  We demonstrate that the conventional application of linear models to the
analysis of optoelectromechanical properties of nanostructures in bandstructure
engineering could be inadequate. The focus of the present paper is on a model
based on the coupled Schrodinger-Poisson system where we account consistently
for the piezoelectric effect and analyze the influence of different nonlinear
terms in strain components. The examples given in this paper show that the
piezoelectric effect contributions are essential and have to be accounted for
with fully coupled models. While in structural applications of piezoelectric
materials at larger scales, the minimization of the full electromechanical
energy is now a routine in many engineering applications, in bandstructure
engineering conventional approaches are still based on linear models with
minimization of uncoupled, purely elastic energy functionals with respect to
displacements. Generalizations of the existing models for bandstructure
calculations are presented in this paper in the context of coupled effects.
