Local buckling of shear-deformable composite laminated beams with flanges and webs made of unsymmetrically layered laminates

在过去的几十年里，薄板或壳形式的复合材料结构在工程科学的许多不同分支中的应用越来越多，例如在航空航天或汽车工程中，但也在土木工程应用中。由于其优异的比强度和刚度特性，复合材料层合板或壳体在轻量化工程应用中占有重要地位。通常，复合材料层压板是由各向异性和单向纤维增强层（例如，塑料基体中的碳纤维或玻璃纤维）组成的层状板或壳。在土木工程应用中，最基本的结构元件是承受轴向和弯曲载荷的棱柱梁。由于它们的细长和整体薄壁性质，需要考虑整体屈曲（即弯曲屈曲、弯扭屈曲和侧向屈曲）以及局部屈曲等稳定性问题。本文研究的是局部屈曲问题，即复合材料薄壁层合梁翼缘和腹板的局部屈曲。为此，应使用离散板模型，其中考虑到相邻梁段相交位置处的弹性夹紧，将腹板和翼缘视为独立板。除了纯粹的封闭形式的解析解，使用适当的形状函数的所有相关的屈曲自由度的瑞利商，级数展开结合里兹方法将使分析和调查的局部屈曲行为的复合材料层合梁考虑横向剪切变形和典型的耦合效应，因为它们发生在复合材料层合板。具体而言，应明确考虑非对称层压板的弯曲-延伸耦合以及非正交各向异性层压板铺层的弯曲-扭转耦合。直到今天，还没有任何调查可以系统地处理这些影响，因此需要进行大量的研究。一旦适当的局部屈曲分析方法得到发展，屈曲问题将转化为一个优化问题。通过数学规划和非线性优化，梁的设计将被确定，表现出最高的可能的屈曲阻力，这是一个重要的因素，任何实际应用中，复合材料层压梁的使用。最后，通过系统的屈曲试验，验证了本文所提出的分析方法和主要屈曲特征。

Composite structures in the form of thin laminated plates or shells have found an increasing use in many different branches of engineering science, e.g. in aerospace or automotive engineering, but also in civil engineering applications over the last few decades. Due to their excellent specific strength and stiffness properties, composite laminates or shells are prominently found in lightweight engineering applications. Generally, composite laminates are layered plates or shells consisting of anisotropic and unidirectionally fiber-reinforced layers, e.g. carbon or glass fibers in a plastic matrix.In civil engineering applications, the most basic structural elements are prismatic beams under axial and bending load. Due to their slenderness and their overall thin-walled nature, stability problems such as global buckling (i.e. flexural buckling, flexural-torsional buckling and lateral buckling) as well as local buckling need to be taken into account. The current research project is devoted to the investigation of local buckling problems, i.e. the local buckling of flanges and webs of thin-walled composite laminated beams. For this purpose, discrete plate models shall be used in which webs and flanges are considered as being separate plates considering elastic clampings at those locations where adjacent beam segments intersect. Besides purely closed-form analytical solutions using the Rayleigh quotient employing adequate shape functions for all relevant buckling degrees of freedom, series expansions in conjunction with the Ritz method will enable the analysis and investigation of the local buckling behavior of composite laminated beams under consideration of transverse shear deformations and typical coupling effects as they occur in composite laminates. Specifically, bending-extension coupling in the case of unsymmetric laminates as well as bending-twisting coupling in the case of non-orthotropic laminate layups shall be taken into account explicitly. To this day, no investigations are available that would treat these effects in a systematic manner so that a significant requirement for research exists. Once adequate methods for the local buckling analysis have been developed, the buckling problem will be transformed into an optimization problem. By means of mathematical programming and nonlinear optimization, beam designs will be determined which exhibit the highest possible buckling resistance which is an important factor for any practical application where composite laminated beams are employed. Lastly, all developed analysis methods and the main buckling characteristics will be validated by sys-tematic buckling experiments.