应变疲劳可靠性分析的有限元法

Finite Element Method in Strain-Based Fatigue Reliability Analysis

将随机有限元与可靠性理论相结合来计算应变疲劳可靠性.随机有限元采用Taylor展式随机有限元法,可靠性理论采用改进的一次二阶矩法.针对复杂的交变载荷,采用运动强化模型反映塑性应变引起的各向异性和包辛格效应.应力应变曲线以骨架曲线形式表示,描述材料塑性性质和记忆特性,屈服应力增量可用来解决包括材料循环硬化或循环软化影响在内的塑性滞后现象.运用随机有限元计算出局部多轴应力应变的随机响应,推导出了局部应变偏导的迭代格式,从而可求出功能函数的偏导数,根据改进的一次二阶矩法计算可靠度系数.

The stochastic finite element method （SFEM） was combined with the reliability theory to calculate the strain-based fatigue reliability. The Taylor-expansion SFEM under fatigue loading was deduced. In reliability theory the improved first-order second-moment method was used. The aeolotropism and Bauschinger effect resulted from plastic deformation under cyclic loading were reflected by the kinematic hardening model in the SFEM. The transient stress-straln relation curve was denoted by segment polygonal line named framework curve. The usability coefficients expressed the memory characteristic of material. The yield-stress increment could solve the plastic hysteresis problems in SFEM including cycle-hardening or cycle-softening phenomenon. The random responses of local multiaxial stress and strain were calculated by the Taylor-expansion SFEM. The partial derivative iterative formulas of the local strain were deduced. So the partial derivative of the performance function could be obtained, and the improved first-order second-moment method was used to calculate the reliability index.