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An asymptotically correct analysis of passive anisotropic thin-walled open cross-section beam-like structures using the variational asymptotic method (VAM) is extended to include embedded macro fiber composites. Application of the VAM to beam-like structures splits the problem into non-linear 1D theory along the selected beam reference line and linear 2D generalized 5 Â 5 Vlasov theory augmented by a 5 Â 1 actuation vector over the cross-section. The linear 2D cross-sectional theory is validated against the University of Michigan/variational beam sectional analysis 2D finite element software. The validation examples selected were based on practical cross-sectional geometry and material anisotropy under DC actuation voltage. Actuation-induced deformations predicted at the beam reference line are obtained using an intrinsic geometrically exact beam theory for open cross-sections. The predicted generalized deformations are compared with those obtained using the 3D finite element analysis software ANSYS Multiphysics, which further validates the extended theory. The analytical theory is shown to be straightforward to implement and efficient, yet sufficiently reliable to perform interdisciplinary studies and optimization of various engineering applications of such structures.

An asymptotically correct theory for multi-cell thin-wall anisotropic slender beams that includes the shell bending strain measures is extended to include embedded active fibre composites (AFCs). A closed-form solution of the asymptotically correct cross-sectional actuation force and moments is obtained. Active thin-wall beam theories found in the literature neglect the shell bending strains, which lead to incorrect predictions for certain cross-sections, while the theory presented is shown to overcome this shortcoming. The theory is implemented and verified against single-cell examples that were solved using the University of Michigan/Variational Beam Sectional Analysis (UM/VABS) software. The stiffness constants and the actuation vector are obtained for two-cell and three-cell active cross-sections. The theory is argued to be reliable for efficient initial design analysis and interdisciplinary parametric or optimization studies of thin-wall closed cross-section slender beams with no initial twist or obliqueness.

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