adding buckling analysis

[RayanFarhat]

Thank you for your work on this FEM library. It is well designed and very useful for structural analysis tasks.

The library does not currently support structural buckling analysis. This limits its use for stability assessment of slender members and shell structures.

Add linear eigenvalue buckling analysis. Specifically, support for geometric stiffness matrix assembly and solution of the generalized eigenvalue problem to compute critical load factors and corresponding buckling modes.

I don't think this take much work, just adding the buckling formula to the existing axial load reaction after solving.

I am wrong in something? thanks again

[JWock82]

Pynite already considers geometric stiffness for members when performing P-Delta analysis. There are simple closed-form solutions for beams/columns. Plates are another animal. I've not found any published values for a geometric stiffness for quadrilaterals, and I suspect deriving that stiffness matrix involves complex numerical integration of an isoparametric element.

[angelmusonda]

@JWock82 There is a paper in which the geometric stiffness matrix for the DKMQ element has been developed. Irwan Katili, the original maker of the DKMQ element, is among the authors.

https://doi.org/10.1016/j.proeng.2017.01.368