RUI: A New Method to Obtain Highly Accurate Three Dimensional Analysis of Crack Propagation and Stress on Composite Materials

哦，研究人员开发了解决三维裂纹扩展问题的数值方法。为了得到裂纹扩展的实际解，有限元方法需要使用梯度离散(裂纹前沿附近的小单元，其他地方的大单元)或特殊的奇异基函数。梯度离散化使得计算非常昂贵，而奇异基函数破坏了有限元良好的带状结构。因此，标准的有限元方法对于三维裂纹扩展的精确数值模拟是不现实的。有限元解的精度取决于真解的正则性。研究了一种新的处理三维奇点：顶点、边和边-顶点的方法，称为辅助映射法(MAM)。为了消除有限元在存在奇异性时的失效，MAM将应力函数奇异的区域变换为变换后的应力函数具有较高正则性的区域。为了达到这些目的，研究者还研究了三个辅助映射。据估计，美国每年因骨折造成的损失(不包括人员伤亡)超过100亿美元。金属疲劳被认为是最近几起空难的可能原因，老化机队的适航性是一个全国性的问题。材料失效是其他大型工程结构(船舶、桥梁、核电站、水电站等)的主要问题。因此，为了有效的检查和预防性维护计划，需要进行准确的断裂分析。然而，由于断裂力学的复杂几何和非线性特征，分析技术的使用非常有限，在大多数情况下是不实用的。对于这种分析，数值方法似乎是唯一可行的方法。在平面弹性问题应力分析非常成功的基础上，研究了一种能产生高精度三维断裂分析数值模拟的新方法。

Oh The investigator develops numerical methods for solving three-dimensional crack propagation problems. In order to obtain any practical solutions for crack propagation, the Finite Element Method (FEM) requires use of either graded discretizations (very small elements near the crack front, larger elements elsewhere) or special singular basis functions. The graded discretizations make the computation very expensive, while singular basis functions destroy the nice band structure of the FEM. Thus, the standard FEM is impractical for accurate numerical simulation of 3-D crack propagation. The accuracy of the FE solution depends on the regularity of the true solution. The investigator studies a new method, called Method of Auxiliary Mapping (MAM), to deal with three-dimensional singularities: vertex, edge, and edge-vertex. To remove the ineffectiveness of the FEM in the presence of singularities, MAM transforms a region where the stress functions are singular to a region where the transformed stress functions are of higher regularity. The investigator also studies three auxiliary mappings for these purposes. The annual cost of fracture-related damage in the United States (human injury and loss of life aside) has been estimated at more than $10 billion. Metal fatigue has been cited as the probable cause of several recent airline accidents, and the airworthiness of aging fleets is a national concern. Material failures are a major concern for other large engineering structures (ships, bridges, nuclear power plants, hydroelectric dams, and so on). Thus, for effective inspection and preventive maintenance programs, an accurate fracture analysis is demanded. However, because of the complicated geometry and nonlinearities that characterize fracture mechanics, the use of analytical techniques is very limited and in most cases not practical. Numerical methods seem to be the only feasible approach for such analysis. On the basis of very successful results o f the stress analysis for plane elasticity problems, the investigator studies a new method that should yield highly accurate numerical simulation of three-dimensional fracture analysis.