Global-Local Flexural-Torsional Buckling of Composite Laminated Beams

经典的稳定性问题，如整体屈曲（即弯曲屈曲，弯曲-扭转屈曲，侧向屈曲）以及局部屈曲问题，如薄壁各向同性梁的腹板或法兰屈曲，已经被理解，并且可以使用解析或数值方法充分处理。然而，在研究由复合材料制成的剪切变形和各向异性梁的稳定性行为时，存在着大量悬而未决的问题。因此，本研究计划致力于研究考虑同时局部屈曲模式的复合材料层合梁的弯扭屈曲问题，重点是发展高效、准确的封闭形式和半解析方法。局部和全局同时发生的屈曲模式通常被称为相互作用屈曲或全局-局部屈曲，在公开文献中很少得到处理。本研究项目将开发的分析方法旨在纳入复合材料层合板中典型的所有耦合效应，以及横向剪切变形的影响，横向剪切变形对层合结构的屈曲响应有重大影响，因此需要使用高阶剪切变形理论。该研究项目将侧重于开发考虑局部屈曲模式的单轴压缩复合材料层合梁弯扭屈曲评估的封闭形式解析和半解析方法，其中分层建模概念将通过使用几种不同的层合理论（经典层合板理论以及一阶和三阶剪切变形理论）来进行局部屈曲模式。分析方法是基于能量公式结合里兹方法，使用级数展开对所有屈曲自由度进行充分的表示。与有限元计算和参考结果的比较将作为方法的验证。为了突出考虑相互作用屈曲时复合材料层合梁的优化潜力，将采用数学规划方法进行系统优化。

Classical stability problems like global buckling (i.e. flexural buckling, flexural-torsional buckling, lateral buckling) as well as local buckling problems such as web or flange buckling of thin-walled isotropic beams have been understood and can be treated adequately using analytical or numerical methods. A significant number of open questions, however, exist when dealing with the stability behavior of shear deformable and anisotropic beams made of composite laminated materials. The present research proposal is thus devoted to the investigation of the flexural-torsional buckling problem of such composite laminated beams under consideration of simultaneous local buckling modes where the focus is on the development of highly efficient and accurate closed-form and semi-analytical methods. The simultaneous occurrence of local and global buckling modes is often termed as interactive buckling or global-local buckling and has been treated only scarcely in the open literature. The analysis methods that shall be developed in this research project are intended to incorporate all coupling effects as they are typical in composite laminates, as well as the influence of transverse shear deformations that have a significant influence on the buckling response of laminated structures which necessitates the use of higher order shear deformation theories. The research project will focus on the development of closed-form analytical and semi-analytical methods for the assessment of the flexural-torsional buckling of composite laminated beams under uniaxial compression considering local buckling modes wherein a hierarchical modelling concept will be employed by using several different laminate theories (Classical laminated plate theory as well as First-Order and Third-Order Shear Deformation Theory) for the local buckling modes. The analysis methods are based on energy formulations in conjunction with the Ritz method using adequate representations for all buckling degrees of freedom using series expansions. A comparison with finite element computations and reference results will serve as method verification. Systematic optimization routines using the methods of mathematical programming will be employed in order to highlight the optimization potential for composite laminated beams when interactive buckling is considered.