New explicit solution for static shape control of smart laminated cantilever piezo-composite-hybrid plates/beams under thermo-electro-mechanical loads using piezoelectric actuators

In this paper, a new explicit exact analytical solution is proposed for obtaining static deformation and optimal shape control of smart laminated cantilever piezo composite hybrid plates and beams under thermo-electro-mechanical loads using piezoelectric actuators. The linear piezoelectricity and plates theories were adapted for the analysis. A novel double integral multivariable Fourier transformation method combined with discretised higher order partial differential unit step function equations were employed. The effect of various parameters including arbitrary loads such as non-uniform thermal stresses, electrical and mechanical loads, layup thickness, piezoelectric actuators size and placement, stacking sequence, and geometrical dimension were considered. The results were then compared with some published benchmark results and good agreement was observed. Unlike the earlier studies, the proposed method does not require the characteristic and trial deflection function to be predetermined. Both, the embedded and bounded actuators are considered. Until now, the shape control task of reducing mid-plane deformation at free end in smart laminated cantilever plates and beams was unsolvable and approximations were typically employed in numerical analysis Yu et al. (2009). This problem becomes more complicated for wider and longer plates but the method proposed herein successfully resolves this issue.