Coupled electro-thermo-elastic equations applicable for the analysis of smart structures have been derived from first principles. Using the equations and applying layer-by-layer finite element model, the induced potential and mechanical deformations in the piezo and non-piezo core material have been obtained for various cases of actuation and sensing of a smart beam under external mechanical load and actuation potential. The present study clearly brings out the essential difference between sensing and actuation. It is also brought out that the interaction between polarisation and electric field in the piezo continuum leads to non-linear distributed body force and non-symmetric stress tensor. These non-linear effects are found to have significant influence on the deformation of a smart beam under actuation. Shape control studies of multi-patch smart beam have also been investigated.