热环境下不确定性热-结构分析及可靠性研究

发布时间：2018-06-11 13:57

本文选题：动力响应 + 共振可靠度　；参考：《西安电子科技大学》2015年博士论文

【摘要】：实际的工程结构中存在着大量的不确定性,单一的数学模型不足以准确描述工程结构中的不确定性,随着复杂工程结构对计算模型精度的要求不断提高,故必须考虑这些实际存在的不确定因素。本文以机械热结构分析作为基本问题,以不确定性分析方法作为主要的研究内容,提出了适用于热结构问题的不确定性分析方法。其中,针对区间结构分析问题,基于有限元方法,求解了含有区间参数空间结构的瞬态温度场问题,研究了热结构耦合梁的动力响应及其共振非概率可靠性的分析方法,并进一步研究了区间变量相关时结构的非概率可靠性分析方法;针对随机结构分析问题,将加权最小二乘无网格法与随机分析方法相结合,分别研究了随机稳态温度场和瞬态温度场的求解方法。本文的研究内容为如下几个方面:(1)区间参数空间结构的瞬态温度场数值分析。针对含有区间参数的空间薄壁圆管结构,基于区间分析理论,给出其在持续热流作用下瞬态温度场问题的区间分析方法。建立了空间结构的瞬态热分析有限元模型,提出对该模型在空间域和时间域上分别采用有限元离散和差分离散进行求解的过程。并将结构的物性参数均视为区间变量,基于区间扩张理论和Taylor级数展开理论,利用矩阵摄动分析方法获得了区间参数结构瞬态温度场响应的区间范围,数值算例验证了所提出方法的合理性。(2)热结构耦合梁动力响应的区间数值分析。考虑了材料变形与传热的相互影响,建立了梁在热结构耦合下的动力学有限元模型,并给出了对结构瞬态热传导方程与动力学方程进行相互交替迭代求解的计算方法。并针对结构响应不确定性问题,以不确定参数作为约束变量,通过寻求结构响应函数的区间范围,将区间问题转化为优化问题,并采用优化方法给出了结构响应函数的区间界限。算例仿真结果验证了所提方法的可行性,为含有区间变量的热结构耦合梁动力响应问题提供了有效的求解方法。(3)热结构耦合梁共振非概率可靠性研究。针对梁结构在热结构耦合作用时其隐式极限状态函数难以求解的问题,基于振动可靠性理论,将改进Kriging方法与有限元方法相结合,提出了热结构耦合梁共振非概率可靠性分析方法。首先利用Kriging法构建热结构耦合梁可靠性功能函数的近似模型,并采取主动学习法加以改进,而后采用区间变量对梁结构参数进行描述,建立含有超椭球凸集的梁结构共振非概率可靠性模型,最后结合优化方法求解出梁结构共振非概率可靠性指标。通过与Monte-Carlo方法的结果对比表明:文中所提出的方法适用于分析复杂计算问题的非概率可靠性指标,且可以在保证计算精度的同时大幅度提高计算效率。(4)考虑区间变量相关时的非概率可靠性指标和非概率可靠性灵敏度。考虑结构区间变量之间存在约束相关性,提出了利用优化方法求解区间变量相关的结构非概率可靠性指标的计算方法。并利用有限差分理论,推导出区间变量相关时结构非概率可靠性灵敏度的计算公式。通过算例分析了区间变量的独立性和相关性对非概率可靠性指标以及灵敏度的影响,表明了本文所提出方法在实际工程中的实用性。(5)基于Neumann展开Monte-Carlo无网格随机温度场分析方法。对加权最小二乘无网格法在随机温度场中的应用进行了研究。在移动最小二乘近似的基础上,采用罚函数法满足边界条件,通过变分原理详细推导了求解温度场问题的加权最小二乘无网格公式,该方法不需要进行高斯积分,具有计算量小,处理方便等优点。同时考虑结构物理参数和边界条件随机性的影响,利用Neumann展开Monte-Carlo方法对含有随机参数温度场的加权最小二乘无网格方程进行求解,得到了随机温度场响应量的统计特征值,并考察了结构随机变量对节点温度的影响。本文所提出方法还避免了每次抽样过程中的求逆运算,大大提高了计算效率。
[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.
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TB114.3

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