Could you give a little more explanation Ernesto?  What do you mean by distributed moment?  A moment distributed along an edge of a plate model or, perhaps, a moment field specified over the entire plate?  I also don't quite understand how you would apply thermally induced moments to the constitutive equations which relate generalised stresses to generalised strains.  

Hello Angus,

Thank you for your time and for your reply. I'll certainly explain more. By distributed moment, I mean a moment field specified over the entire plate.

Next, the misunderstanding that occurred was due to my mistake. Thank you for pointing it out so I know how to converse about plate theory more accurately. I think I should have said, "...adding resultant thermal moments to the constitutive equations for plates.

More specifically, I am trying to implement the theory in the attached paper and I am specifically talking about Seps and Skappa in equation 43.

Article Asymptotical construction of a fully coupled, Reissner–Mindl...

I'll have to wait to get the reference you sent.

So next question, is it a self-balancing moment field that you want to define, i.e., one in equilibrium with zero applied loads?

Yes, to the best of my knowledge,  I believe it will be self-balancing moments.

Okay.  You are after a self-balancing or hyperstatic moment field, i.e., one that is in equilibrium with zero applied loads - rather like a residual moment field.  Do you know the form of the field or is it going to be a variable in your model?  

My company develops software that analyses plate problems and we can define statically admissible hyperstatic moment fields directly - we use these in our limit analysis software.  You might like to browse our website as much of the details are available there:

www.ramsay-maunder.co.uk

I am not sure how you might do this with conventional FE software like ABAQUS.  Although there are ways in which you can obtain hyperstatic moment fields by, as you say, applying a thermal gradient over the plate, or by, for example, taking the difference between two elastic solutions obtained with different Poisson's ratio values - see appendix 2 of the following document:

http://www.ramsay-maunder.co.uk/downloads/Benchmark%20Challenge%20004.pdf

There is, presumably, an infinity of hyperstatic fields for a given plate configuration.  The approaches identified above will give you a particular hyperstatic field but this is not so easily controlled if you need to define them through thermal gradients or the difference of two elastic solutions with different material properties.

Anyway, some thoughts that might be relevant to your problem.  If there is anything further that I might do then please let me know.

Angus.