基于等效刚度原理的损伤梁位移变化研究

对构件和结构损伤后的力学性能变化研究一直是世界各国学者十分关注的问题。从现有文献得知，大多研究者以损伤力学及断裂力学为基本理论，按照等效应变原理研究结构及构件的损伤。作者根据等效刚度原理定义损伤程度，对损伤采用损伤位置、损伤程度和损伤长度三个参数来描述，从材料力学平面弯曲理论出发，运用小变形的平面弯曲挠曲线近似微分方程，并引入损伤程度的定义，推导出恒载作用下损伤梁转角和挠度方程的隐含表达式。对悬臂损伤梁进行了各种损伤情况下转角和挠度数值计算结果的对比分析，总结出了其位移变化规律。本研究的目的是为了充分有效地认识损伤梁的性能变化，期望为结构的健康检测、损伤识别理论研究奠定基础。

A Study of the displacement change of damaged cantilever beams based on equivalent stiffness principle

Studying the changes of mechanical performance for damaged structures and components have widely drawn the interests of researchers in the world. One can find that from the literature, most of the researchers in this field study damages of the structures according to the theory of equivalent strain based on continuum damage mechanics and fracture mechanics. The conception of equivalent stiffness is used in this paper to simulate structural damage severity. Using this approach, an analytical model, which includes three damage parameters（damage location, damage severity, and length of damage）, is developed for cantilever beams. Solutions for the displacement along the cantilever beams under dead load, for both undamaged state and damaged state, are obtained by solving the equations which are deduced from the theories of plane bending and approximately differential equation of flexural. The change rules of displacement for damaged cantilever beams are summarized from comparing the numerical values. The purpose of this paper is to lay groundwork for future studies about structural health monitoring and damage identification.