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Second-order second moment reliability index


Of curvature. By (12) and (13) can be obtained at the checking point in the design of curvature,[link widoczny dla zalogowanych],: Ⅱ,: 1,2, ..., n a 1. (14) from Differential Geometry we know that the limit state surface at the design point of the principal curvatures of and for the K = Σ = Σ a. (15) J: lJ = 1 and because matrix A is the matrix of normal orthogonal transform, there are at A = BH, from the date of the orthogonal matrix we can see, * 242 * Harbin Engineering University Vol 25 Die Day =,={?:;;,[link widoczny dla zalogowanych], Also known by the Matrix Method: aji = ΣHblHu + ΣHb2H + ... + ΣHbHw, the right-hand side of each one pair of J. Summation, for example, to the first m (m = 1,2,[link widoczny dla zalogowanych], ... n) term sum, there ΣΣHbH: Σ (HvblH + H2ib2Hv + ... + J = 1i = 1J = 1HbH) = b is therefore Σ = Σ,. = T. (16) J = 1J = 1 where: (J. = 1,2, ..., n) is the main diagonal elements of matrix B, the value of the type (16) generation (15) may be expressed as = Σ A,[link widoczny dla zalogowanych], (17) Differential geometry known by the average principal curvature radius R can be expressed as R =. (1 』so, you can type (10) is approximately expressed as g (1,) = a (y a LU r) + l Chu 2. (19) by (19) yields = +2 = 1 +. (20) where: for the structure function g (Y) of the mean, or the structure function g (Y) the standard deviation. Therefore, the second-order reliability index for the second wind::. (21) 3, an example of a structure based limit state equation g () = 3.2 +0.3 x +0.06 x-2. Where:. And as independent standard normal random variable,[link widoczny dla zalogowanych], find the reliability index. Solutions calculated using different methods, the results shown in Table 1, Table 1 and P values compared Table1Comparisonof1] andPf Note: 1) the number of Monte Carlo sampling n = 300000; 98% confidence limits = (2.206 × 10 ~, 3.66 × 10), 2) the relative error value is calculated based on Monte Carlo. 4 Conclusion In this paper, the main curvature of the structure given in the form of second-order second moment reliability index of the expression, at its core: 1) to consider the structure function in the design checking point at the start of the second term, and to avoid the second order partial derivatives of the function of functionally eigenvalues and eigenvectors, the method is simple. 2) can be seen from the example of the method has good accuracy. Therefore, the method presented in this paper has a strong value. References: [1] An Weiguang, Zhu Weibing, Yan heart pool. Stochastic finite element method in the uncertainty analysis [J]. Harbin Engineering University, 2002,23 (1): l32 a l35. [2] An Weiguang, beam wave. Stochastic finite element-based structural system reliability analysis [J]. Harbin Engineering University, 1999,20 (2) :75-78. [3] An Weiguang. With failure analysis of the structure of relevant variables [J]. Shipbuilding Engineering, Harbin Institute of Technology, 1988,9 (1) :9-17. [4] An Weiguang. Two-dimensional unit normal lower limit of reliability estimation of bilateral [J]. Harbin Engineering University, 1995,16 (4): 2l-29. [5] SankaranMahadevan. Multiplelinearizatlonmethodfornon-linearreliabilityanalysis [J]. JEngMech, 2001,127 (11): l165 a ll72. [6] An Weiguang. Reliability comparison of several calculation methods [J]. Strength and the Environment, 1988 (4) :51-57. [7] ZHAOYG, ONOT. NewapproximationsforSORM: part1 [J]. JEngMech, 1999,125 (1) :79-93. [8] An Weiguang, Zhou Jiansheng. Weapons and equipment (products) of the complete analysis [J]. Harbin Engineering University, 2001,22 (3) :42-46. [9] An Weiguang. Structural system reliability and reliability-based optimum design [M]. Beijing: National Defence Industry Press, 1997. [10] DAM. Engineering structure reliability theory and application [M]. Dalian: Dalian University of Technology Press, 1996. [11] Dong Cong. Modern structural system reliability theory and its application [M]. Beijing: Science Press, 2001. [Editor: Li Ling Chu]

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