendoc

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##### Re: Simple plate in biaxial tensile stress fails primarily by buckling?
« Reply #6 on: May 11, 2016, 02:40:30 PM »
James,

Thanks for the response.  I've gone through the forum post you provided, and just about every report available for my part that mentions buckling, and I still can't find any evidence that HS is actually reducing my buckling spans.  Can you provide an example?  Maybe I'm just not looking in the right place.

Thanks!