一种功能梯度Timoshenko梁的损伤识别方法

为了获得功能梯度材料的高精度损伤识别方法，本文基于动力学方法，通过对状态空间变量进行变量替换，求得了沿轴向指数分布的功能梯度Timoshenko梁的传递矩阵，通过分析裂纹对结构局部柔度的影响，采用扭转弹簧模拟裂纹对结构局部柔度的贡献，建立了功能梯度Timoshenko梁的表面裂纹传递矩阵，并且推导了复杂边界条件下多跨梁的理论模型。通过将非线性方程组转化为单一目标函数优化问题，并将增广拉格朗日算法与差分进化算法相结合对结构进行损伤识别。计算实例表明，本文提出的方法具有精度高、收敛快等特点，且适用于复杂边界条件下多损伤模型的损伤识别。

Damage identification method for functionally graded Timoshenko beams

To acquire high precision damage identification method for functionally graded materials, based on the state space variable replacement, the transfer matrix of the functionally graded Timoshenko beam along the axial exponential distribution is obtained. By analyzing the influence of crack on the local flexibility of structure, the contribution of the crack to the local stiffness of the structure is simulated by the torsion spring. The surface crack transfer matrix of functionally graded Timoshenko beams is established. And the theoretical model of multi-span beam under complex boundary conditions is derived. In this paper, the nonlinear equations are transformed into a single objective function optimization problem. The generalized Lagrange algorithm and differential evolution algorithm are combined to identify the damage of the structure. Computational examples show that the proposed algorithm has the characteristics of high precision and fast convergence and is suitable for damage identification of multi-damage model under complex boundary conditions.