Research On The Fatigue Life And Reliability Of Mechanical Structure Under Non-gaussian Random Loading

The random loadings exist extensively in the service environment of the military armaments. It is of great significane to study the issues about fatigue life and reliability of structural components under random loadings. Traditionally, the random loading fatigue damage calculation is always based on the assumption of Gaussian distribution. However, many observed results have confirmed that many key structures in different kinds of military equipments are subjected to non-Gaussian random loadings recently. The methods based on Gaussian distribution assumption will introduce great computational errors for non-Gaussian random loadings.To solve the problems of fatigue life prediction and reliability analysis of weapon equipments working under random loadings, this dissertation has systematically studied the following problems: the statistical analysis of non-Gaussian random loadings, the dynamic response analysis of structures under non-Gaussian random excitations, the fatigue life calculation and reliability analysis of non-Gaussian random loadings, and the relevant random vibration accelerated test technology. The researches of this dissertation can provide technical support for the fatigue life calculation and reliability analysis of military armaments working under random loadings. The main contributions of this dissertation are summarized as follows:1. The probability density function models for symmetrical and skewed non-Gaussian random loadings are established.This is the basic of fatigue life prediction, reliability analysis and the relevant accelerated test technique. The explicit closed-form expressions for non-Gaussian processes are derived based on the relationships of the moments in different orders of Gaussian process and the estimated higher-order moments of non-Gaussian process from sample time histories. The probability density distribution models based on Gaussian mixture model are validated by simulated signals and measured signals.2. The calculation method of stress responses under non-Gaussian excitations is developed.The calculated stress responses are the inputs for fatigue damage estimation. The non-Gaussian random excitations are divided into two categories: the steady non-Gaussian and burst non-Gaussian, based on the time-domain properties of the signals. From the analysis results of the cantilever beam, a flowchart of stress response calculation under non-Gaussian random excitation for normal structures is presented.3. The fatigue damage calculation methods for narrowband and broadband non-Gaussian random loadings are proposed respectively.For the narrowband non-Gaussian random loadings, the shortcomings of the methods based on nonlinear transformations are analyzed firstly, and then the b-th moment method is proposed to circumvent these shortcomings. For the broadband non-Gaussian random loadings, the theory of Gaussian mixture model is introduced to the frequency-domain, and the concept of probabilistic power spectral density(PPSD) is proposed. After that by combining the PPSD with the Dirlik formula, the GMM-Dirlik method for broadband non-Gaussian random loadings is developed. The fatigue damage calculation methods for narrowband and broadband non-Gaussian random loadings are validated by different examples separately.4. The fatigue reliability analysis method of mechanical components under random loadings is established.The cause of the uncertainty of the random loading fatigue damage is divided to the randomness from the external loading(external cause) and the randomness of the fatigue property of the structure itself(internal cause). For the high-cycle-fatigue(HCF) problem, the randomness of the rainflow cycles number in specified time duration is negligible based on the large-number theorem. The uncertainty of fatigue damage induced by the rainflow cycle distribution can be modelled by normal distribution. The P-S-N curve is chosen to characterize the randomness of the fatigue property of the structure, and a P-S-N curve evaluation method based on fatigue data under random loading is proposed. The fatigue reliability analysis method is developed by combining the external cause and internal cause of the randomness of fatigue damage.5. The research of random vibration accelerated test method is carried out.The relationships between the excitation root mean square(RMS) level and the stress response RMS level are firstly analyzed. A step further, the relationships between the acceleration factor and the excitation RMS level are determined. After that the flowchart for determining an accelerated test scheme is proposed. The mathematical model for calculating the fatigue reliability of the product under service loading based on the the accelerated fatigue test data is established.In summary, this dissertation has studied the problem about non-Gaussian random loading fatigue life prediction and reliability analysis systematically, and solved some critical problem in this area. The results of this dissertation have great significances to solve the problem of life prediction, reliability analysis and evaluation of weapon equipments.