【作者】 王承强；

【导师】 钟万勰；

【作者基本信息】 大连理工大学 ， 固体力学， 2003， 博士

【摘要】 断裂力学是50年代开始蓬勃发展起来的固体力学新分支，有微观断裂力学与宏观断裂力学之分。一方面，需要深入到微观领域弄清微观的断裂机理，才能深入了解宏观断裂的现象。另一方面，宏观断裂力学仍然没有发展完善，尤其是在工程实际中的应用还远未成熟，即使平面弹塑性断裂力学也依然有许多亟待解决的问题。应力强度因子准则和COD准则分别是线弹性断裂力学和弹塑性断裂力学中非常重要的断裂准则，确定应力强度因子的方法和COD的计算仍是人们继续关心的问题。 随着计算机的发展，计算机技术、计算数学和力学交叉而产生了一个新的学科分支，这就是计算力学。如今计算和试验及理论分析已经成为力学工作者解决工程和科学中的力学问题的三大支柱。计算力学与断裂力学学科相互交叉、相互渗透便产生了断裂力学新分支计算断裂力学。本博士学位论文内容就属于这一范畴，针对平面弹塑性断裂的一系列问题，提出了一类新的解析与有限元结合解法--半解析有限元法。应用弹性力学哈密顿体系理论，在裂纹尖端构造出满足不同裂纹表面边界条件的一类裂纹奇异解析元，该类超级单元能够准确描述不同简化模型下的裂纹尖端场。将该类超级单元与普通有限单元相结合便构成半解析的有限元法，可较为方便地计算弹塑性裂纹尖端场。该方法兼顾了解析法和有限元法的优点，既能够满足精度要求又简单灵活。本论文的主要研究工作如下： 1．从弹性力学哈密顿体系理论出发，利用平面弹性力学极坐标系下的本征向量展开求解，推导了环形圆形域裂纹边作用有均布压力、线性压力和均布剪切力情况下的特解，从而得到了裂纹表面作用有以上三种荷载情况下的裂纹尖端场的解析解，为进一步构造进行弹塑性裂纹分析的奇异解析元奠定了理论基础。 2．在哈密顿体系下，将平面扇形域的本征向量展开求解与变分原理相结合，构造了一类裂纹弹性解析元，建立了解析元的出口刚度阵。该类解析元可与普通有限单元相结合，形成半解析的有限元法。应用该半解析有限元法可计算Ⅰ型、Ⅱ型以及Ⅰ+Ⅱ混合型裂纹的应力强度因子。文中作了大量的裂纹应力强度因子计算，与边界配置法、传统有限元法以及解析法进行了系统的比较，结果表明该方法用于应力强度因子计算不但精度较高，而且简便易行，便于工程实际应用。文中还进行了不同解析元出口节点数时应力强度因子的计算，结果表明本文方法有很好的收敛性。 3。将上面的半解析有限元法应用于弹塑性断裂力学中的Dugdale模型，分别构造了基于Ⅰ型和Ⅱ型Dugdale模型的裂纹解析元，并建立了解析单元的出口刚度阵和荷载向量的列式。该类超级单元能够准确地描述基于Dugdale模型的裂纹尖端场，可与普通有限单元相结合，构成半解析有限元法。应用该方法通过增量迭代计算，能够得到工程应用中所关心的裂纹塑性区尺寸和裂纹尖端张开或滑开位移。数值计算结果表明本文半解析有限元法具有较好的精度和收敛性.值得一提的是，对n型Dugdale模型的数值计算在以往的研究中还没有见到。 4.将这一套新的半解析有限元法应用到混凝土断裂力学，来解决基于双线性粘聚力模型的混凝土裂缝扩展问题。实现了统一框架下模拟混凝土裂缝起裂、稳定扩展、不稳定扩展直至断裂破坏的不同裂缝扩展阶段，追踪了混凝土断裂的全过程。不但具有较高的精度，而且避免了应用普通有限元分析该类问题时自适应网格划分必须额外考虑双线性粘聚力分布所带来的困难。将本文的半解析有限元法应用于双K断裂参数的计算，简单易行，计算双K断裂参数的同时可以得到裂缝尖端张开位移和虚拟裂缝长度等参量，无需分开计算。本文方法同样适用于其它混凝土断裂模型的断裂参数的计算。更多还原

【Abstract】 Fracture mechanics is a new branch of solid mechanics, which has developed since 50th. It can be classified as micro-fracture mechanics and macro-facture mechanics. On one hand, it’s necessary to make clear the microcosmic mechanism of fracture. On the other hand, macro-fracture mechanics has not developed perfectly and needs to be studied continuatively, especially the application in the practical engineering. Even the plane elastic-plastic fracture mechanics has many unsolved problems. The stress intensity factor (SIF) criterion and crack opening displacement (COD) criterion are very important fracture criterions in the linear elastic fracture mechanics (LEFM) and the elastic-plastic fracture mechanics respectively. The method of determining the stress intensity factors and COD computations are problems still concerned by researchers.With the development of computer, computer technology, computational mathematics and mechanics intercross each other and give birth to a new branch of academic study, that is the computational mechanics. Now computation, experiment and theoretical analysis become the three main supports for mechanics researchers to solve problems in engineering and science. Computational mechanics and fracture mechanics intercross and give birth to a new branch of fracture mechanics-the computational fracture mechanics. The contents of the doctoral dissertation belong to the category. A kind of new combination of analytical and finite element methods-semi-analytical finite element method is presented for a series of problems in the plane elastic-plastic fracture mechanics. Employed the Hamiltonian system theories of elastic mechanics, a series of crack singular analytical elements satisfying different boundary conditions along crack surfaces in the vicinity of crack tip are constructed. These hyper-elements can describe the crack tip fields accurately for different simplified fracture models. Implemented the hyper-elements into ordinate finite element system, a kind of semi-analytical finite element method is then constructed. Using the method, we can evaluate the elastic-plastic field of crack tip easily. This method has both advantages of analytical method and finite element method. It is accurate, simple and efficient. The main research work of the thesis covers the following aspects:1. Special solutions for the ring circular domain with crack surfaces acted on uniform compressive force, linear compressive force and linear shearing force are deduced in polar coordinate employed the eigenfunction expansion technique in the Hamiltonian system of elastic mechanics. Combined with the general solution for the above problems, the analytical solutions for crack tip fields with surfaces acted on the above three kinds of loads are obtained. These solutions offer theoretical basis to construct analytical elements for plastic analysis of crack.2. A kind of crack elastic analytical elements is constructed employed the eigenfunction expansion solutions and variational principle in the Hamiltonian system theory. The formulations for the stiffness matrices of the analytical elements are deduced. These elements can be combined with the ordinary finite elements to form a semi-analytical finite element method. Using the semi-analytical finite element method, we can evaluate the stress intensity factors for cracks of mode I , mode II and mode I + II directly. Many typical problems arestudied and compared with boundary collocation method, traditional finite element method and analytical methods. The results indicate that the method is accurate and simple for stress intensity factor computation and is easy to be used in practical engineering. The influence of the external nodal number of the analytical element on the accuracy of stress intensity factor computation is investigated in detail. The results show that the method has good convergent property.3. Extended the semi-analytical finite element method into the Dugdale model of elastic-plastic fracture mechanics, the analytical elements based on t更多还原