【作者】 李冉；

【导师】 杨绿峰；

【作者基本信息】 广西大学 ， 结构工程， 2004， 硕士

【摘要】 本文依据有限元理论和线弹性断裂力学理论等，建立了关于断裂力学的广义参数有限元的计算理论和方法，并利用该方法对一些算例进行了相应的数值试验。 本文的主要工作有： 1．根据等参元理论并利用F90语言编制有限元计算程序，并应用于断裂分析的等参奇异元中。 2．利用1／4边节点法，推导了结构断裂分析的等参数奇异单元，并编制了F90程序。算例表明，这类单元具有较好的计算精度，能正确反映裂纹尖端应力场的奇异性。 3．建立了结构断裂分析的广义参数有限元法的计算模型，推导了奇异域单元和过渡元的刚度方程，利用F90语言编制相应的计算程序，进行大量的数值计算，并和等参奇异元理论的计算结果进行了比较和相互验证。证明了广义参数有限元在断裂问题应用上的优越性。理论分析表明，广义参数有限元法利用整体场和局部单元场相协调的理论导出广义参数位移场，经过单元分析建立奇异区条单元和过渡单元的控制方程，不仅可以避免复杂的单元刚度矩阵转换计算，以及由此带来的过大计算量，同时解决了单元间的位移协调问题。更多还原

【Abstract】 This dissertation establishes the finite elements with generalized degrees of freedom in fracture mechanics on the basis of finite elements theory and linear elastic fracture mechanics theory. It also gives relevant numerical tests to demonstrate the accuracy and efficiency of this method.The main contributions of the thesis are as follows:1. Based on isoparametric element theory and Fortran 90, the finite elements program for normal plane problem is composed;2. Based on the isoparametric singular element theory a quarter singular element is developed, the finite elements program for fracture analysis of structures is put forward using Fortran 90. Examples show that this element is accurate, and reflects the singular property of the stress field around the crack tip.3. The finite elements with generalized degrees of freedom developed for fracture analysis of structures. The singular strip element and transition element are constructed based on the theory of globed field assorting with local field. A large quantity ofnumerical calculating is undertaken. The results of them are compared with those resulted from isoparametric singular element theory, thus the advantage of the finite elements with generalized degrees of freedom is demenstrated in fracture analysis of structures.更多还原