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Hi Sean,
Would it be possible to explain twisting curvature using an example of the physical world?
From the blender sketch, does it mean rotation of element ABCD in its own plane?
The easiest way to try and understand twisting curvature is to start with the regular bending curvatures, kxx and kyy - these are easy enough to conceptualise as a measure of the degree to which the plate is bent in the x and y direction.
Consider taking an A4 sheet of paper and bending the two long edges towards each other, or the two short edges towards each other. The curvatures kxx and kyy are derived from the bent shape of the paper in each of these deformed states: one where the curvature is aligned with the length (x-direction), and one with the width (y-direction).
Now, the twisting curvature, kxy, represents how the surface twists, or how the slope in one direction changes as you move in the perpendicular direction.
To visualise this, imagine holding down one corner of the paper flat on the table, and gently lifting the diagonally opposite corner upwards, while allowing the other two corners to follow naturally. You’ll notice that the paper doesn’t simply bend along a line — it warps or twists. This warping is what twisting curvature captures.
Seán
Awesome,
quite clear now.
Thanks Sean
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