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【摘要】：不含交叉項和完全二次型的二次多項式傳統(tǒng)響應面法的應用最為廣泛，但是它們在效率和精度兩個方面往往不能兼得�？紤]交叉項的自適應響應面法則可以在這兩個方面之間達到一個很好的平衡。為進一步提高精度要求，通過引入多次更新樣本中心思想和迭代收斂準則，本文對考慮交叉項的自適應響應面法進行了改進。對4種不同類型的數(shù)值算例分析可知：改進之后的考慮交叉項的迭代自適應響應面法效率較高，且計算結果精度得到提高。 基于響應面法的結構可靠度分析，較多針對于僅含有一個功能函數(shù)的單一失效模式的構件可靠度情況，并能得到較理想的結果。然而，對于經(jīng)典體系可靠度和一般體系可靠度問題而言，，往往含有多個功能函數(shù)。學者們往往通過引入多重響應面的方法對其進行處理，卻丟失了響應面法在效率和精度這兩方面的優(yōu)點�；诘葍r極值事件理論，可將經(jīng)典結構體系可靠度問題和一般結構體系可靠度問題均轉化為僅含一個功能函數(shù)的簡單等價可靠度問題形式，從而可使響應面法能在體系可靠度分析中得以很好地運用，即保證了運算效率，又可得到滿足精度要求的結果。因此，本文將改進后的考慮交叉項的迭代自適應響應面法與體系可靠度分析相結合，構造了基于迭代自適應響應面法的體系可靠度分析方法，并為之設計了實現(xiàn)步驟。本文通過5個不同類型的算例對建議算法進行了驗證，結果表明：本文建議方法合理有效，且具有較高的精度和效率。 本文針對某一實際工程網(wǎng)架結構，首先進行了ANSYS有限元建模和結構靜力分析。經(jīng)分析可知：該結構在線性靜力分析時，結構性能良好；在非線性靜力分析時，結構承載能力較高。然后，采用本文建議的結構可靠度分析方法對該結構進行了4種不同工況的體系可靠度分析，結果表明：該結構體系具有較高的可靠度。本文又分析了雪荷載隨機變量對該結構體系可靠度的影響，結果顯示雪荷載均值和積雪分布系數(shù)對其影響較大。 最后，本文對結構構件可靠度和體系可靠度的關系進行了探索性研究，這部分可以看作是對基于結構體系可靠度的結構優(yōu)化設計方法或者直接基于體系可靠度結構設計方法研究的初步探索性研究。本文將體系可靠度分析方法和基于構件可靠度的結構優(yōu)化設計理論相結合，針對簡單三桿桁架結構，對其最低構件可靠指標約束限值與優(yōu)化后結構的體系可靠指標的關系進行了分析，結果表明兩者大致成線性關系，并給出了相應的表達式。
[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.
【學位授予單位】：重慶大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TU311.2

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本文編號：2237954