This book contains several examples aimed at comparing analytical and numerical (FEA) solutions for shells:
http://members.ozemail.com.au/~comecau/quad_shell.htm
Hi Benny,
Derivation of stiffness matrices for shell elements is a pretty complex problem; its solution is usually a trade secret of software companies developing FEA codes. I would suggest you to have a look at the following webpage that provides reference to a book devoted to that subject...
If your set of requirements to FEM software is rather specific (individual), you may consider development of a customized product that would have exactly the set of features that you need. The advantage would be full control over the software codes, so making amendments and updates would be...
Usually, when you buy a textbook, it is just a book with lots of formulas, etc., but with very few really working source codes (if any at all). However, the book that I advised you to consider also contains all the source codes on CD-ROM (and the pre-compiled executables, GUI interface, etc.)...
Brief answer (at least for linear static analysis) is: its OK to refine the mesh as much as you need, to obtain more accurate results.For example, the following analysis of a statically (wind-) loaded perforated panel, based on quadrilaterals using the Mindlin approach, works just fine...
The best way to go would be to obtain working FEA codes capable of solving some real-life problems,together with detailed description of how those codes work. That would serve as a framework for your own software development. Below is a reference to a book that contains all that: theory...
Essentially, you are dealing with multi-layered plate and/or shell elements. Mathematically, it means that the compliance matrix (the matrix of elastic constants) is formed by specific algorithms, more complex than those involved in modeling of homogeneous isotropic materials. The stress...
It depends on what exactly class of problems you are going to solve using the FEA. For example, if you intend to work with shells, a very important branch of mathematics to study would be the differential geometry of curved surfaces.
In order to accurately evaluate all the properties of such object, you definitely need to use FEA of multi-layered shell (for very accurate and flexible modeling you may want to consider some in-house software development). Going with just isotropic model would, most likely, lead to incorrect...
As an example, consider so-called "shallow shell", which is geometrically close to plate, but has some curvature; the corresponding images can be found on the following webpage:
http://members.ozemail.com.au/~comecau/quad_shell_shallow_shell.htm
Suppose, a vertical, distributed load is applied...
Your algorithm must perform a number of operations, using the matrix of directional cosines. The full algorithm and its source codes can be found in the following book: "Computational Geometry of Surfaces and Its Application to the Finite Element Analysis of Shells" by O.Axenenko and A.Tsvelikh...
It is hard to say how credible are the mathematical fundamentals of the method supposedly implemented in that software. As usual, practical comparison with some good-quality FEA packages is a must. Things to compare: CPU usage, RAM usage, time efficiency; complexity of the models and the...
Frankly, it sounds like a whole research and development project by itself. You may consider development of a customized software program that would incorporate both the FEA and some further evaluation of the obtained numerical results according to the standards that you've mentioned. For the...
The following page contains description of an approach to solve problems of stress analysis of plates resting on elastic foundation:
http://members.ozemail.com.au/~comecau/quad_plate_elastic_support.htm
Hope this helps.
There is a website devoted specifically to shell buckling problems:
http://shellbuckling.com/
In particular, there is a whole list of professionals working in that area; you may consider contacting them to obtain assistance.
You may need a separate software tool for that; here is just one that might be appropriate for your purposes:
http://members.ozemail.com.au/~comecau/rn.htm
http://members.ozemail.com.au/~comecau/quad_surface.htm
You might want to use some customized software for that problem. Here is an example; perhaps that looks similar to the problem you are solving:
http://members.ozemail.com.au/~comecau/quad_shell_wtank_ir.htm
The accuracy of the FEA is a broad topic. The best way to evaluate precision of a particular FEA software tool is to compare analytical and numerical solutions for models when analytical solutions are available. The fact is that not only simple beam problems allow such comparison: plate and...
