Within recent years, Crack analysis in adhesive layers has become a topic of interest for many researchers. A common model which is used incorporates a 3-region elasticity problem consisting of only 2 materials, the adhesive layer bounded by 2 layers of a stiffer elastic substrate. Cracks have been experimentally observed to propagate in straight paths as well as wavy paths within the adhesive layer and even at its boundaries. A theoretical model based on work done by Fleck, Hutchinson, and Suo (1991) is used to study crack path selection. Complex stress potential functions are employed to develop a symbolic derivation. The method of distributed dislocations is utilized to represent the crack. A series of Chebyshev polynomials to approximate the unknown dislocations. The resulting integral equations are solved through the collocation method and the series coefficients are recovered. Several numerical packages, Mathcad 5.0+ and Mathematica 2.2.1, were used to study the computational aspects of the problem. The focus of the research was to develop efficient modular software packages to be run on a standard PC system. Several numerical techniques were utilized to reduce computational time and control the numerical accuracy of the problem. Some of these techniques included a "numerical freeze" algorithm, Fast Fourier Transform techniques, Gaussian inversion, Gaussian quadrature and Romberg quadrature. The numerically sensitive regions were identified. Finally, recommendations for future work and possible solutions to handle the numerically sensitive regions were presented. / Master of Science

In this thesis, we have developed a Subtructured Finite Element / eXtended Finite Element (S-FE/XFE) method. The S-FE/XFE method consists in decomposing the geometry into safe FE-domains and cracked XFE-domains, and solving the interface problem with the Finite Element Tearing and Interconnecting method (FETI).This method allows for handling complex crack configurations in 3D structures with common commercial FE software that do not feature the XFEM. The method is also extended to a mixed dimensional formulation, where the FE-domain is discretised with shell elements while the XFE-domain is modelled with three-dimensional solid elements. This is the so-called S-FE Shell/XFE 3D method. The mixed dimensional formulation is more convenient than a full XFE-3D formulation because it significantly reduces the computational cost and it is more accurate compared to a full shell model because it includes three-dimensional local features such as three-dimensional crack. The compatibility of the displacements through the interface is ensured using the Reissner-Mindlin equation. The method has been extensively validated towards both academic problems and semi-industrial benchmarks in order to demonstrate the benefits of this approach. Among them, the S-FE/XFE method is applied to a crack analysis in a section of a compressor drum of a turbofan engine. The results obtained with the S-FE/XFE method are compared with those obtained with a standard FE computation. Furthermore, two applications of the S-FE shell/XFE 3D approach are proposed. First the load carrying capacity of a section of stiffened panel containing a through-the-thickness crack is investigated (this is the one-bay crack configuration). Second, the ability of the method for handling small surface cracks in large finite element models is addressed by looking at a generic 'large pressure panel' presenting realistic crack configurations.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第15580号 / 工博第3292号 / 新制||工||1497(附属図書館) / 28101 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 杉浦 邦征, 教授 田村 武, 准教授 宇都宮 智昭 / 学位規則第4条第1項該当