本文關(guān)鍵詞： 反問題 熱傳導(dǎo)問題 有限塊體法 功能梯度材料 移動(dòng)邊界 邊界型有限塊體法 摩擦分析　出處：《太原理工大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：功能梯度材料是一類物理性質(zhì)與位置坐標(biāo)有關(guān)的特殊的復(fù)合材料。該材料廣泛應(yīng)用于航空器材的熱障涂層、生物醫(yī)學(xué)的骨科植入材料、固體氧化物燃料電極等高科技領(lǐng)域。一般地,很難找到功能梯度材料上力學(xué)問題的基本解,而且傳統(tǒng)數(shù)值算法如有限元法求解該類問題時(shí)網(wǎng)格劃分繁瑣,精度略低�；跓o網(wǎng)格法提出的有限塊體法(FBM)在建立系統(tǒng)代數(shù)方程時(shí)不需要基本解,具有配點(diǎn)靈活、精度較高的特點(diǎn)。本文通過有限塊體法求解功能梯度材料的移動(dòng)反邊界問題、二維熱傳導(dǎo)問題以及一致接觸類摩擦問題。本文考慮煉鋼爐上的移動(dòng)反邊界問題并對其內(nèi)層腐蝕邊界進(jìn)行探測與動(dòng)態(tài)識(shí)別,煉鋼爐的復(fù)合結(jié)構(gòu)通過多層功能梯度材料模擬,借助于適度大小的虛擬矩形域可求得腐蝕點(diǎn)位置信息。此外邊界修正的Chebyshev零點(diǎn)的引入進(jìn)一步提升了有限塊體法的收斂性。本文還研究了功能梯度圓環(huán)上的二維熱傳導(dǎo)問題。由于功能梯度圓環(huán)的物理屬性與圓環(huán)半徑相關(guān),本文采用基于極坐標(biāo)的有限塊體法進(jìn)行求解,并給出極坐標(biāo)下有限塊體法的熱傳導(dǎo)方程和邊界條件的矩陣形式。最后本文研究了壓縮載荷下彈性地基上的平?jīng)_頭模型并提出邊界型有限塊體法。通過理論推導(dǎo)可以看出,采用邊界型有限塊體法分析一致接觸類摩擦問題,可以減少平衡方程中未知量的個(gè)數(shù)、提高求解效率。本文列舉了五個(gè)數(shù)值算例,并通過與有限元法(FEM)和徑向基函數(shù)(RBF)的比較來展現(xiàn)有限塊體法的優(yōu)勢。數(shù)值結(jié)果表明:有限塊體法有高穩(wěn)定性、高效率、高精度的特點(diǎn)。
[Abstract]:Functionally graded material (FGM) is a kind of special composite material whose physical properties are related to position coordinates. It is widely used in thermal barrier coating of aeronautical equipment and orthopedic implant material in biomedicine. In general, it is difficult to find the basic solution of mechanical problems on functionally graded materials in high-tech fields such as solid oxide fuel electrodes, and the traditional numerical algorithms such as finite element method are tedious to solve such problems. The finite block method (FBM) based on meshless method does not need the basic solution when establishing the algebraic equation of the system, and it is flexible in collocation. The finite block method is used to solve the moving inverse boundary problem of functionally graded materials. In this paper, the problem of moving inverse boundary on steelmaking furnace is considered, and the inner layer corrosion boundary is detected and dynamically identified. The composite structure of steelmaking furnace is simulated by multi-layer functionally gradient material. In addition, the introduction of Chebyshev 00:00 with boundary correction further improves the convergence of the finite block method. The functional ladder is also studied in this paper. Two-dimensional heat conduction problem on a circular ring. The physical properties of the functionally gradient ring are related to the radius of the ring. In this paper, a finite block method based on polar coordinates is used to solve the problem. The heat conduction equation and the matrix form of boundary conditions of finite block method in polar coordinates are given. Finally, the flat punch model of elastic foundation under compression load is studied and the boundary finite block method is presented. You can see. The boundary finite block method can reduce the number of unknowns in the equilibrium equation and improve the efficiency of solving the uniform contact friction problems. Five numerical examples are given in this paper. Compared with the finite element method (FEMM) and the radial basis function (RBF), the advantages of the finite block method are demonstrated. The numerical results show that the finite block method has the characteristics of high stability, high efficiency and high accuracy.
【學(xué)位授予單位】：太原理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TB34

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本文編號：1469050