基于Liouville方程的管节点疲劳寿命可靠度预测方法

通过建立Liouville概率密度演化方程来求解疲劳裂纹扩展尺寸的概率密度函数,以预测海洋平台管节点疲劳寿命的可靠度.通过频域与时域计算相结合的方式分析交变应力的随机过程统计特性,采用基于标准正交基的随机过程展开法,将结构交变应力的随机过程分解为确定时间函数与独立随机变量系的线性组合形式,将裂纹扩展速率方程变换为第一类随机微分方程,从而建立了Liouville概率密度演化方程,并运用数值方法对其求解.同时,通过算例验证了该方法的有效性.结果表明,所提出的方法与Monte-Carlo模拟方法的计算结果较吻合.

Tubular Joint Fatigue Life Reliability Prediction Method Based on Liouville Equation

The offshore platform tubular joint fatigue life reliability prediction was achieved by employing the Liouville probability density evolution equation to obtain the fatigue crack probability density function (PDF). In this method the statistical characteristics of alternating stress stochastic process was gained by combining frequency domain and time domain calculation. The expansion method of stochastic processes based on normalized orthogonal bases was employed to expand alternating stress stochastic process as linear combination of time functions and independent random variables. The crack propagation rate equation was converted into the first class of stochastic differential equations in order to set up the Liouville probability density evolution equation, and the numerical analysis method was employed to solve it. The example verified the validity and simplicity of the proposed method.