【作者】 马洪波；

【导师】 陈建军；

【作者基本信息】 西安电子科技大学 ， 机械制造及其自动化， 2004， 博士

【摘要】 基于概率的结构分析和优化设计有着广泛的工程背景和重要的理论意义与学术价值。文中针对杆系结构(桁架、刚架)在可靠性分析和基于可靠性的优化设计中可能出现的各种随机情况开展了深入系统的研究，主要内容包括： 1．考虑结构本身参数的随机性，包括物理参数、几何参数以及外加作用载荷参数等分别或同时为随机变量时，应用随机因子法进行结构分析；应用二阶矩法进行可靠性分析；基于可靠性理论中的3σ准则，对结构的边界条件含有随机因素时的结构响应量进行了分析和计算。 2．应用随机因子法研究了桁架结构的物理参数和几何尺寸分别或同时为随机变量时，结构动力特性的概率分析与求解的方法，基于结构振动理论的Rayleigh(瑞利)商公式，利用代数综合法，导出了结构固有频率随机变量数字特征的计算表达式，通过算例考察了结构物理参数和几何参数的随机性对结构动力特性的影响。 3．研究了基于可靠性的结构灵敏度分析方法，导出了结构位移和单元应力的可靠性指标对于设计变量的灵敏度计算表达式，给出了灵敏度计算的半解析表达式，将基于可靠性指标的灵敏度分析在形式上转化为常规的灵敏度分析，使基于可靠性的结构灵敏度计算大为简化。 4．在结构可靠性分析和敏度分析的基础上，开展了随机杆系结构基于可靠性的尺寸优化设计和形状优化设计。分别构建了以结构尺寸和形状参数为设计变量，以结构总重量均值为目标函数，以结构位移和单元应力的可靠性指标等为约束条件的优化设计数学模型，分别利用数学规划方法和遗传算法求解。优化过程中同时考虑了结构多种随机性因素，对结构的位移和应力等概率(可靠度)约束进行了等价显示化处理。 5．对随机杆系结构在随机荷载作用下的随机规划问题进行了研究，构建了以杆系截面积随机变量为设计变量、以结构重量均值极小化为目标函数、同时具有位移和应力概率约束的结构优化设计数学模型，并提出了将随机优化模型等价转化的求解策略。 6．针对基于体系可靠性约束优化设计的关键问题一结构体系可靠性的分析和计算，在基于结构各单元失效相互独立假设的基础上，提出了以各单元失效概率摘要之和近似体系失效概率的处理方法，并给出了体系可靠性分配和再分配的方法，以确保结构体系在优化过程中的可靠性，实现了结构基于体系可靠性的优化设计。 7.针对抛物面天线结构，给出天线结构在保精度和保强度两种情况下的可靠性分析和计算方法，构建了随机参数天线结构在随机荷载作用下的有限元分析、可靠性分析和基于可靠性的优化设计的模型，推导了反射面精度可靠度和压杆稳定性可靠性分析计算表达式。以某8米口径抛物面天线为例，进行了基于概率的天线结构尺寸和形状优化设计。关键词:随机结构随机因子法可靠性分析动力特性敏度分析尺寸优化 形状优化随机优化体系可靠性天线结构更多还原

【Abstract】 The structural analysis and optimization design based on probability have wide engineering background and are of important theoretical significance and research worthiness. This paper mainly has the research of random factors presented in reliability analysis and optimization design based on probability of all kinds engineering structures (including truss and beam structures etc.). The main contents of the paper are as follows:1. The Random Factor Method is utilized to proceed structural reliability analysis which considered randomness of structures, including structural own material parameters such as physical parameters and geometric parameters, and some stochastic parameters involved in the loads applied. The 3 σ criterion of reliability theory is applied to analyze and compute the structural responses while the structural boundary conditions are stochastic. Several numerical examples show the correctness and validity of the theory and method.2. The Random Factor Method is utilized to study the probabilistic analysis and computational method of structural dynamic characteristic while the structural physical parameters and geometric parameters are stochastic variables respectively or simultaneously. The results of numerical examples indicate that the method derived in this paper is correct and valid.3. The structural sensitivity analysis based on reliability is preceded. The sensitivity computational expressions of reliability index with respect to design variables are derived. And the semi-analytical expressions for sensitivity computation are presented. Thus the sensitivity analysis based on reliability is transformed into regular sensitivity analysis. And then the sensitivity analysis based on reliability can be simplified greatly.4. Based on the reliability analysis and sensitivity analysis above, the dimensional optimization and shape optimization based on reliability are developed. The mathematical programming methods are applied in optimization. In optimization models, the structural total weights (or fabricating costs) are regarded as objective functions and reliability indexes of structural displacements and elemental stresses as constraint conditions.5. If the randomness of design variables were considered in optimization, then a regular optimization based on reliability would be transferred to a stochastic programming issue. A method, which is utilized to find the upper and lower bounds of design variables, is proposed in the paper. By the method, the structural stochastic programming model can be transformed to solve.6. The key problem of optimization based on structural system reliability constraints is the analysis and computation of system reliability. In the paper, based on the hypothesis that the failure of every poles is independent and by the method of reliability assign and reassign, the difficult problem of disposing the structure system reliability constraints is solved. Based on sensitivity information, the given system failure probability can be replaced by the sum of every element failure probability. And then the structural optimization design based on system reliability is preceded.7. With the assurance of structural precision accuracy and strength, the reliability analysis and computation method is presented for paraboloid antenna backup structures. And the reliability computational expressions for compression bar stability are derived. For stochastic parameters antenna structures with stochastic loads applied, the models of finite element analysis, reliability analysis and the optimization design based on reliability are constructed. And then the antenna backup structure dimensional and shape optimization designs based on probability are proceeded.更多还原