摘要
本文主要研究了结构断裂分析的一种新型有限元方法即Williams广义参数单元法。建立了Ⅰ-Ⅱ复合裂纹、Ⅰ型及Ⅱ型裂纹问题的Williams单元的有限元计算格式,编制了相应的FORTRAN90程序,并与本文用奇异元法分析的Ⅰ型、Ⅱ型裂纹问题的解进行了分析对比。
本文的主要研究工作及贡献有:
1、依据线弹性断裂力学及等参元理论,建立了结构断裂分析的奇异单元,编制了FORTRAN90程序,并着重地分析了滑开型(Ⅱ型)及Ⅰ-Ⅱ复合型裂纹问题的应力强度因子。
2、建立了Ⅰ-Ⅱ复合型、Ⅰ型及Ⅱ型裂纹问题的Williams单元的有限元计算格式,编制了相应的FORTRAN90程序,详细地分析了W广义参数单元法中三个重要参数即级数项数m,径向离散数n、径向离散比例因子α对应力强度因子计算精度的影响,并给出了建议值。着重分析了Ⅰ型及Ⅱ型裂纹问题中应力强度因子随着a/w、h/w变化而变化的规律及奇异区尺寸的敏感性问题,提出了Ⅰ、Ⅱ型裂纹问题中应力强度因子解析解关于h/w的修正公式,给出了裂纹尖端最佳奇异区尺寸的范围。理论分析及算例分析表明,在结构断裂问题分析中Williams广义参数单元法是一种高效率、高精度、原理清晰、单元构造简单的很有发展前景的数值方法。
This dissertation mainly has researched one new finite element method in the structural fracture analysis which is called Williams element with generalized DOR The computational format of FEM with Williams element and the corresponding Fortran 90 procedure has been established about theⅠ-Ⅱ-mixed mode, mode I and mode II crack problems .The results calculated by Williams element was analyzed and compared with the singular element studied in the dissertation.
The main research and the contribution of the thesis are as follows:
1. Based on the linear elastic fracture mechanics and isoparametric element theory, singular element on the structural fracture analysis has been established and the homologous Fortran 90 procedure has been compiled. The stress intensity factor (SIF) are analyzed and calculated emphatically about theⅠ-Ⅱ-mixed mode, modeⅡcrack problems.
2. The Williams element with generalized DOF are developed forⅠ-Ⅱ-mixed mode, modeⅠand modeⅡcrack problems, and respective Fortran 90 procedure are organized. The influence of the radial discretizing ratio, radial partition number in singular domain and the number of the terms of the Williams expansions on computing precision of SIF is illustrated, their design values are presented. The relationship between between SIF and the diffirent a/w and varing h/w about mode I and modeⅡcrack problems has analyzed emphatically, respecatively. The sensitive question of the strss intensity factor on the singular area size in the singular domain are proposed, and the scope of the best singular area size around the crack tip are shown. The correctional formula of Originally analytic solution about stress intensity factor for modeⅠand modeⅡcrack problems are presented. The theoretical analysis and the example analysis indicated that the Williams element with generalized DOF is one kind of numerical method with high efficiency, high accuracy, clear principle, simple unit structure, and it is prospective very much in the structural fracture problem analysis.
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