發(fā)布時間：2018-06-11 13:57

  本文選題：動力響應 + 共振可靠度　； 參考：《西安電子科技大學》2015年博士論文

【摘要】：實際的工程結構中存在著大量的不確定性,單一的數(shù)學模型不足以準確描述工程結構中的不確定性,隨著復雜工程結構對計算模型精度的要求不斷提高,故必須考慮這些實際存在的不確定因素。本文以機械熱結構分析作為基本問題,以不確定性分析方法作為主要的研究內容,提出了適用于熱結構問題的不確定性分析方法。其中,針對區(qū)間結構分析問題,基于有限元方法,求解了含有區(qū)間參數(shù)空間結構的瞬態(tài)溫度場問題,研究了熱結構耦合梁的動力響應及其共振非概率可靠性的分析方法,并進一步研究了區(qū)間變量相關時結構的非概率可靠性分析方法;針對隨機結構分析問題,將加權最小二乘無網(wǎng)格法與隨機分析方法相結合,分別研究了隨機穩(wěn)態(tài)溫度場和瞬態(tài)溫度場的求解方法。本文的研究內容為如下幾個方面:(1)區(qū)間參數(shù)空間結構的瞬態(tài)溫度場數(shù)值分析。針對含有區(qū)間參數(shù)的空間薄壁圓管結構,基于區(qū)間分析理論,給出其在持續(xù)熱流作用下瞬態(tài)溫度場問題的區(qū)間分析方法。建立了空間結構的瞬態(tài)熱分析有限元模型,提出對該模型在空間域和時間域上分別采用有限元離散和差分離散進行求解的過程。并將結構的物性參數(shù)均視為區(qū)間變量,基于區(qū)間擴張理論和Taylor級數(shù)展開理論,利用矩陣攝動分析方法獲得了區(qū)間參數(shù)結構瞬態(tài)溫度場響應的區(qū)間范圍,數(shù)值算例驗證了所提出方法的合理性。(2)熱結構耦合梁動力響應的區(qū)間數(shù)值分析�？紤]了材料變形與傳熱的相互影響,建立了梁在熱結構耦合下的動力學有限元模型,并給出了對結構瞬態(tài)熱傳導方程與動力學方程進行相互交替迭代求解的計算方法。并針對結構響應不確定性問題,以不確定參數(shù)作為約束變量,通過尋求結構響應函數(shù)的區(qū)間范圍,將區(qū)間問題轉化為優(yōu)化問題,并采用優(yōu)化方法給出了結構響應函數(shù)的區(qū)間界限。算例仿真結果驗證了所提方法的可行性,為含有區(qū)間變量的熱結構耦合梁動力響應問題提供了有效的求解方法。(3)熱結構耦合梁共振非概率可靠性研究。針對梁結構在熱結構耦合作用時其隱式極限狀態(tài)函數(shù)難以求解的問題,基于振動可靠性理論,將改進Kriging方法與有限元方法相結合,提出了熱結構耦合梁共振非概率可靠性分析方法。首先利用Kriging法構建熱結構耦合梁可靠性功能函數(shù)的近似模型,并采取主動學習法加以改進,而后采用區(qū)間變量對梁結構參數(shù)進行描述,建立含有超橢球凸集的梁結構共振非概率可靠性模型,最后結合優(yōu)化方法求解出梁結構共振非概率可靠性指標。通過與Monte-Carlo方法的結果對比表明:文中所提出的方法適用于分析復雜計算問題的非概率可靠性指標,且可以在保證計算精度的同時大幅度提高計算效率。(4)考慮區(qū)間變量相關時的非概率可靠性指標和非概率可靠性靈敏度�？紤]結構區(qū)間變量之間存在約束相關性,提出了利用優(yōu)化方法求解區(qū)間變量相關的結構非概率可靠性指標的計算方法。并利用有限差分理論,推導出區(qū)間變量相關時結構非概率可靠性靈敏度的計算公式。通過算例分析了區(qū)間變量的獨立性和相關性對非概率可靠性指標以及靈敏度的影響,表明了本文所提出方法在實際工程中的實用性。(5)基于Neumann展開Monte-Carlo無網(wǎng)格隨機溫度場分析方法。對加權最小二乘無網(wǎng)格法在隨機溫度場中的應用進行了研究。在移動最小二乘近似的基礎上,采用罰函數(shù)法滿足邊界條件,通過變分原理詳細推導了求解溫度場問題的加權最小二乘無網(wǎng)格公式,該方法不需要進行高斯積分,具有計算量小,處理方便等優(yōu)點。同時考慮結構物理參數(shù)和邊界條件隨機性的影響,利用Neumann展開Monte-Carlo方法對含有隨機參數(shù)溫度場的加權最小二乘無網(wǎng)格方程進行求解,得到了隨機溫度場響應量的統(tǒng)計特征值,并考察了結構隨機變量對節(jié)點溫度的影響。本文所提出方法還避免了每次抽樣過程中的求逆運算,大大提高了計算效率。
[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.
【學位授予單位】：西安電子科技大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：TB114.3

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