本文選題：功能梯度梁式結(jié)構(gòu)　切入點：Timoshenko梁　出處：《廣西大學》2017年碩士論文　論文類型：學位論文

【摘要】：功能梯度材料(FGM)作為一種性能獨特優(yōu)良的新型材料,由不同材料組分在宏觀上沿空間某一方向呈梯度非均勻連續(xù)變化,其材料的宏觀性能也呈連續(xù)變化。功能梯度材料在航空航天、土木工程、能源、傳感器、光電等眾多領(lǐng)域得到了進一步發(fā)展和應用�，F(xiàn)役結(jié)構(gòu)和功能梯度材料結(jié)構(gòu)在服役過程中由于受到外界條件作用導致結(jié)構(gòu)發(fā)生損傷,可靠度下降,甚至導致事故發(fā)生,因此在工程中需及時評定結(jié)構(gòu)的健康狀況,識別出結(jié)構(gòu)早期損傷從而采取有效措施,這對國民經(jīng)濟和安全均具有重要意義。本文首先在前人對功能梯度Timoshenko梁和高階剪切梁的有限元格式基礎(chǔ)上,推導出單元剛度矩陣和質(zhì)量矩陣的顯式積分表達式,然后以功能梯度Timoshenko梁和高階剪切梁為研究對象引入直接代數(shù)法(單元模態(tài)應變能法)和間接代數(shù)方法對梁結(jié)構(gòu)參數(shù)靈敏度進行探討并進一步分析不同邊界條件和噪音對靈敏度系數(shù)的影響。針對功能梯度Timoshenko梁和高階剪切梁,基于單元模態(tài)應變能法推導出了損傷識別方程組,并引入Tikhonov正則化和遺傳算法對損傷方程組進行求解,分析了損傷位置、損傷程度、梯度指數(shù)、邊界條件和噪音對識別結(jié)果的影響。數(shù)值算例表明,該方法能較有效地識別出功能梯度Timoshenko梁和高階梁的損傷位置和損傷程度,功能梯度高階梁在邊界處較難識別;不同邊界條件下,兩端固定梁的識別效果最好,懸臂梁在邊界處較難識別;在噪音條件下,兩種梁的偏差系數(shù)均較小,說明該方法具有一定抗噪音能力。針對工程實際中的不確定性因素,引入概率統(tǒng)計識別理論進行損傷識別�？紤]模型誤差和測量誤差存在,在一定置信水平內(nèi)通過損傷前后單元概率密度變化識別出結(jié)構(gòu)損傷。概率統(tǒng)計損傷識別方程組同樣屬于反問題,分別采用L曲線方法和奇異值截斷法進行求解并對進行對比。分析了不同損傷程度、損傷位置、梯度指數(shù)以及邊界條件和噪音對識別結(jié)果的影響。數(shù)值算例結(jié)果表明:L曲線法比奇異值截斷方法效果更好,奇異值截斷方法對這兩種梁容易出現(xiàn)非損傷單元的干擾,易發(fā)生誤判和漏判。概率統(tǒng)計識別方法對于不確定性分析效果較好,損傷程度越大識別效果越好,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.
【學位授予單位】：廣西大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TB34

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