Analysis of active closed cross-section slender beams based on asymptotically correct thin-wall beam theory

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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