發(fā)布時(shí)間：2018-03-16 00:40

  本文選題：裂紋　切入點(diǎn)：內(nèi)聚力模型　出處：《中原工學(xué)院》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：溫度變化是混凝土等工程結(jié)構(gòu)中裂紋產(chǎn)生和擴(kuò)展的的重要原因,熱彈性斷裂力學(xué)的理論研究和數(shù)值模擬具有重要的工程實(shí)際意義。盡管研究人員在熱彈性斷裂力學(xué)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(chǎng)的不連續(xù)性、裂尖場(chǎng)的奇異性以及開裂標(biāo)準(zhǔn)等問題一直是該問題數(shù)值模擬研究領(lǐng)域中的熱點(diǎn)。本文將裂紋段模型和內(nèi)聚力模型應(yīng)用到熱彈性斷裂力學(xué)的數(shù)值模擬中,應(yīng)用無網(wǎng)格法建立了二維熱彈性斷裂力學(xué)問題的無網(wǎng)格數(shù)值計(jì)算框架,并編寫計(jì)算程序后通過具體實(shí)例驗(yàn)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(dāng)裂紋尖端附近的無網(wǎng)格法節(jié)點(diǎn)的主應(yīng)力達(dá)到失效應(yīng)力時(shí),在該節(jié)點(diǎn)引入裂紋段以模擬裂紋的擴(kuò)展。應(yīng)用移動(dòng)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(diǎn)附加自由度模擬位移場(chǎng)和溫度場(chǎng)的不連續(xù)性,實(shí)現(xiàn)位移場(chǎng)和溫度場(chǎng)的離散。(2)在彈性斷裂力學(xué)的內(nèi)聚力模型基礎(chǔ)上,引入與位移場(chǎng)耦合的裂紋面熱流量和溫度跳躍本構(gòu)關(guān)系,建立了熱-力耦合的內(nèi)聚力模型軟化本構(gòu)關(guān)系,模擬裂紋面復(fù)雜的應(yīng)力傳遞和熱傳導(dǎo)行為,避開了裂尖場(chǎng)的奇異性問題。(3)基于裂紋段模型和內(nèi)聚力模型,應(yīng)用無網(wǎng)格方法建立了熱彈性斷裂力學(xué)的無網(wǎng)格數(shù)值計(jì)算框架,給出了當(dāng)前非線性問題的迭代求解方法。應(yīng)用Fortran語言編寫了數(shù)值計(jì)算程序,并應(yīng)用該方法分別對(duì)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(kuò)展等問題進(jìn)行了數(shù)值計(jì)算。數(shù)值算例結(jié)果表明,本方法可以取得較好的計(jì)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(xué)位授予單位】：中原工學(xué)院
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O346.1

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本文編號(hào)：1617593