Crawley-Luis-type one-dimensional model for piezoelectric actuation and sensing of laminated composite structures with bonding compliance

The seminal work of Crawley and Luis (AIAA Journal, Vol. 25, No. 10, 1987, pp. 1373–1385) introduced a one-dimensional (1D) shear-lag model for piezoelectric patch actuators bonded to isotropic beams, which continues to guide transducer design for applications such as energy harvesting, vibration control, and structural health monitoring. Nearly four decades later, this model has still not been extended to laminated composite host structures, despite their widespread use in advanced systems. This work presents the first 1D analytical model for the actuation and sensing response of composite laminates bonded with piezoelectric patch transducers through a compliant adhesive layer. The host laminate and transducer are modelled as small-width beams under plane stress or as infinite-width panels under plane strain conditions, using the first-order shear deformation theory. The transducer-laminate interaction involves both interfacial shear and peel stresses, resulting in a seventh-order differential equation for the former. Closed-form solutions are obtained for both actuation and sensing cases, which are validated by comparison with existing solutions for isotropic substrates and further assessed against continuum-based finite element results from ABAQUS for composite substrates, showing good agreement. Numerical studies examine the influences of adhesive thickness, laminate symmetry, ply angle, and transducer thickness on interfacial stresses and sensor voltage. Comparisons with shear-lag and classical laminate theory models highlight the importance of incorporating peel stress and shear deformation for accurate predictions.