Geometrically nonlinear analysis of composite beams using Wiener-Milenković parameters

Abstract

This paper presents a geometrically nonlinear analysis of composite beams including static, dynamic, and eigenvalue analyses. With the increase in size and flexibility of engineering components such as wind turbine blades, geometric nonlinearity plays an increasingly significant role in structural analysis. The Geometric Exact Beam Theory (GEBT), pioneered by Reissner and extended by Hodges, is adopted as the foundation for this work. Special emphasis is placed on the vectorial parameterization of finite rotation, which is a fundamental aspect in the geometrically nonlinear formulation. This method is introduced based on Euler's rotation theorem and the property of rotation operation: the length preservation of the rotated vector. The GEBT is then implemented with the Wiener-Milenković parameters using a mixed formulation. Several numerical examples are studied based on the derived theory, and the results are compared with analytical solutions and those available in the literature. The analysis of a realistic composite wind turbine blade is provided to show the capability of the present model for generalized composite slender structures. It concludes that the proposed model can be used as a beam tool in a multibody framework whose valid range of rotation is up to 2π.