本文選題：動(dòng)力響應(yīng) + 共振可靠度��； 參考：《西安電子科技大學(xué)》2015年博士論文

【摘要】：實(shí)際的工程結(jié)構(gòu)中存在著大量的不確定性,單一的數(shù)學(xué)模型不足以準(zhǔn)確描述工程結(jié)構(gòu)中的不確定性,隨著復(fù)雜工程結(jié)構(gòu)對(duì)計(jì)算模型精度的要求不斷提高,故必須考慮這些實(shí)際存在的不確定因素。本文以機(jī)械熱結(jié)構(gòu)分析作為基本問題,以不確定性分析方法作為主要的研究?jī)?nèi)容,提出了適用于熱結(jié)構(gòu)問題的不確定性分析方法。其中,針對(duì)區(qū)間結(jié)構(gòu)分析問題,基于有限元方法,求解了含有區(qū)間參數(shù)空間結(jié)構(gòu)的瞬態(tài)溫度場(chǎng)問題,研究了熱結(jié)構(gòu)耦合梁的動(dòng)力響應(yīng)及其共振非概率可靠性的分析方法,并進(jìn)一步研究了區(qū)間變量相關(guān)時(shí)結(jié)構(gòu)的非概率可靠性分析方法;針對(duì)隨機(jī)結(jié)構(gòu)分析問題,將加權(quán)最小二乘無(wú)網(wǎng)格法與隨機(jī)分析方法相結(jié)合,分別研究了隨機(jī)穩(wěn)態(tài)溫度場(chǎng)和瞬態(tài)溫度場(chǎng)的求解方法。本文的研究?jī)?nèi)容為如下幾個(gè)方面:(1)區(qū)間參數(shù)空間結(jié)構(gòu)的瞬態(tài)溫度場(chǎng)數(shù)值分析。針對(duì)含有區(qū)間參數(shù)的空間薄壁圓管結(jié)構(gòu),基于區(qū)間分析理論,給出其在持續(xù)熱流作用下瞬態(tài)溫度場(chǎng)問題的區(qū)間分析方法。建立了空間結(jié)構(gòu)的瞬態(tài)熱分析有限元模型,提出對(duì)該模型在空間域和時(shí)間域上分別采用有限元離散和差分離散進(jìn)行求解的過程。并將結(jié)構(gòu)的物性參數(shù)均視為區(qū)間變量,基于區(qū)間擴(kuò)張理論和Taylor級(jí)數(shù)展開理論,利用矩陣攝動(dòng)分析方法獲得了區(qū)間參數(shù)結(jié)構(gòu)瞬態(tài)溫度場(chǎng)響應(yīng)的區(qū)間范圍,數(shù)值算例驗(yàn)證了所提出方法的合理性。(2)熱結(jié)構(gòu)耦合梁動(dòng)力響應(yīng)的區(qū)間數(shù)值分析�？紤]了材料變形與傳熱的相互影響,建立了梁在熱結(jié)構(gòu)耦合下的動(dòng)力學(xué)有限元模型,并給出了對(duì)結(jié)構(gòu)瞬態(tài)熱傳導(dǎo)方程與動(dòng)力學(xué)方程進(jìn)行相互交替迭代求解的計(jì)算方法。并針對(duì)結(jié)構(gòu)響應(yīng)不確定性問題,以不確定參數(shù)作為約束變量,通過尋求結(jié)構(gòu)響應(yīng)函數(shù)的區(qū)間范圍,將區(qū)間問題轉(zhuǎn)化為優(yōu)化問題,并采用優(yōu)化方法給出了結(jié)構(gòu)響應(yīng)函數(shù)的區(qū)間界限。算例仿真結(jié)果驗(yàn)證了所提方法的可行性,為含有區(qū)間變量的熱結(jié)構(gòu)耦合梁動(dòng)力響應(yīng)問題提供了有效的求解方法。(3)熱結(jié)構(gòu)耦合梁共振非概率可靠性研究。針對(duì)梁結(jié)構(gòu)在熱結(jié)構(gòu)耦合作用時(shí)其隱式極限狀態(tài)函數(shù)難以求解的問題,基于振動(dòng)可靠性理論,將改進(jìn)Kriging方法與有限元方法相結(jié)合,提出了熱結(jié)構(gòu)耦合梁共振非概率可靠性分析方法。首先利用Kriging法構(gòu)建熱結(jié)構(gòu)耦合梁可靠性功能函數(shù)的近似模型,并采取主動(dòng)學(xué)習(xí)法加以改進(jìn),而后采用區(qū)間變量對(duì)梁結(jié)構(gòu)參數(shù)進(jìn)行描述,建立含有超橢球凸集的梁結(jié)構(gòu)共振非概率可靠性模型,最后結(jié)合優(yōu)化方法求解出梁結(jié)構(gòu)共振非概率可靠性指標(biāo)。通過與Monte-Carlo方法的結(jié)果對(duì)比表明:文中所提出的方法適用于分析復(fù)雜計(jì)算問題的非概率可靠性指標(biāo),且可以在保證計(jì)算精度的同時(shí)大幅度提高計(jì)算效率。(4)考慮區(qū)間變量相關(guān)時(shí)的非概率可靠性指標(biāo)和非概率可靠性靈敏度�？紤]結(jié)構(gòu)區(qū)間變量之間存在約束相關(guān)性,提出了利用優(yōu)化方法求解區(qū)間變量相關(guān)的結(jié)構(gòu)非概率可靠性指標(biāo)的計(jì)算方法。并利用有限差分理論,推導(dǎo)出區(qū)間變量相關(guān)時(shí)結(jié)構(gòu)非概率可靠性靈敏度的計(jì)算公式。通過算例分析了區(qū)間變量的獨(dú)立性和相關(guān)性對(duì)非概率可靠性指標(biāo)以及靈敏度的影響,表明了本文所提出方法在實(shí)際工程中的實(shí)用性。(5)基于Neumann展開Monte-Carlo無(wú)網(wǎng)格隨機(jī)溫度場(chǎng)分析方法。對(duì)加權(quán)最小二乘無(wú)網(wǎng)格法在隨機(jī)溫度場(chǎng)中的應(yīng)用進(jìn)行了研究。在移動(dòng)最小二乘近似的基礎(chǔ)上,采用罰函數(shù)法滿足邊界條件,通過變分原理詳細(xì)推導(dǎo)了求解溫度場(chǎng)問題的加權(quán)最小二乘無(wú)網(wǎng)格公式,該方法不需要進(jìn)行高斯積分,具有計(jì)算量小,處理方便等優(yōu)點(diǎn)。同時(shí)考慮結(jié)構(gòu)物理參數(shù)和邊界條件隨機(jī)性的影響,利用Neumann展開Monte-Carlo方法對(duì)含有隨機(jī)參數(shù)溫度場(chǎng)的加權(quán)最小二乘無(wú)網(wǎng)格方程進(jìn)行求解,得到了隨機(jī)溫度場(chǎng)響應(yīng)量的統(tǒng)計(jì)特征值,并考察了結(jié)構(gòu)隨機(jī)變量對(duì)節(jié)點(diǎn)溫度的影響。本文所提出方法還避免了每次抽樣過程中的求逆運(yùn)算,大大提高了計(jì)算效率。
[Abstract]:There are a lot of uncertainties in the actual engineering structure. A single mathematical model is not enough to accurately describe the uncertainty in the engineering structure. With the increasing requirement of the precision of the computational model, it is necessary to consider these actual uncertainties. This paper takes the mechanical thermal structure analysis as the basic problem. As the main research content, the uncertainty analysis method is applied to the problem of thermal structure. The transient temperature field with interval parameter space structure is solved based on the finite element method. The dynamic response of the coupled beam with thermal structure and its resonance inprobability are studied. The analysis method of rate reliability is studied, and the non probabilistic reliability analysis method for interval dependent structure is further studied. The method of solving the stochastic steady-state temperature field and transient temperature field is studied by combining the weighted least squares meshless method with the stochastic analysis method. The following aspects are as follows: (1) the numerical analysis of transient temperature field of space structure with interval parameters. Based on the interval analysis theory, an interval analysis method for the transient temperature field problem under the action of continuous heat flow is presented for space thin-walled circular tube structures with interval parameters. A finite element model for transient thermal analysis of space structure is established. In the spatial domain and the time domain, the finite element discrete and differential dispersion are used respectively. The parameters of the structure are considered as interval variables. Based on the interval expansion theory and the Taylor series expansion theory, the interval range of the transient temperature field response of the interval parameter structure is obtained by the matrix perturbation analysis. A numerical example is given to verify the rationality of the proposed method. (2) an interval numerical analysis of the dynamic response of a coupled thermal structure is taken into account. Considering the interaction between the material deformation and the heat transfer, the dynamic finite element model of the beam under the thermal structure coupling is established, and the transient heat conduction equation and the dynamic equation of the structure are iteratively solved. In view of the uncertainty of structural response, the interval problem is transformed into an optimization problem by using the uncertain parameters as a constraint variable and the interval range of the structural response function is sought, and the interval boundary of the structural response function is given by the optimization method. The example is used to verify the feasibility of the proposed method. An effective solution to the dynamic response of a coupled beam with interval variables is provided. (3) the study of the non probabilistic reliability of the resonance of a coupled beam of thermal structure. The problem that the implicit limit state function of the beam structure is difficult to be solved when the structure is coupled to the thermal structure is difficult to be solved. Based on the theory of vibration reliability, the improved Kriging method is connected with the finite element method. In addition, a non probabilistic reliability analysis method for the resonance of the coupled beam of thermal structure is proposed. First, the approximate model of the functional function of the reliability of the coupled beam of the thermal structure is constructed by using the Kriging method, and the active learning method is adopted to improve it. Then the structural parameters of the beam are described with the interval variable, and the resonance non probability of the beam with a superellipsoid convex set is built. The reliability model is used to solve the non probability reliability index of the beam structure with the optimization method. The comparison with the results of the Monte-Carlo method shows that the proposed method is suitable for the analysis of the non probability reliability index of the complex calculation problem, and can greatly improve the calculation efficiency while guaranteeing the calculation precision. (4) consideration of the calculation efficiency. The non probabilistic reliability index and non probabilistic reliability sensitivity of interval variables are considered. Considering the existence of constraint correlation between structural interval variables, a method of calculating the non probabilistic reliability index of structure related to interval variables is proposed by using the optimization method. The formula of probability reliability sensitivity is calculated. Through an example, the influence of the independence and correlation of interval variables on the non probabilistic reliability index and sensitivity is analyzed. It shows the practicability of the proposed method in the actual project. (5) the Monte-Carlo unnet lattice random temperature field analysis method based on the Neumann is used. The application of the meshless method in the random temperature field is studied. On the basis of the moving least square approximation, the penalty function method is used to satisfy the boundary conditions. The weighted least square meshless formula for solving the problem of temperature field is derived in detail by the variational principle. The method does not need to carry out the Gauss integral, and the calculation is small and the treatment is convenient. At the same time, taking into account the influence of the structural physical parameters and the randomness of the boundary conditions, the Neumann Monte-Carlo method is used to solve the weighted least square meshless equation with random parameters, and the statistical characteristics of the response of the random temperature field are obtained, and the influence of the structural random variable on the temperature of the node is examined. The method proposed in this paper also avoids the inverse operation in every sampling process, which greatly improves the computation efficiency.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：TB114.3

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