Finite element strong and weak form

[oesa28337]

Hello,

I have a question about strong and weak form. We use weak form in FEM as it contains only first derivative of the displacement function, so we can use displacement functions with C0 continuity. This can help reducing the computation time. However, strain (and in turn stress) should be C-1 continuous. Does that mean that we get discontinuities in the stress and strain solutions? This is contrary to my observation of any FEA of stress field, which seems to be continuous. Also, in FEM displacement functions, what if, if I use a quadratic polynomial? Does it mean that now I have C2 continuous shape function?
Any comments, very welcome.

 

[bkal]

When you talk about your observation of FEA stress fields, what you are probably observing are smoothed / averaged stresses and strains. This is usually calculated in a post-processing phase. I suggest you compare non-smoothed values with smoothed values.

 

[csk62]

Take a look at Hilbert and Sobolev spaces.

 

[Tash1233]

This is simply what I remember from my FEA classes. I think you are right, that stresses and stresses are not C1 continuous anymore. All we impose during the formulation is continuity of the primary variable and balance of forces and that is all we can expect.

 

[ShellsPlatesMeshes]

In case of FEA of thin (Kirchhoff-Love) plates: the displacements are excellent; the results for bending moments and shear forces are very good for elements whose shapes are close to rectangular, but the numerical errors increase (in case of shear forces - significantly) for those elements that are distorted. Mesh regularity is the key for numerical correctness.