基于内聚力和裂纹段模型的热弹性断裂力学的无网格方法

发布时间：2018-03-16 00:40

本文选题：裂纹　切入点：内聚力模型　出处：《中原工学院》2017年硕士论文　论文类型：学位论文

【摘要】：温度变化是混凝土等工程结构中裂纹产生和扩展的的重要原因,热弹性断裂力学的理论研究和数值模拟具有重要的工程实际意义。尽管研究人员在热弹性断裂力学的数值模拟方面取得了大量的研究成果,但是温度和位移场的不连续性、裂尖场的奇异性以及开裂标准等问题一直是该问题数值模拟研究领域中的热点。本文将裂纹段模型和内聚力模型应用到热弹性断裂力学的数值模拟中,应用无网格法建立了二维热弹性断裂力学问题的无网格数值计算框架,并编写计算程序后通过具体实例验证了方法的有效性。完成的主要工作如下:(1)在问题域中用一系列相互衔接的裂纹段代替传统的连续裂纹,当裂纹尖端附近的无网格法节点的主应力达到失效应力时,在该节点引入裂纹段以模拟裂纹的扩展。应用移动最小二乘近似形函数的单位分解特征,通过跳跃函数和节点附加自由度模拟位移场和温度场的不连续性,实现位移场和温度场的离散。(2)在弹性断裂力学的内聚力模型基础上,引入与位移场耦合的裂纹面热流量和温度跳跃本构关系,建立了热-力耦合的内聚力模型软化本构关系,模拟裂纹面复杂的应力传递和热传导行为,避开了裂尖场的奇异性问题。(3)基于裂纹段模型和内聚力模型,应用无网格方法建立了热弹性断裂力学的无网格数值计算框架,给出了当前非线性问题的迭代求解方法。应用Fortran语言编写了数值计算程序,并应用该方法分别对矩形板的中心裂纹、矩形板中的平行裂纹、含裂纹板的弯曲变形、方形板中的裂纹扩展等问题进行了数值计算。数值算例结果表明,本方法可以取得较好的计算效果。
[Abstract]:Temperature change is an important reason for crack generation and propagation in concrete and other engineering structures. The theoretical study and numerical simulation of thermoelastic fracture mechanics have important practical significance in engineering. Although researchers have made a lot of achievements in numerical simulation of thermoelastic fracture mechanics, the temperature and displacement fields are discontinuous. The singularity of crack tip field and crack criterion are always the hot topics in the field of numerical simulation. In this paper, the crack segment model and cohesive force model are applied to the numerical simulation of thermoelastic fracture mechanics. A meshless numerical calculation framework for two-dimensional thermoelastic fracture mechanics is established by using the meshless method. The validity of the method is verified by a practical example. The main work accomplished is as follows: 1) in the problem domain, a series of interlocking crack segments are used to replace the traditional continuous cracks. When the principal stress of the meshless node near the crack tip reaches the failure stress, the crack segment is introduced to simulate the crack propagation. Based on the cohesive force model of elastic fracture mechanics, the discontinuity of displacement field and temperature field is simulated by jumping function and additional degree of freedom. By introducing the constitutive relation of heat flux and temperature jump of crack surface coupled with displacement field, a thermo-mechanical coupling cohesive force model is established to soften the constitutive relation and simulate the complex stress transfer and heat conduction behavior of crack surface. The singularity problem of crack tip field is avoided. (3) based on crack segment model and cohesive force model, a meshless numerical calculation framework of thermoelastic fracture mechanics is established by means of meshless method. In this paper, an iterative method for solving nonlinear problems is presented. The numerical calculation program is compiled by using Fortran language. The method is applied to the bending deformation of rectangular plates with central cracks, parallel cracks in rectangular plates, and plates with cracks, respectively. Numerical results of crack propagation in square plates show that the proposed method can achieve good results.
【学位授予单位】：中原工学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O346.1

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