Hybrid-Trefftz finite element model of smart doubly curved laminated composite shells

Abstract A novel smart hybrid-Trefftz finite element (HTFE) model has been developed for the analysis of smart doubly curved (DC) laminated composite shells integrated with a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow> <mml:mn>31</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> macro fiber composite piezoelectric layer acting as the distributed actuator. The substrates of these smart shells include symmetric and antisymmetric spherical, paraboloid, and hyperboloid laminated shells. This HTFE model avoids the complex task of deriving the particular solutions for simultaneous governing partial differential equations (PDEs) of the element domain. The Trefftz functions here are constructed in straightforwardly manner from a finite number of free-field exact solutions of the homogeneous simultaneous governing PDEs of the element domain, without transforming them into a single governing equation. Exact solutions for the smart DC shells have also been derived here for validating the HTFE model. It is found that the HTFE model of smart DC shells accurately predicts the passive and active responses of the substrate DC laminated composite shells.