Geometrically Nonlinear Theory of Composite Beams with Deformable Cross Sections

Aone-dimensional theory of slender structures with heterogeneous anisotropic material distribution is presented. It expands Cosserat’s description of beam kinematics by allowing deformation of the beam cross sections. For that purpose, a Ritz approximation is introduced on the cross-sectional displacement field, which defines additional elastic degrees of freedom (finite-sectionmodes) in the one-dimensionalmodel. This results in an extended set of beam dynamic equations that includes direct measures of both the large global displacement and rotations of a reference line, and the small local deformations of the cross sections. Two situations are studied in which this approach provides a simpler alternative to shell models with comparable fidelity. First, we look at the detailed structural response of composite beams with distributed loads. In particular, the case of a composite box beamwith embedded piezoelectric actuators is considered. Second, this methodology is applied to study the low-frequency response characterization of composite beams. Numerical results in both cases show that a reduced set of finite-section modes allows a full description of the actual three-dimensional displacement field using a strictly one-dimensional formulation.