Design Sensitivity Analysis of Composite Thin-walled Profiles including Torsion and Shear Warping

The present work deals with the design sensitivity analysis of thin-walled laminated composite beam cross-section bending-torsion properties. These properties are expressed as integrals based on the cross-section geometry, on the warping functions for torsion, shear bending and shear warping, and on the individual stiffness of the laminates that constitute the cross-section. Among these properties, we may emphasize the location of the shear center, the torsion stiffness, the warping stiffness and the shear coefficients. A variational continuum formulation for the design sensitivity analysis of crosssection bending-torsion properties is presented. The formulation is based on the concept of adjoint system, which suffers a specific adjoint warping for each of the properties. The developed formulation can be applied in a unified way to open, closed or hybrid cross-sections, with simply connected or multi-connected domains. The lamina orientation and the laminate thickness are selected as the de-sign variables. For the sensitivity calculations, the cross-section may be modeled throughout design elements to which the element sensitivity equations correspond. Geometrically, the de-sign elements may coincide, with the laminates that constitute the cross-section.