基于单元模态应变能和遗传算法功能梯度Timoshenko梁和高阶剪切梁的结构损伤识别研究

发布时间：2018-03-13 16:40

本文选题：功能梯度梁式结构　切入点：Timoshenko梁　出处：《广西大学》2017年硕士论文　论文类型：学位论文

【摘要】：功能梯度材料(FGM)作为一种性能独特优良的新型材料,由不同材料组分在宏观上沿空间某一方向呈梯度非均匀连续变化,其材料的宏观性能也呈连续变化。功能梯度材料在航空航天、土木工程、能源、传感器、光电等众多领域得到了进一步发展和应用。现役结构和功能梯度材料结构在服役过程中由于受到外界条件作用导致结构发生损伤,可靠度下降,甚至导致事故发生,因此在工程中需及时评定结构的健康状况,识别出结构早期损伤从而采取有效措施,这对国民经济和安全均具有重要意义。本文首先在前人对功能梯度Timoshenko梁和高阶剪切梁的有限元格式基础上,推导出单元刚度矩阵和质量矩阵的显式积分表达式,然后以功能梯度Timoshenko梁和高阶剪切梁为研究对象引入直接代数法(单元模态应变能法)和间接代数方法对梁结构参数灵敏度进行探讨并进一步分析不同边界条件和噪音对灵敏度系数的影响。针对功能梯度Timoshenko梁和高阶剪切梁,基于单元模态应变能法推导出了损伤识别方程组,并引入Tikhonov正则化和遗传算法对损伤方程组进行求解,分析了损伤位置、损伤程度、梯度指数、边界条件和噪音对识别结果的影响。数值算例表明,该方法能较有效地识别出功能梯度Timoshenko梁和高阶梁的损伤位置和损伤程度,功能梯度高阶梁在边界处较难识别;不同边界条件下,两端固定梁的识别效果最好,悬臂梁在边界处较难识别;在噪音条件下,两种梁的偏差系数均较小,说明该方法具有一定抗噪音能力。针对工程实际中的不确定性因素,引入概率统计识别理论进行损伤识别。考虑模型误差和测量误差存在,在一定置信水平内通过损伤前后单元概率密度变化识别出结构损伤。概率统计损伤识别方程组同样属于反问题,分别采用L曲线方法和奇异值截断法进行求解并对进行对比。分析了不同损伤程度、损伤位置、梯度指数以及边界条件和噪音对识别结果的影响。数值算例结果表明:L曲线法比奇异值截断方法效果更好,奇异值截断方法对这两种梁容易出现非损伤单元的干扰,易发生误判和漏判。概率统计识别方法对于不确定性分析效果较好,损伤程度越大识别效果越好,并具有一定的抗噪音能力。
[Abstract]:As a new material with unique and excellent properties, functionally graded materials (FGM) vary from different material components to gradient nonuniform and continuous in a certain direction of space macroscopically. The macroscopical properties of its materials also show continuous changes. Functionally graded materials are used in aerospace, civil engineering, energy, sensors, Many fields, such as optoelectronics, have been further developed and applied. In the course of service, the active structure and functionally graded material structure have been damaged by external conditions, and the reliability has been reduced, and even accidents have occurred. Therefore, it is necessary to assess the health status of the structure in time, identify the early damage of the structure and take effective measures. This is of great significance to national economy and safety. In this paper, the explicit integral expressions of element stiffness matrix and mass matrix are derived based on the finite element schemes of functionally gradient Timoshenko beams and high-order shear beams. Then direct algebraic method (element mode strain energy method) and indirect algebraic method are introduced to study the sensitivity of structural parameters of functionally graded Timoshenko beam and high order shear beam. Effect of noise on sensitivity coefficient. For functionally graded Timoshenko beams and high-order shear beams, Based on the strain energy method of element mode, the damage identification equations are derived, and Tikhonov regularization and genetic algorithm are introduced to solve the damage equations. The damage location, damage degree and gradient exponent are analyzed. Numerical examples show that the proposed method can effectively identify the damage location and damage degree of functionally graded Timoshenko beams and higher-order beams, and it is difficult to identify functionally graded high-order beams at the boundary. Under different boundary conditions, the identification effect of the fixed beam at both ends is the best, the cantilever beam is difficult to identify at the boundary, and the deviation coefficient of the two beams is smaller under the noise condition. It is shown that the method has certain anti-noise ability. In view of the uncertain factors in engineering practice, the probabilistic and statistical identification theory is introduced to identify the damage, considering the existence of model error and measurement error. In a certain confidence level, structural damage is identified by the change of unit probability density before and after damage. The system of probabilistic statistical damage identification is also an inverse problem. The L-curve method and singular value truncation method are used to solve and compare the results. The effect of gradient exponent, boundary condition and noise on the recognition results. The numerical results show that the ratio L curve method is more effective than the singular value truncation method, and the singular value truncation method is prone to the interference of the two kinds of beams. The probability and statistics identification method is more effective for uncertainty analysis, the greater the degree of damage is, the better the recognition effect is, and it has a certain ability to resist noise.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB34

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