本文選題：裂紋　切入點：內聚力模型　出處：《中原工學院》2017年碩士論文　論文類型：學位論文

【摘要】：溫度變化是混凝土等工程結構中裂紋產生和擴展的的重要原因,熱彈性斷裂力學的理論研究和數(shù)值模擬具有重要的工程實際意義。盡管研究人員在熱彈性斷裂力學的數(shù)值模擬方面取得了大量的研究成果,但是溫度和位移場的不連續(xù)性、裂尖場的奇異性以及開裂標準等問題一直是該問題數(shù)值模擬研究領域中的熱點。本文將裂紋段模型和內聚力模型應用到熱彈性斷裂力學的數(shù)值模擬中,應用無網格法建立了二維熱彈性斷裂力學問題的無網格數(shù)值計算框架,并編寫計算程序后通過具體實例驗證了方法的有效性。完成的主要工作如下:(1)在問題域中用一系列相互銜接的裂紋段代替?zhèn)鹘y(tǒng)的連續(xù)裂紋,當裂紋尖端附近的無網格法節(jié)點的主應力達到失效應力時,在該節(jié)點引入裂紋段以模擬裂紋的擴展。應用移動最小二乘近似形函數(shù)的單位分解特征,通過跳躍函數(shù)和節(jié)點附加自由度模擬位移場和溫度場的不連續(xù)性,實現(xiàn)位移場和溫度場的離散。(2)在彈性斷裂力學的內聚力模型基礎上,引入與位移場耦合的裂紋面熱流量和溫度跳躍本構關系,建立了熱-力耦合的內聚力模型軟化本構關系,模擬裂紋面復雜的應力傳遞和熱傳導行為,避開了裂尖場的奇異性問題。(3)基于裂紋段模型和內聚力模型,應用無網格方法建立了熱彈性斷裂力學的無網格數(shù)值計算框架,給出了當前非線性問題的迭代求解方法。應用Fortran語言編寫了數(shù)值計算程序,并應用該方法分別對矩形板的中心裂紋、矩形板中的平行裂紋、含裂紋板的彎曲變形、方形板中的裂紋擴展等問題進行了數(shù)值計算。數(shù)值算例結果表明,本方法可以取得較好的計算效果。
[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.
【學位授予單位】：中原工學院
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O346.1

【相似文獻】

相關期刊論文 前10條

1 ;《熱彈性學》[J];固體力學學報;1988年01期

2 王玲;;線性熱彈性系統(tǒng)解的存在性[J];河南科技;2013年24期

3 隋鳴,李曉春;一類熱彈性系統(tǒng)的變結構控制[J];吉林大學學報(理學版);2004年04期

4 徐紅玉,張元沖,宋亞勤,陳殿云;兩微極磁熱彈性固體分界面上波的反射與折射[J];力學學報;2005年06期

5 田曉耕;張婕;沈亞鵬;;不同理論下廣義壓電熱彈性問題的有限元求解[J];力學學報;2006年04期

6 R·庫瑪;M·辛;吳承平;;具有兩個馳豫時間的熱彈性立方晶體材料中平面波的傳播[J];應用數(shù)學和力學;2007年05期

7 萬建軍;張同斌;;周期復合材料等效熱彈性性能的數(shù)值計算[J];河南科技大學學報(自然科學版);2009年04期

8 肖淳;;熱彈性方程的均勻化[J];湛江師范學院學報;2011年06期

9 田曉耕;沈亞鵬;;廣義熱彈性問題研究進展[J];力學進展;2012年01期

10 王元淳,片山忠一,松本，

本文編號：1617593