【作者】 杜娟；

【导师】 严波；

【作者基本信息】 重庆大学 ， 固体力学， 2005， 硕士

【摘要】 近来,随着对航空飞行器安全的要求越来越高,航空飞行器结构的裂纹等缺陷的修补问题显得越来越重要。在解决此类带裂纹结构的修补方法中,用纤维增强复合材料胶接修补的方法已得到广泛重视和研究,具有广阔的应用前景。裂纹板的疲劳寿命或服役寿命是由修补后裂纹板的疲劳裂纹扩展行为决定,因此,对裂纹板用复合材料修补后疲劳裂纹扩展行为的评估具有重要的设计指导意义和应用价值。本文在已有的有限元-边界元耦合分域算法的基础上,提出了一种改进的有限元-边界元耦合分域算法。改进后的方法放弃了原方法中要求各子域界面上有限单元和边界单元结点位置协调一致的条件,特别适用于模拟裂纹扩展问题。由于有限元方法适合于分析复合材料问题,而边界元方法更适合于模拟裂纹扩展问题,该算法将所分析问题的区域分解成两个分别由有限元和边界元离散的子域,并分别建立两子域的平衡方程。由于有限元平衡方程涉及结点位移和等效结点力,而边界元方程则是由结点位移和结点面力描述的,根据虚功原理,在界面上的任意有限单元的等效结点力所作的虚功等于处于界面上的单元面内的面力所作的虚功,从而建立起有限元的等效结点力和边界元的结点面力之间的关系。在满足两子域界面上位移和面力协调连续的条件下,通过迭代得到问题的解。在迭代求解过程中,引入动态松弛系数,使收敛得以加速。编制了本文提出的有限元-边界元耦合分域算法的计算程序,并利用该程序分析了三个算例,算例结果与用有限元法、边界元法和现有的耦合分域算法的数值计算结果一致,验证了本文算法的正确性和可行性。最后利用本文提出的算法分析了金属裂纹板复合材料单侧修补问题,并得到裂纹应力强度因子沿裂纹前沿的分布规律。由于该算法不要求各子域界面上有限单元和边界单元结点位置协调一致,在模拟金属裂纹板修补后裂纹的扩展过程中,无需在每一增量步中修正有限单元网格,重新计算单元刚度矩阵,因而具有独特的优势。更多还原

【Abstract】 Repairs of cracked components in aerospace structures are becoming more and moreimportant due to the requirement of operation safety. The repair methods based onadhesively bonded composite patches have been demonstrated to be very promising tothese cracked structures. Fatigue crack growth behavior of cracked panels after beingrepaired decides the extension of fatigue life or service life of the repaired structures.Therefore, the evaluation of fatigue crack growth behavior of cracked panels repairedwith a FRP composite patch becomes a focus in this research area.An improved algorithm coupling finite element-boundary element based on aniterative method is presented in this paper. An advantage of the algorithm proposed isthat the positions of the nodes on the interface of the two sub-domains can beinconsistent. It will be more efficient in some situations such as the simulation of crackpropagation. Based on the facts that the boundary element method (BEM) is moreaccurate to determine stress intensity factors and the FEM is more powerful to analyzeFRP composite laminates, this algorithm essentially involves subdivision of theanalyzed domain into sub-regions being independently modeled by the two methods.The original problem is restored with continuity and equilibrium conditions beingsatisfied on the interface of the two sub-regions. It is noted that the governing equationof the FE sub-domain involves nodal displacements and forces, and the primaryunknowns in the BE sub-domain are nodal displacements and tractions. The basic ideahere is to use the virtual work principle to set up this relation between the nodaltractions and nodal forces. To speed up the convergence rate of the iterative algorithm, adynamically changing relaxation parameter during iteration is introduced.This decomposition algorithm with finite element-boundary element (FE-BE)coupling is programmed. The validity of the proposed algorithm is demonstrated by theconsistence of the results of two numerical examples obtained by the proposed methodand those by the FEM, the BEM and another FE-BE coupling method. Finally, acracked aluminum panel repaired with a composite repairing patch is analyzed by theproposed algorithm, and the distribution of stress intensity factor (SIF) along crack frontis obtained. Because the position of the nodes on the interface of the FE and BEsub-domains can be completely independent, there is no need to modify the FE meshand the stiffness matrix of FE sub-domain in each increment step during the simulationof crack propagation of cracked panel.更多还原