Can anyone please provide me a list of governing equations of structural/solid mechanics which are used by FEA softwares during solving. And how are these fundamental equations implemented onto each and every element in FEA? (And also, can these equations be different for different element types)?
I am already aware that FEA softwares basically makes use of these governing equations of structural/solid mechanics and apply its own Finite Element procedure in order to compute and approximate the results (such as displacements, stresses, energy etc) for each of the nodes and elements. But what fundamental equations and how are they incorporated for each of the elements, I couldn't understand it. These governing equations are essentially partial differential equations (whose solution is basically approximated by the FEA solver) but which ones, don't exactly know.
Just talking about simple static structural analysis here, with structure being in elastic range all the time.