本文選題：擴(kuò)展有限元法 + 單元子域劃分�。� 參考：《哈爾濱工業(yè)大學(xué)》2017年碩士論文

【摘要】：在實(shí)際工程結(jié)構(gòu)中,結(jié)構(gòu)由于受力強(qiáng)度超過(guò)自身抗拉強(qiáng)度會(huì)產(chǎn)生裂縫,并且材料本身也經(jīng)常存在各種缺陷如裂紋、夾雜、空洞等等,這些都會(huì)影響結(jié)構(gòu)的受力性能,因此有必要對(duì)存在裂紋的結(jié)構(gòu)進(jìn)行受力分析,確保工程結(jié)構(gòu)的正常使用。傳統(tǒng)有限元方法是一種典型且經(jīng)常使用的數(shù)值模擬方法,但是在模擬帶裂紋結(jié)構(gòu)時(shí)存在瓶頸,這主要是因?yàn)閭鹘y(tǒng)擴(kuò)展有限元方法劃分網(wǎng)格時(shí)要求與裂紋邊重合,裂紋擴(kuò)展的不確定性極大地增加了計(jì)算上的難度和時(shí)間。擴(kuò)展有限元是在傳統(tǒng)有限元方法的基礎(chǔ)上發(fā)展而來(lái)的,其在處理裂紋時(shí)可以獨(dú)立于網(wǎng)格劃分,在處理裂紋模型時(shí)顯示了極大的優(yōu)越性,被認(rèn)為是處理裂紋時(shí)最有效的數(shù)值方法。本文在matlab平臺(tái)上,利用擴(kuò)展有限元法對(duì)裂紋發(fā)生分叉、交叉時(shí)的情形進(jìn)行了模擬,實(shí)現(xiàn)了對(duì)含粘聚力裂紋的動(dòng)態(tài)擴(kuò)展的數(shù)值模擬,主要研究?jī)?nèi)容和結(jié)論如下:(1)在單位分解法的基礎(chǔ)上,詳細(xì)闡述了擴(kuò)展有限元法的基本原理,介紹了如何利用水平集法表征裂縫的幾何信息。推導(dǎo)了擴(kuò)展有限元法中,當(dāng)裂紋界面不存在相互作用力以及存在粘聚力時(shí)的積分弱形式和離散方程,得到了兩種情形下的剛度矩陣表達(dá)式。(2)在靜態(tài)裂縫算例中(即線彈性斷裂模型),提出了單元、節(jié)點(diǎn)編碼形式和改進(jìn)的單元子域劃分方案,對(duì)靜態(tài)裂紋模型的計(jì)算流程進(jìn)行了梳理,對(duì)靜態(tài)單一裂紋、分叉裂紋、交叉裂紋模型進(jìn)行了數(shù)值模擬,得到了模型的變形圖以及頂部節(jié)點(diǎn)豎向位移與節(jié)點(diǎn)之間的關(guān)系。(3)在動(dòng)態(tài)裂紋擴(kuò)展模型中,本文提出了一種界面粘聚力本構(gòu)模型,該模型可以同時(shí)考慮裂紋界面法向應(yīng)力和切向應(yīng)力的影響,并且提出了一種改進(jìn)的數(shù)值積分方案,使得積分點(diǎn)的劃分大大簡(jiǎn)化。在此基礎(chǔ)上提出了裂紋動(dòng)態(tài)擴(kuò)展的計(jì)算流程。對(duì)單邊切口三點(diǎn)支撐梁進(jìn)行了數(shù)值模擬,分析了裂紋擴(kuò)展路徑、荷載-CMOD關(guān)系曲線、荷載-加載點(diǎn)豎向位移曲線等等,結(jié)果表明數(shù)值分析和實(shí)驗(yàn)結(jié)果擬合程度較好。對(duì)影響數(shù)值分析的幾個(gè)參數(shù)如擴(kuò)展步長(zhǎng)設(shè)置、裂紋尖端影響半徑大小等進(jìn)行了分析,提出了合適的取值范圍。
[Abstract]:In the actual engineering structure, the structure will produce cracks because the stress intensity exceeds its own tensile strength, and the material itself often has various defects such as cracks, inclusions, voids, etc., all of which will affect the mechanical performance of the structure.Therefore, it is necessary to analyze the stress of the structures with cracks to ensure the normal use of engineering structures.The traditional finite element method is a typical and often used numerical simulation method, but there is a bottleneck in simulating the structure with cracks, which is mainly due to the coincidence between the traditional extended finite element method and the crack edge in meshing.The uncertainty of crack propagation greatly increases the computational difficulty and time.The extended finite element method is developed on the basis of the traditional finite element method. It can be separated from the mesh when dealing with the crack. It shows great superiority in dealing with the crack model and is considered to be the most effective numerical method in dealing with the crack.In this paper, the propagation finite element method is used to simulate the dynamic propagation of crack with cohesive force on matlab platform.The main contents and conclusions are as follows: (1) based on the unit decomposition method, the basic principle of extended finite element method (EFEM) is described in detail, and how to use the horizontal set method to characterize the geometric information of cracks is introduced.In the extended finite element method, the integral weak form and discrete equation are derived when there is no interaction at the crack interface and there is cohesion.In this paper, the expression of stiffness matrix in two cases is obtained. In the static crack example (linear elastic fracture model), the element, the node coding form and the improved subdomain partition scheme of the element are proposed.The calculation flow of static crack model is combed, and the static single crack, bifurcation crack and cross crack model are numerically simulated.The deformation diagram of the model and the relationship between the vertical displacement of the top node and the joint are obtained. In the dynamic crack growth model, a constitutive model of the interface cohesion force is proposed in this paper.The influence of normal stress and tangential stress on crack interface can be considered in this model, and an improved numerical integration scheme is proposed, which simplifies the division of integral points.On this basis, the calculation flow of crack dynamic propagation is presented.Numerical simulation of three-point beam with one-sided notch is carried out, crack propagation path, load-CMOD relation curve, vertical displacement curve of load-loading point and so on are analyzed. The results show that the numerical analysis and experimental results fit well.Several parameters affecting numerical analysis, such as the setting of propagation step size and the influence radius of crack tip, are analyzed, and the appropriate range of values is put forward.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TU755.7

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本文編號(hào)：1756031