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How to interpolate the bending moment result of an arbitrary point within the shell element ?

How to interpolate the bending moment result of an arbitrary point within the shell element ?

How to interpolate the bending moment result of an arbitrary point within the shell element ?

(OP)
Dear colleague,

I have a math problem that I get stuck:

Once having done the FEA, for each shell element (either 3 or 4-noded element), I already have the displacement (3 translations and 3 rotations) (note that for shell elements, rotation about the axis perpendicular to its plane is zero anyway). Also, I already have the results of Mx, My, Fx, Fy, Fz of all the nodes of the element of interest.

My question is: I am interested in finding the bending moment Mx and My of a point, within one element. How can I interpolate the results of the element nodes to get the result of the point I want ?

Thank you in advance.

NTCONLINE

RE: How to interpolate the bending moment result of an arbitrary point within the shell element ?

you're not using a post-processor to display the results ??

there are lots of interpolation strategies to map a surface from a set of points.

Maybe look into how post-processors display results ?

Do you also have element centroidal results ?

Be careful using results from 3 noded triangles. It'd be better (IMO) to use results from the surrounding quads.

another day in paradise, or is paradise one day closer ?

RE: How to interpolate the bending moment result of an arbitrary point within the shell element ?

One way to get the result at your point is query solution option like moving over the element, post processing shows how the solution varies by live values.

Another option is if you know element formulation and shape functions, you can manually calculate it. This is some what tedious. Look into theory manual of software.

Another option is to see whether your point happens to be Gauss point and results at Guass point option is available.

RE: How to interpolate the bending moment result of an arbitrary point within the shell element ?

(OP)
My point of interest is an arbitrary point, and not necessary at Gauss Points, unfortunately. I am unsure if I can use the Shape Functions of the element to interpolate the result at the point!

RE: How to interpolate the bending moment result of an arbitrary point within the shell element ?

∑M=0, ∑F=0 at a point?

RE: How to interpolate the bending moment result of an arbitrary point within the shell element ?

A standard way is to use the shape functions of the element and the Gauss point values (2x2 in a QUAD4), in order to obtain the stress at a given point (P) within the element (see e.g., Cook et. al, Concepts and Applications of FEA, 4th ed., p.232 - stress calculation). The equation given for 2x2 quadrature, is: σp = Sum Ni*σi, where σp is the value at the point P of interest, Ni the shape function, and σi is the Gauss point values (stress in this example). Sum goes from 1 to 4 in the case of a QUAD4 with 2x2 Gauss points. If you are not interested in theory, and you just need to obtain the value at a certain location, most FEA software will contour the extrapolated values inside the elements and at the nodes (where extrapolated values are averaged quite often at common nodes, or unaveraged/jumps if one wants to look on the quality of the mesh and the discrepancy/difference of the stress results produced by elements e.g., at a common node - should be small if the mesh is capturing the stress variation well).

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