How does ANSYS convert the strain of nodes at the element level to the strains of nodes for the entire model (especially for the middle points)?

Dear forum members,

I am currently working on developing finite element analysis (FEA) code in MATLAB, where I'm utilizing quadratic tetrahedral elements. For this purpose, I have exported the necessary values and matrices from ANSYS. After calculating the strain for each element, I proceeded to average the values for overlapping nodes at the element level. This approach seems to work well for the corner nodes of each element; however, I encounter inconsistencies when it comes to middle points. In some cases, even when the nodes are not duplicated, the values vary.

Could anyone provide insight into why such discrepancies may occur? Your expertise and advice would be greatly appreciated as I navigate through this issue.

Thank you for your time and assistance.

Answer 1

[Balavignesh]

Hi Daeho,

As per my understanding, you are encountering issues when you are calculating strain for middle nodes of the model. The issue you're encountering is related to how strain values are interpolated and averaged across elements in finite element analysis (FEA). In particular, quadratic and tetrahedral elements (which have both corner and mid-side nodes) present unique challenges when averaging strain values at nodes.

To obtain strain values at the nodes, the strain values at the integration points are interpolated to the nodes. This interpolation is done using the shape functions of the elements. Mid-side nodes in quadratic elements are not as straightforward as corner nodes. They are influenced by the strains from the adjacent elements differently due to ther position and nature of the shape functions.

Possible reasons for discepanices:

• The interpolation of strains from integration points to nodes can introduce errors, especially for mid-side nodes where the shape functions are more complex. Use higher-order interpolation methods to transfer strains from integration points to nodes. This can help reduce errors, especially for mid-side nodes.
• The method used to average the strains at shared nodes can significantly impact the results. A simple arithmetic average may not always be the best approach. Instead of a simple average, I suggest you use a weighted average based on the contribution of each element to the node. This can be based on the volume or area associated with each element.
• Ensure that the mesh quality is high. Use mesh refinement and optimization techniques to improve element shapes.

Hope that helps!

Balavignesh