| A three-step methodology is presented for high-fidelity modeling of slender structures with embedded actuators and sensors. The solution to the three-dimensional problem of solid electromechanics in the slender domain is sought through the identification of two different scales in the system. The variational formulation of the problem is then asymptotically approximated at each level, defining, first, a linearized local problem at the cross section under the assumption of small local strains and, then, a geometrically-nonlinear long-scale problem along the dominant dimension. Each problem is solved independently and their combined solution provides an asymptotic approximation to the electroelastic field in the original domain. This approach can be used to define the solid part in a fluid-structure interaction problem. The proposed formulation can model anisotropic non-homogeneous slender structures with embedded piezoelectric actuators and sensors, hygrothermal effects, and arbitrary geometrical definitions of the cross section (thin-walled or solid, closed- or open-cell) and the reference line (initially curved and twisted). In addition to this, a Ritz-based method is used to define a modal approximation to the local cross-sectional warping displacements to account for particular deformation shapes (e.g., airfoil camber bending in a wing). Numerical results are used to illustrate the formulation. They include comparison with three-dimensional finite-element models, conventional beam theories, and analytical results. The formulation yields numerically-efficient low-order structural models, and this is illustrated by the nonlinear structural response analysis of a complete flexible aircraft. The integration of the models in high-fidelity aeroelastic analysis is finally exemplified by steady-state results on a very flexible swept wing in transonic flow. |
