Free-edge effects at circular holes in composite laminated structures

复合材料层合结构中的应力集中问题，如所谓的自由边缘效应，是由自由层合板边缘附近存在的显著的、可能是奇异的层间应力组成的，这往往会导致相应的破坏模式，如边缘分层。虽然相当经典的直板自由板边缘的情况已经进行了近50年的科学研究，但相关的应力集中问题，如复合材料层合板圆孔处的自由边效应，已被处理的深度要小得多。本课题致力于平面复合材料层合结构圆孔附近自由边缘效应的闭合解析和半解析研究。除了相当直接地确定脱层力和力矩外，还应发展几种近似的LayerWise分析方法，这些方法可细分为具有足够的应力形状函数的方法和使用位移场的LayerWise近似的方法。应采用的另一种分析方法是所谓的边界有限元方法(BfeM)，它使用孔表面的2D离散化，而在径向，所有状态变量的半解析公式可以根据变分原理得到。因此，边界元结合了有限元和边界元各自的优点，是一种很有吸引力的分析自由边效应等复杂应力集中问题的方法。最后，利用数学规划的方法将自由边缘效应问题转化为优化问题，以明确当圆形层合孔的自由边缘应力是研究的重点时，可以挖掘哪些优化潜力。

Stress concentration problems in composite laminated structures such as the so-called free-edge effect consist of significant and potentially singular interlaminar stresses in the vicinity of free laminate edges which often leads to according failure modes such as edge delaminations. While the rather classical situation of a straight free laminate edge has been under scientific investigation for nearly 50 years, related stress concentration problems such as the free-edge effect at circular holes in composite laminates have been treated at much lesser depth. This project is devoted to the closed-form analytical and semi-analytical investigation of the free-edge effect in the vicinity of circular holes in plane composite laminated structures. Besides the rather straightforward determination of delamination forces and moments, several approximate layerwise analysis approaches shall be developed which can be subdivided into methods that work with adequate shape functions for the stresses and those that use layerwise approximations of the displacement field. A further analysis method that shall be employed is the so-called Boundary-Finite-Element-Method (BFEM) that uses a 2D discretization of the hole surface while in the radial direction semi-analytical formulations for all state variable can be derived from a variational principle. Consequently, the BFEM incorporates the distinct advantages of the Finite Element Method and the Boundary Element Method and thus is an attractive analysis approach for sophisticated stress concentration problems such as the free-edge effect. Lastly, the free-edge effect problem shall be transformed into an optimization problem by employing the means of the methods mathematical programming in order to clarify which optimization potential can be exploited when free-edge stresses at circular laminate holes are the focus of the investigations.