2lai,
For most stress analysts, the beam and shell elements are the "bread and butter" element choices. Solid elements are not as common since they are not a particularly good choice for many models. However, for some models, solid elements are required. The fact that you have never used a beam or shell element indicates that you may want to further expand your knowledge of FEM.
As Blas mentioned, in reality all models are nonlinear, though many can be idealized as linear. You say "With shell mesh, the static and nonlinear analysis generates different results." The way this is worded, it does not make sense. Since you can have a nonlinear static analysis, are you implying the analysis is dynamic? What is the form of non-linearity? Geometry (and what type), material, or other?
Composites, just as every other material, have temperature dependent properties (i.e. nonlinear). However, it is uncommon to analyze it is nonlinear just because of this. An exception would be a bond line anlaysis in a joint where the temperature dependent properties and plasticity significantly affect the response. But for general analysis, it is far more common to analyze with room temp properties and then apply "knockdowns" to to account for strength differences. Applying temperature dependent properties at each lamina, and solving as nonlinear, is probably reserved for a research solution.
Based on your comments, I would recommend further investigation into the analysis approaches of composites and FEM. Everything you have indicated seems to be far from the "norm". I think one of the more difficult things about composites is knowing what is important and what is not, and how to incorporate that into a FEM. If your company or industry does not have a lot of background in that, you can easily go in the wrong direction. If you don't have the right software (i.e. shell elements) and/or the direction based on industry solutions, it will be difficult to get a useful result. Good luck.
Brian