损伤弹性梁的静力学行为分析

根据损伤连续介质力学理论，建立了计及剪切变形效应的具有损伤的线弹性梁的静、动力学行为分析的数学模型.在平面静态情况下，对问题进行了解耦，得到了挠度、转角和损伤分别满足的微分方程，并得到了通解.在不同的边界条件下，得到了挠度、转角和损伤的解析表达式.作为数值算例，给出了在均布载荷作用下的挠度、转角和损伤曲线，考察了损伤对梁的力学行为的影响.

Static Analysis for Damaged Elastic Beams

Based on the mechanics of continuous damage, equations governing static and dynamical behaviors of linear elastic beams with damage are derived, in which the effect of shearing deformation is taken into account. For static plane problems, the equations are decoupled. Differential equations of deflection, rotation angle and damage, together with their general solutions, are presented. Analytic expressions of deflection, rotation angle, and damage are obtained under different boundary conditions. As numerical examples, curves of deflection, rotation angle and damage under a uniform load are given. The influence of damage on the mechanical property of the beam is investigated.