含缺陷的超薄多涂层结构应力场的奇异边界法研究

More and more surface coatings have been designed and utilized in the modern mechanical industry and national defense technology due to its outstanding properties of high temperature, wear and corrosion resistances. However, accurate numerical analysis of thin-layered coating systems presents a great challenge to researchers in computational mechanics, because most of the coatings are made in the forms of ultra-thin films with the thickness in the orders of micro- or nano-scales. The traditional numerical techniques for such problems encounter several bottleneck issues, such as the tedious mesh generation for complicated domain problems, expensive numerical computation, difficult numerical integrations of singular and nearly singular integrals, and computational instability of ill-conditioned dense matrix. Based on applicant’s research backgrounds in recent five years, this proposal makes the first attempt to apply the semi-analytical singular boundary method (SBM), a recent strong-form meshless boundary collocation method, for the stress analysis of ultra-thin and multilayered coating systems containing coating defects. This proposal will further circumvent critical problems associated with the traditional SBM for multilayered coating systems, such as how to accurately calculate the nearly singular fundamental solutions. In addition, we will introduce the fast multipole method (FMM) for the fast solution of dense matrix equations and achieve the solution of large-scale problems with several million degrees of freedom on a desktop computer. The overall purpose of this proposal is to develop a fast multipole SBM for the stress analysis of ultra-thin and multilayered coating systems containing coating defects, and provide an alternative numerical technique for structural optimization design of coating materials.

表面涂层材料以优异的耐高温、耐磨损、耐腐蚀性能，在现代机械加工和国防尖端技术领域得到了广泛的应用。涂层材料的厚度一般在微米甚至纳米级，特殊的几何构造导致传统方法在数值模拟此类问题时常遇到复杂域网格剖分困难、计算量大、奇异与近奇异积分计算和病态稠密矩阵计算不稳定等瓶颈问题。基于申请者近五年的研究工作，本项目拟发展无网格、无数值积分、仅需边界配点的半解析奇异边界法，数值模拟含缺陷(孔洞、夹杂等)超薄多涂层结构的应力分布，重点解决奇异边界法模拟此类问题时涉及到的基本解近奇异性等关键技术难题。此外，结合快速多极算法，发展奇异边界法稠密矩阵方程的快速求解技术，实现快速有效地模拟上百万自由度的大规模多涂层结构问题。目标是发展能够有效模拟含缺陷的超薄多涂层结构应力场的快速多极奇异边界法，为涂层材料的优化设计提供一种新的数值计算方法。

表面涂层材料以优异的耐高温、耐磨损、耐腐蚀性能，在现代机械加工和国防尖端技术领域得到了广泛的应用。涂层材料的厚度一般在微米甚至纳米级，特殊的几何构造导致传统方法在数值模拟此类问题时常遇到复杂域网格剖分困难、计算量大、奇异与近奇异积分计算和病态稠密矩阵计算不稳定等瓶颈问题。本项目拟基于无网格、无数值积分、仅需边界配点的半解析奇异边界法，数值模拟含缺陷(孔洞、夹渣等)超薄多涂层结构的应力场分布，重点解决奇异边界法模拟此类问题时涉及到的基本解近奇异性等关键技术难题。此外，结合快速多极算法，发展奇异边界法稠密矩阵方程的快速求解技术，实现快速有效地模拟上百万自由度的大规模多涂层结构问题。目标是发展能够有效模拟含缺陷的超薄多涂层结构应力场的快速多极奇异边界法，为涂层材料的优化设计提供一种新的数值计算方法。