Cross-section optimal design of composite laminated thin-walled beams

This paper aims to perform optimal design of cross-section properties of thin-walled laminated composite beams. 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 constituting the cross-section. The finite element method is used in discretizing the theory. For design sensitivity calculations, the cross-section is modelled throughout design elements. Geometrically, these elements may coincide with the laminates that constitute the cross-section. The developed formulation is based on the concept of adjoint structure. After a warping function is calculated for the cross-section, an adjoint problem may be formulated for each of the properties and a corresponding adjoint warping is determined. It can be applied in a unified way to open, closed or hybrid cross-sections. Design optimization is performed by nonlinear programming techniques. Laminate thickness and lamina orientations are considered as design variables.