Triangular thick plate stiffness matrix transformation

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SUMMARY

The discussion centers on the transformation of the stiffness matrix for thick triangular plates using the shape function Ni = ai + bi*x + ci*y. The author questions whether it is necessary to transform this stiffness matrix to global coordinates, especially since the local edges of the triangle are consistently aligned with the global X-axis in the illustrations. It is established that transformation is essential to ensure accurate representation and alignment with the global coordinate system. The discussion also seeks clarity on the method for performing this transformation, particularly regarding the selection of a base point for rotation.

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  • Understanding of stiffness matrix formulation for thick triangular plates
  • Familiarity with shape functions in finite element analysis
  • Knowledge of coordinate transformation techniques
  • Basic principles of structural mechanics
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  • Learn about the selection of base points for rotation in coordinate transformations
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Structural engineers, finite element analysts, and students studying advanced mechanics of materials will benefit from this discussion, particularly those focused on stiffness matrix formulation and coordinate transformations in structural analysis.

Ronankeating
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Hi community member,

Regarding the book that I'm reading original writer has used Ni = ai + bi*x + ci*y shape function for the formulation of stiffness matrix for thick triangular plates.

The writer has not mentioned in the article that the resulting stiffness matrix is required to be transformed to global coordinates. What arised my suspicion was, in the illustrations local 1-2 edge of triangle is always aligned to global X-axis. Is it coincidental or "must" to perform the transformation to that specific shape function?

If transformation is required at all to match the exact illustrations, how should be performed, I mean how to choose the base point for rotation, rotation around any arbitrary vertex will work ?


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