Shell structure buckling analysis

[peto24ap]

Hello,

I would like to perform a buckling analysis of a thin concrete doubly curved shell structure (architectural / structural). I am writing my own code and as a shell element I am using a combination of a plane stress triangle (for membrane forces) and DKT triangle (for plate part of the stiffness matrix). Linear analysis works well, but for buckling analysis I am missing a geometric stiffness matrix for DKT element.

Do you know some good reference where I can find more about how to construct geometric stiffness matrix for DKT elemets ?

Thank you !

 

[ShellsPlatesMeshes]

There is a book devoted to static modeling of shells, with all derivations of the stiffness matrices and source codes on a CD (provided with the book). Calculation of geometrical parameters (the Lame coefficients, curvatures, etc.) is described in a standalone chapter of the book; the algorithm is also described in detail.
Below is a link to a brief overview of the book:

http://members.ozemail.com.au/~comecau/quad_shell.htm

The book is available from Amazon (hardcover or paperback):

http://www.amazon.com/Computational-Geometry-Surfaces-Application-Analysis/dp/0646594044

http://www.amazon.com/Computational-Geometry-Surfaces-Application-Analysis/dp/0646930818

Hope this helps.

 

[peto24ap]

Many thanks for your advice. This book looks pretty interesting - only positive customer reviews on Amazon. But I would appreciate a little less expensive answer for my non-profit project

 

[ShellsPlatesMeshes]

Well, the authors seem to have spent quite a few years developing such a sophisticated finite element and implementing the maths in the codes. Essentially, you get what you pay for.

 

[WARose]

Probably the best reference I have on concrete shell buckling is: 'Concrete Shell Buckling', by: Popov, et al, ACI Special Publications, SP-67, 1981. If I recall correctly, it's more geared to finding safe buckling values than modeling techniques. And that is a point that can't be emphasized enough: FEA software will spit all sorts of buckling values out at you.....but that doesn't mean they will work. Thin walled structures are sometimes limited by (among other things) imperfection sensitivity. This can greatly reduce a value of a theoretical buckling stress.