Global-Local Flexural-Torsional Buckling of Composite Laminated Beams

各向同性薄壁梁的整体屈曲(即弯曲屈曲、弯扭屈曲、侧向屈曲)等经典稳定性问题以及腹板或翼缘屈曲等局部屈曲问题已被人们所熟知，并可用解析或数值方法进行充分处理。然而，在处理由复合材料层合材料制成的剪切变形和各向异性梁的稳定行为时，存在着相当多的未决问题。因此，本研究方案致力于研究同时考虑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、精确的闭合形式和半解析方法。局部屈曲和整体屈曲同时发生的现象通常被称为交互屈曲或全局-局部屈曲，在公开文献中很少涉及。在本研究项目中应发展的分析方法旨在考虑复合材料层合板中常见的所有耦合效应，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具有显著影响，这就需要使用高阶剪切变形理论。该研究项目将致力于发展考虑局部屈曲模式的复合材料层合梁在单轴压缩下弯扭屈曲的闭合解析和半解析方法，其中局部屈曲模式将采用层合板理论(经典层合板理论以及一阶和三阶剪切变形理论)的分层建模概念。分析方法基于能量公式，结合里兹法，使用级数展开法对所有屈曲自由度进行适当的表示。与有限元计算和参考结果的比较将作为方法的验证。为了突出复合材料层合梁在考虑相互屈曲时的优化潜力，将采用数学规划方法的系统优化程序。

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.