發(fā)布時(shí)間：2018-06-20 14:06

  本文選題：隨機(jī)均化 + 非均質(zhì)材料　； 參考：《西安電子科技大學(xué)》2015年碩士論文

【摘要】：二相非均質(zhì)材料是基體和增強(qiáng)體(或夾雜)組合而成,它可以充分發(fā)揮其組分材料的優(yōu)點(diǎn),同時(shí)克服單一材料的缺陷。由于非均質(zhì)材料具有高強(qiáng)度、低密度、易加工、可設(shè)計(jì)性強(qiáng)、耐侵蝕等各種優(yōu)良特質(zhì),因而廣泛地應(yīng)用于現(xiàn)代國民生產(chǎn)生活的各個(gè)方面,非均質(zhì)材料結(jié)構(gòu)與力學(xué)性能的研究也日益成為熱點(diǎn)研究課題。此外,材料在加工制造過程中不可避免地要受到各種隨機(jī)因素的影響,因此在對(duì)非均質(zhì)材料的等效力學(xué)性質(zhì)進(jìn)行分析研究時(shí),非常有必要考慮其微觀結(jié)構(gòu)參數(shù)的隨機(jī)性以及同一成分參數(shù)間的相關(guān)性。本文在有限變形條件下,對(duì)非均質(zhì)材料進(jìn)行了力學(xué)和熱彈性的隨機(jī)均化分析。首先介紹了非均質(zhì)材料分類與應(yīng)用、相關(guān)研究的背景和現(xiàn)狀。然后給出了表征體積單元(RVE)的定義及生成方法。在此基礎(chǔ)上,給出了力學(xué)和熱彈性兩種情況下的基于有限單元法(FEM)的均化方法,包括邊界條件的介紹及微觀與宏觀尺度下材料等效特性的求解。在蒙特卡洛法的基礎(chǔ)上,給出了力學(xué)和熱彈性兩種情況下的隨機(jī)均化框架,對(duì)非均質(zhì)材料整體宏觀隨機(jī)等效性質(zhì)及其數(shù)字特征值進(jìn)行了求解。最后給出了力學(xué)及熱彈性下的隨機(jī)均化分析算例。在算例中,考慮材料微觀結(jié)構(gòu)形態(tài)及各組分性質(zhì)的隨機(jī)性以及同一組分參數(shù)之間的相關(guān)性,首先使用隨機(jī)序列添加法(RSA)生成非均質(zhì)材料的三維表征體積單元,其內(nèi)部的夾雜顆粒呈隨機(jī)分布;進(jìn)而采用數(shù)值收斂法確定了不同體積分?jǐn)?shù)下表征體積單元的尺寸;將多尺度方法、有限單元法和蒙特卡洛法相結(jié)合,求解了非均質(zhì)材料的隨機(jī)等效性質(zhì),如力學(xué)分析中通過將不同類型的邊界條件施加于表征體積單元得到了等效剪切張量、第一Piola-Kirchhoff應(yīng)力、應(yīng)變能等參數(shù),而在熱彈性分析中則將求解過程分解成力學(xué)求解和熱學(xué)求解兩個(gè)階段,得到了應(yīng)力張量、熱流量張量、變形梯度張量等有效性質(zhì);最后通過數(shù)理統(tǒng)計(jì)方法求得了各等效量的數(shù)字特征值并考察了不同隨機(jī)參數(shù)及其相關(guān)性對(duì)材料隨機(jī)等效特性的影響程度。
[Abstract]:Two-phase heterogeneous materials are composed of matrix and reinforcements (or inclusions), which can give full play to the advantages of their component materials and overcome the defects of single materials. Due to its high strength, low density, easy processing, good designability, corrosion resistance and so on, heterogeneous materials are widely used in all aspects of modern national production and life. The research on the structure and mechanical properties of heterogeneous materials has become a hot topic. In addition, the material is inevitably affected by various random factors in the process of manufacturing. Therefore, in the analysis of the equivalent mechanical properties of heterogeneous materials, It is necessary to consider the randomness of the microstructure parameters and the correlation among the same component parameters. In this paper, the random homogenization analysis of mechanics and thermoelasticity of heterogeneous materials is carried out under the condition of finite deformation. Firstly, the classification and application of heterogeneous materials, the background and status of related research are introduced. Then, the definition and generation method of the representation volume unit RVEare given. On this basis, a homogenization method based on finite element method (FEMM) for both mechanical and thermoelastic cases is presented, including the introduction of boundary conditions and the solution of the equivalent properties of materials at micro and macro scales. On the basis of Monte Carlo method, the random homogenization frame under two conditions of mechanics and thermoelasticity is given, and the macroscopic stochastic equivalent properties of heterogeneous materials and their numerical eigenvalues are solved. Finally, an example of random homogenization analysis under mechanics and thermoelasticity is given. In the example, considering the randomness of the microstructure and properties of each component and the correlation between the parameters of the same component, the random sequence addition method (RSAs) is used to generate the three-dimensional representation volume unit of the heterogeneous material. The inclusion particles are randomly distributed in its interior, and then the size of the volumetric element is determined by numerical convergence method, and the multi-scale method, the finite element method and the Monte Carlo method are combined. The random equivalent properties of heterogeneous materials are solved. For example, the equivalent shear Zhang Liang, the first Piola-Kirchhoff stress, the strain energy and so on are obtained by applying different boundary conditions to the characterizing volume element in mechanical analysis. In thermoelastic analysis, the solution process is decomposed into two stages: mechanical solution and thermal solution. The effective properties of stress Zhang Liang, heat flow rate Zhang Liang and deformation gradient Zhang Liang are obtained. Finally, the numerical eigenvalues of the equivalent quantities are obtained by mathematical statistical method, and the influence of different random parameters and their correlation on the random equivalent properties of materials is investigated.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TB301

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