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Yes, red is thicker, blue is thinner. Design objective is to minimize compliance (maximize stiffness). I guess if we clamp the sides, the result will be opposite: thicker outside, thinner inside. I think topology optimization is ideal for this case, if you intend to keep the slab mid-plane flat...

Here is the formula of B for arbitrary quadrilateral (see attached picture). It follows what called iso-parametric formulation. Simply replace the B matrix in the formula I previously posted with this new one. Also, please check it before use (I don't ussually get things right at the first...

I wrote a simple Matlab code (about 500 lines) that does the buckling analysis (and of course linear analysis) for 2D steel frames with tappered sections (I-beam and square tube). I can give for free. It has to be upgraded in order to do the post-buckling load-displacement analysis, if that is...

How about the manual of FE-Safe? I think it is concise: pretty practical, with enough theory.

I put together a formula in the attached picture. I am not sure if it's right. Some one who knows about this, please confirm. The formula if for C0 mindlin plate. Note that the formula is good for rectangular elements only. For arbitrary quadrilaterals, the kinematic matrix B need to be...

Here is the smooth result.http://files.engineering.com/getfile.aspx?folder=f7d4c526-1cc2-4a49-b161-aa7054f9f2cc&file=smoother.gif

Thanks Greg to remind me of Optistruct. I just did a quick check and the result is rather interesting. Attached are screen shots for your comments. Boundary condition: simply supported all sides; load : uniform (not the acceleration). If we allow steep change in thickness, it shows smth like...

I think it is a good idea to link VBA in Excel to C code. Beside the fact that C is fast, there are state of the art sparse solvers such as superLU that are free. I don't recommend you to write a linear solver of your own. Yes, you can link VBA to C codes. A colleague of mine just presented in...