一种Timoshenko裂纹梁的静力挠度分析方法

建立了一种Timoshenko裂纹梁的分析模型并且获得了闭合形式的挠度解析解。首先,在一致梁的理论框架下,通过引入δ函数模拟裂纹导致的局部柔度,建立用广义函数表示的Timoshenko裂纹梁的微分控制方程,进而得到挠度的闭合形式的解答;其次,根据线弹性断裂力学理论,利用转角及挠度突变与局部柔度系数的关系,建立Timoshenko裂纹梁的模型参数与裂纹深度的显式表示;最后,通过对裂纹深度与挠度、转角和曲率间关系的分析,总结了结构响应的损伤敏感性及其特征,并且通过与引入裂纹奇异单元的有限元结果进行比较,验证了本文所建分析模型及求解方法的正确性。研究结果表明,本文所建立的Timoshenko裂纹梁的分析模型,具有较高的计算精度和效率,在结构模型修正和损伤识别中具有良好的应用前景。

A Method for Static Deflection Analysis for Cracked Timoshenko Beam

An analysis model of cracked Timoshenko beam was proposed and the closed form solution of the deflection is obtained in the paper.Firstly,in the framework of the consistent beam theory,the Dirac δ function was adopted to simulate the local flexibility caused by the crack.The differential governing equation of the cracked Timoshenko beam was built by using of the generalized functions,and then the deflection was deduced in a closed form.Secondly,according to the linearly elastic fracture mechanics,the model parameters of the cracked Timoshenko beam were derived from the relationship between the crack depth and the sudden changes in the deflection and slope.Finally,the effects of crack depth on the deflection,slop and curvature were analyzed,and the damage sensitivity of the structural responses was studied.Meanwhile,the numerical simulation was carried out by introducing the singular crack element into the FE analysis.The numerical simulations were compared with the analysis solution to validate the proposed approach for cracked Timoshenko beam.The results demonstrate that the proposed model and solutions are accurate and efficient,which has promising feasibility in structural model updating and damage identification.