基于刚度衰减下的桁架系統的疲劳可靠性分析

在疲劳载荷作用下，元件物理性能的衰减过程是十分复杂的，而由元件组成的结构系统不是一个简单的拓扑结构，其物理性能在疲劳载荷作用下的变化更为复杂。为了定量分析结构系统在不同寿命期内的刚度可靠性，建立起结构物理性能衰减的精确公式是至关重要的。本文从损伤力学角度出发，结合断裂力学中理论断裂强度公式，利用应变等效性假设，基于剩余强度衰减模型，推导出弹性模量衰减公式，从而给出了疲劳载荷作用下系统刚度的可靠性衰减公式。最后，结合杆元桁架系统刚度矩阵，推导出桁架系统节点位移在不同使用寿命期的计算公式，进而求出系统刚度的疲劳可靠性指标。

Fatigue Reliability Analysis of Truss Structure Based on Stiffness Decay

The process of physical property decay of element is very complex under fatigue loads. The structural system that consists of the elements is not a simple topological structure, whose change of physical properties is more complex. In order to analyze quantitatively the structural stiffness reliability at different life cycles, it is important to establish the accurate formula of physical property decay. As viewed from damage mechanics, combining with the formula of theoretical fracture strength, using strain equivalent assumption and based on the model of residual strength decay, the formula of elastic modulus decay was deduced. Moreover, the formula of structural stiffness reliability decay was given under fatigue loads. By combining with stiffness matrix of truss structural system, the formula of joint displacement was deduced in different service life cycles and fatigue reliability index of structural stiffness was solved.