Joint Elastic and Piezoelectric Tailoring of Composite Box Beams: Constructive Force Participation and Limits of Pure Twist

Joint elastic and piezoelectric tailoring can recruit non-torsional actuator resultants to assist twist, but this assistance restricts deformation purity. For symmetric positive-definite stiffness, the classical three-vector Gram inequality yields a sharp participation–purity bound: when no generalized force opposes twist, energy-metric purity cannot exceed the ratio of relaxed to blocked torsional stiffness. A closed torque-share threshold quantifies cancellation above this ceiling on the positive-torque branch. Extension–bending and shear–torsion block contributions are invariant under the stated physical reference changes, separating elastic-coupling assistance from shear-center relabeling. Exact conic and linear-programming voltage allocations remove voltage-pattern bias from structural comparisons. In a piezocomposite-box benchmark, the best attained uniform-wall joint gain is 10.53% at 20% axial/flexural floors and a retained torsional-stiffness floor, while a fixed representative’s purity frontier follows the predicted cancellation threshold. At fixed material volume, host redistribution and host-angle tailoring dominate the additional gain; tested constructive and near-symmetric candidates give framed-shell gains of 26.75–31.45%, with a 1.83% section-model increment from actuator-angle freedom beyond the thickness/host result at the selected ratio. Laminate-shell and published passive sectional-matrix comparisons delimit the applicability of the sectional predictions.