【作者】 秦飞；

【导师】 杜庆华； 岑章志；

【作者基本信息】 清华大学 ， 固体力学， 1996， 博士

【摘要】 本文采用边界元数值计算和自洽理论相结合的方法研究多裂纹体(主要研究岩石、混凝土类材料)在受压情况下的力学行为。通过数值模拟裂纹扩展过程和对裂纹体即时等效弹性模量的计算,研究了裂纹体的强度劣化过程,揭示了裂纹扩展与裂纹体整体响应之间的对应关系。 在现有文献调研基础上,对研究多裂纹体的主要方法进行介绍和比较,并讨论了各研究方法的优点以及局限性;简要介绍了边界元方法在处理裂纹问题时的优势,回顾了前人的主要工作。并将含裂纹岩石类材料在受压载荷下的宏观及细观行为特点进行归纳,并建立分析模型。 建立了单裂纹扩展分析的边界元方法,通过引入适用于岩石、混凝土材料的粘性力裂纹模型,给出了以裂纹扩展步长作为控制变量的增量迭代算法。 讨论了计算等效材料常数的自洽方法,给出了计算等效材料常数的一般公式。 建立了有序多裂纹体问题的边界元求解方法;推导并给出了非对称各向异性材料的基本解;论述了处理角点问题的各种方法并给出了不连续单元的单元模式;建立了相应的增量迭代算法;给出一些数值算例。更多还原

【Abstract】 In this thesis, rock-like cracked materials were studied by boundary element method(BEM) with self-consistent schemes. The behavior of rock with orderly distributed cracks has been investigated. The propagating process of crack was simulated by marching the crack tip step by step.By means of computation of the instant equivalent elastic modulus with a self-consistent schemes and sub-domain BEM, the overall response of cracked body was analyzed by analyzing the propagation of one main crack.In the first place, some research methods such as Continuum Damage Mechanics, self-consistent scheme and other approaches had been examined. The previous works of other researchers have been reviewed.Secondly,the cracked body with single crack was investigated by sub-domain BEM. The cohesive crack model was introduced to the analysis of rock-like materials. An incremental iteration algorithm which has marching crack tip as the increment control variable had been established.Thirdly, the self-consistent schemes to determine the equivalent elastic modulus were discussed. The general formulations for the computation of equivalent elastic modulus were given.Finally, sub-domain BEM for analyzing cracked body had been investigated. The existence of friction sliding between crack surfaces leads to the non-symmetric and anisotropical equivalent elastic matrix, thus the relevant fundamentalsolutions should be found. Discontinuous boundary elements were used at the corners of sub-domains. An increment algorithm with three layer iterations was given. Some numerical examples were studied. The results seem to be satisfactory as comparing with the experimental data.更多还原