RE:Frameless glass cantilevered stair balustrade
In fact glass is one of the most linear elastic materials we use. Non-linearity comes in to play when you have large deflections, and this is sometimes significant for glass, so you may have geometric non-linearity but not really material non-linearity. This may be particulalrly the case where you are dealing with connections and are interested in localised effects around the connections. Of course, you might be talking about the connection fasteners which, being steel most probably, may have non-linear characteristics. However, if you are into non-linear territory whith your connections, I would begin to fear for the force/stress distributions in the glass fixing if the fastener is deforming significantly.
By all means, I would recommend, as someone has already, studying the institution's handbook and also Haldiman's book.
Mounting the fasteners in the holes is critical. Too much distortion could allow the fastener to overcome the resiliant bearing and produce metal to glass contact, which you must avoid. You should also look at, and try to limit, differential movements between the treads (or whatever they are fixed to) and to make them stiff so you don't set up secondary forces between the fixings that are hard to predict. If you can do that, you may not need to resort to FE, which might not give you the answers you are looking for and may even raise more questions that answers! Manual design methods may suffice unless it is a very specialised or tricky application.