Stiffness Matrix of Frictionless Plate Support: Puzzling Differences

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Discussion Overview

The discussion revolves around the stiffness matrix of a plate supported by frictionless edges, focusing on the differences between the Kxx and Kyy values obtained from a finite element analysis (FEA) model. Participants explore the implications of boundary conditions and element types in the context of structural analysis.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions why the Kxx and Kyy values are not equivalent or close to each other in the stiffness matrix for a plate supported by frictionless edges.
  • Another participant seeks clarification on whether the arrows in the model represent boundary conditions (BCs) and if the BCs are consistent across different sections of the plate.
  • A participant explains their attempt to achieve equal Kxx and Kyy by dividing the plate homogeneously, noting that this led to a triangular base instead of a circular edge.
  • It is mentioned that the defined frictionless support along the edge should theoretically yield the same stiffness values, but the software (ANSYS) displays them differently.
  • One participant shares that changing the support type to fixed resulted in equal Kxx and Kyy values, suggesting a potential influence of support type on the stiffness matrix.
  • A participant emphasizes the importance of understanding support types and constraints in FEA, suggesting a focus on nodes rather than physical shapes for better analysis.
  • Another participant inquires about the type of elements used in the model and suggests considering elements with mid-side nodes for a more accurate representation of the curved outer edge.

Areas of Agreement / Disagreement

Participants express differing views on the reasons behind the discrepancies in Kxx and Kyy values, with no consensus reached regarding the underlying causes. The discussion remains unresolved as participants explore various factors influencing the stiffness matrix.

Contextual Notes

There are limitations regarding the assumptions made about boundary conditions and the representation of the plate geometry, which may affect the results. The discussion also highlights the dependency on the choice of finite element types and their implications for the analysis.

Mohamed_Wael
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Hi all,
In the attached photo, you can find a plate supported along the edge by "frictionless" support and I am trying to obtain the stiffness matrix using the node at the center. I wonder why the Kxx and Kyy (highlighted) are not equivalent or even near to each other, any suggestions?
 
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Im not familiar with ANSYS, but are those arrows your BCs (the supports)? It looks like you have "BCs" at the centerpoints between the edge nodes...Is that the case?

Also, are the BCs on the upper right hand side of the upper right half the same as the BCs on the lower left (asking because the arrows are different)?

Also, can you explain what you mean by the stiffness matrix at the node at the center? The Stiffness matrix applies to the entire structure (or a substructure), and doesn't describe a single point.
 
First thanks for your care,
1-actually I wanted to divide the plate in such homogeneous way trying to get equal Kxx and Kyy, but this lead to triangular base and not circular edge, but when u define the boundary conditions you define it for the circular edge geometry, that's why they look like flying supports.
2-I defined a frictionless support allover the edge they should be the same, I don't know why Ansys mark them in this way
3-when I extract the stiffness matrix I should define the DOF by selecting the nodes and the required DOF, that's what I mean
4-I have just tried changing the type of support to fixed support and I got equal Kxx and Kyy! i will attach the image.
thanks again
 

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Good to hear.

The "support type" (constraints or BCs) is very critical in FEA. When I was learning, my constraints were the cause of most of my mistakes. It helps to think of things in terms of nodes instead of physical shapes (that is, as a series of triangles instead of a circle).
 
What kind of elements are you using for this model? Have you considered using elements with mid-side nodes to allow for a curved outer edge?
 

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