基于迭代自适应响应面法的结构体系可靠度研究

发布时间：2018-09-11 21:49

【摘要】：不含交叉项和完全二次型的二次多项式传统响应面法的应用最为广泛，但是它们在效率和精度两个方面往往不能兼得。考虑交叉项的自适应响应面法则可以在这两个方面之间达到一个很好的平衡。为进一步提高精度要求，通过引入多次更新样本中心思想和迭代收敛准则，本文对考虑交叉项的自适应响应面法进行了改进。对4种不同类型的数值算例分析可知：改进之后的考虑交叉项的迭代自适应响应面法效率较高，且计算结果精度得到提高。基于响应面法的结构可靠度分析，较多针对于仅含有一个功能函数的单一失效模式的构件可靠度情况，并能得到较理想的结果。然而，对于经典体系可靠度和一般体系可靠度问题而言，，往往含有多个功能函数。学者们往往通过引入多重响应面的方法对其进行处理，却丢失了响应面法在效率和精度这两方面的优点。基于等价极值事件理论，可将经典结构体系可靠度问题和一般结构体系可靠度问题均转化为仅含一个功能函数的简单等价可靠度问题形式，从而可使响应面法能在体系可靠度分析中得以很好地运用，即保证了运算效率，又可得到满足精度要求的结果。因此，本文将改进后的考虑交叉项的迭代自适应响应面法与体系可靠度分析相结合，构造了基于迭代自适应响应面法的体系可靠度分析方法，并为之设计了实现步骤。本文通过5个不同类型的算例对建议算法进行了验证，结果表明：本文建议方法合理有效，且具有较高的精度和效率。本文针对某一实际工程网架结构，首先进行了ANSYS有限元建模和结构静力分析。经分析可知：该结构在线性静力分析时，结构性能良好；在非线性静力分析时，结构承载能力较高。然后，采用本文建议的结构可靠度分析方法对该结构进行了4种不同工况的体系可靠度分析，结果表明：该结构体系具有较高的可靠度。本文又分析了雪荷载随机变量对该结构体系可靠度的影响，结果显示雪荷载均值和积雪分布系数对其影响较大。最后，本文对结构构件可靠度和体系可靠度的关系进行了探索性研究，这部分可以看作是对基于结构体系可靠度的结构优化设计方法或者直接基于体系可靠度结构设计方法研究的初步探索性研究。本文将体系可靠度分析方法和基于构件可靠度的结构优化设计理论相结合，针对简单三杆桁架结构，对其最低构件可靠指标约束限值与优化后结构的体系可靠指标的关系进行了分析，结果表明两者大致成线性关系，并给出了相应的表达式。
[Abstract]:The traditional response surface method for quadratic polynomials without crossover terms and complete quadratic forms is the most widely used, but they can not be obtained both in efficiency and precision. The adaptive response surface rule considering crossover terms can achieve a good balance between these two aspects. In order to improve the precision, the adaptive response surface method considering the crossover term is improved by introducing the idea of multiple update samples and iterative convergence criterion. The numerical examples of four different types show that the improved iterative adaptive response surface method considering crossover terms is more efficient and the accuracy of the calculation results is improved. The structural reliability analysis based on the response surface method is more suitable for the reliability of a single failure mode with only one functional function, and the results are satisfactory. However, for classical system reliability and general system reliability problems, there are many functional functions. Scholars often use the method of multiple response surface to deal with it, but they lose the advantages of response surface method in efficiency and precision. Based on the equivalent extreme event theory, the classical structural system reliability problem and the general structural system reliability problem can be transformed into a simple equivalent reliability problem with only one function. Therefore, the response surface method can be applied to the reliability analysis of the system, which ensures the operation efficiency and obtains the results that meet the precision requirements. Therefore, the improved iterative adaptive response surface method considering crossover terms is combined with the system reliability analysis, and a system reliability analysis method based on the iterative adaptive response surface method is constructed, and the implementation steps are designed for it. In this paper, the proposed algorithm is verified by five different types of examples. The results show that the proposed method is reasonable and effective, and has high accuracy and efficiency. In this paper, ANSYS finite element modeling and structural static analysis are carried out for a practical grid structure. The analysis shows that the structure has good performance in linear static analysis and high bearing capacity in nonlinear static analysis. Then, the structural reliability analysis method proposed in this paper is used to analyze the system reliability of the structure under four different working conditions. The results show that the structure system has higher reliability. The influence of the random variable of snow load on the reliability of the structure is also analyzed. The results show that the mean value of snow load and the snow distribution coefficient have great influence on the reliability of the structure. Finally, the relationship between structural component reliability and system reliability is studied. This part can be regarded as a preliminary exploratory study of the structural optimization design method based on the reliability of the structure system or the structural design method directly based on the reliability of the structure system. In this paper, the reliability analysis method of the system is combined with the structural optimization design theory based on the reliability of the component, aiming at the simple three-bar truss structure. The relationship between the constraint limit of the minimum component reliability index and the system reliability index of the optimized structure is analyzed. The results show that the relationship between them is approximately linear and the corresponding expression is given.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU311.2

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