Each lamina is generally orthotropic Piecewise linear variation of electromagnetic potential through the depth of each piezoelectric lamina Piezoelectric surface is grounded where it is in contact with structural composite material Linear variation of temperature through the plate thickness Displacement assumptions consistent with Mindlin theory Nonlinear strains consistent with von Karman approximation
= i th element node displacement vector; five displacements per node: u, v, w, x, y = i th element node electromagnetic potential = i th element Gauss point transverse shear stress resultant vector; two per node: Q x and Q y
Results have demonstrated the impact of piezoelectric coupling on the buckling load magnitudes by calculating the buckling loads that include the piezoelectric effect (coupled) and exclude the effects (uncoupled). As would be expected, the relatively weak PVDF layers do not significantly alter the calculated results when considering piezoelectric coupling. The net increase is about 3% for the thermal loaded ten-layer laminate (PVDF/0/90/0/90) s.
However, adding the relatively stiff PZT as the top and bottom layers produces significant differences between the uncoupled and coupled results. A reversal of stress is required to cause buckling in the coupled analyses due to the sign on the pyroelectric constant for the PZT material. Neglecting the sign change, an increase of approximately 67% is observed in the absolute buckling load magnitude for the coupled analysis compared with the uncoupled analysis.
Looking into different stacking sequences – symmetric and anti-symmetric stacking Looking into the effect of the piezoelectric thickness effect on buckling for the two cases above.
Six layer laminate: (PZT5/0/90)s Simply supported a = b = 0.2m h = 0.001 m