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，是由自由层合边缘附近的显著的和潜在的单一层间应力组成的，这往往导致边缘分层等不同的破坏模式。虽然在近50年的科学研究中，人们已经研究了相当经典的直自由层合板边缘的情况，但相关的应力集中问题，如复合材料层合板中圆孔的自由边缘效应，在较浅的深度上得到了处理。本项目致力于平面复合材料层合结构中圆孔附近自由边缘效应的封闭解析和半解析研究。除了相当直接地确定分层力和力矩外，还应开发几种近似的分层分析方法，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分层近似的方法。应采用的进一步分析方法是所谓的边界有限元法（BFEM），该方法使用孔表面的二维离散化，而在径向上，所有状态变量的半解析公式可以由变分原理导出。因此，BFEM结合了有限元法和边界元法的明显优点，因此是一种有吸引力的分析方法，用于复杂的应力集中问题，如自由边效应。最后，利用该方法的数学规划方法，将自由边效应问题转化为优化问题，明确以圆形层合孔的自由边应力为研究重点时，可以利用哪些优化潜力。

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.