Actuation of Slender Thin-wall Anisotropic Open Cross-section Beams Based on Asymptotically Correct Vlasov Theory

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 × 5 Vlasov theory augmented by a 5 × 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.