李顶河：复合材料结构损伤问题的逐层理论研究，清华大学博士学位论文，2014年11月
现有的复合材料加筋层合结构和夹芯结构建模与分析方法主要是基于等效思 想的,随着复合材料结构设计理念和要求的不断提高,需要有一种既可以得到板 壳的精确应力位移结果,又可以在没有任何假设的情况下考虑任意复杂的加强 筋结构和夹芯结构的分析方法。本文结合逐层理论应力分析精度高和三维实体 元建模能力强的优点,建立了复合材料加筋结构和夹芯结构的逐层/实体元方法 (Layerwise/Solid-Element,LW/SE)。对于复合材料加筋结构(夹芯结构),分别利 用逐层理论和八节点实体单元建立复合材料板壳结构(上下面板结构)和加强筋 结构(芯子结构)的控制方程,然后基于板壳结构(上下面板结构)与加强筋结 构(芯子结构)之间的位移协调关系和内力平衡条件得到复合材料加筋层合板壳 结构(夹芯结构)逐层/实体元方法的控制方程。
通过数值算例验证了逐层/实体元方法分析复合材料加筋层合板壳和夹芯结构 的静动力响应问题的正确性,并建立了复合材料夹芯结构的静动力半解析和有限 差分灵敏度分析方法。利用非线性 Hertz 接触律和渐进损伤模型,将逐层/实体元 方法应用于复合材料加筋层合板壳和夹芯结构中低速冲击响应的分析和损伤的预 测问题中,建立了一种渐进损伤分析方法,该分析方法能够得到加筋复合材料层 合板和夹芯结构精确的局部冲击响应和损伤分布。
在复合材料结构的实际损伤问题中,基体裂纹和层间分层损伤往往是同时存 在的,而现有扩展有限元方法对复合材料结构的基体裂纹和分层损伤是分开研究 的,且只能处理穿透型基体裂纹。本文结合逐层理论和扩展有限元方法的优点, 建立了含多层分层和基体裂纹损伤复合材料层合结构的扩展逐层理论 (Extended Layerwise method,XLWM)。将传统逐层理论厚度方向上的插值节点由层间界面 处改为数学层中性面处,并在位移模式中分别引入弱不连续和强不连续函数来模 拟层间界面的应变不连续和分层区域的位移不连续现象。厚度方向上位移插值点 位于层合结构上下表面和各单层的中性面上,所以扩展逐层方法可以很方便地和 扩展有限元方法相结合用来模拟层合结构的面内基体裂纹。
利用各向异性材料的相互作用积分和最大周向应力准则,将扩展逐层理论应 用于复合材料层合结构的裂纹任意扩展问题上,并重点研究了裂纹尖端应力强度 因子在层合板厚度方向上的变化规律。
As the design concept and requirements of composite structures improving, it is nec- essary to develop an analysis method which not only can obtain the accurate displacements and stresses of composite laminated plates/shells and facesheets but also can consider the arbitrarily complex stiffeners and core without any assumptions and simplifications. Based on the high precision of layerwise theory (LW) and modeling ability of the 3D solid finite element method (FEM), a layerwise/solid-element (LW/SE) method is estab- lished for the stiffened composite laminated shells/plates and sandwich structures. In the present LW/SE method, the layerwise theory is used to model the behavior of the com- posite laminated shells/plates or facesheets, and the eight-node solid element is employed to discrete the stiffeners or core. And then, based on the governing equations of the shell- s/plates and stiffeners (facesheets and core), the governing equations of the composite stiffened laminated shells/plates (sandwich structures) is assembled by using the com- patibility conditions and the internal force equilibrium conditions at the joint interface between shells/plates and stiffeners (facesheets and core).
To demonstrate the excellent predictive capability of this LW/SE method, sever- al numerical examples are carried out to investigate the problem of static analysis and free vibration analysis for the stiffened composite laminated shells/plates and sandwich structures. The semi-analytical and finite difference method of the statics and dynamic- s sensitivity analysis are developed for the composite sandwich structures. In addition, based on the modified nonlinear Hertz contact low and the progressive failure model, L- W/SE method is applied to the low-velocity impact responses analysis and impact-induced damages prediction, and a progressive failure analysis method is established for the stiff- ened composite laminated shells/plates and sandwich structures. Accurate local impact responses and damages distribution can be obtained by the presented progressive failure analysis method.
In the practical damage problems of composite structures, the in-plane matrix cracks always exist alongside the delaminations under impact loading. Although the shell el- ements method improved by XFEM are applied to model thick-through cracks or de- laminations individually for the composite laminated structures, there is no work has yet
been reported for the typical damage pattern including matrix crack and delamination. In this work, an extended layerwise method (XLWM) is developed to model the com- posite laminated structures with multiple delaminations and matrix cracks based on the advantages of layerwise method and the extend finite element method (XFEM). In the displacement field, the nodes in the thickness direction are located at the middle surface of each single mathematic layer, the top surface and the bottom surface of the composite laminates. The displacement field contains the linear Lagrange interpolation functions, the one-dimensional weak discontinuous function and strong discontinuous function. The strong and weak discontinuous function are applied to model the displacement discontinu- ity induced by delaminations and the strain discontinuity induced by the interface between the layers, respectively. Because the nodes in the thickness direction are located at the middle surface of each single layer, the extended layerwise method can be conveniently employed to deal with the in-plane matrix cracks combined with the XFEM.
In addition, by using the interaction integral method and the maximum circumfer- ential tensile criterion of orthotropic materials, XLWM is applied to the prediction of the crack arbitrarily growth for the composite laminated plates. The distribution of the stress intensity factor (SIF) along the thickness direction are investigated.