A Study On Damage Identification Of Functionally Graded Timoshenko Beam And Higher Order Shear Beam Structures On Modal Strain Energy And Genetic Algorithm

Functional Gradient Material(FGM),as a new type of material with excellent properties,which continuously changed in a certain direction along the space by different material components,and the macroscopic properties of the material are continuously changed.Functional gradient materials have been further developed and applied in aerospace,civil engineering,energy,sensors,optoelectronics and many other areas.The existing structure and functionally graded material structure are influenced by external conditions which would lead to the structure damage,reliability degradation,and even results in accidents during its service.Therefore,it is necessary to timely motore the health status of the structure and to identify the early damage of the structure in order to take effective measures,which is of great significance to the national economy and safety.In this paper,the explicit integral expression of the element stiffness matrix and the mass matrix based on the functional gradient Timoshenko beam and the high-order shear beam finite element scheme is firstly deduced.Then,the functional gradient Timoshenko beam and high-order shear beam are used to study the sensitivity of the beam structure parameters by a direct algebraic method(element modal strain energy method)and an indirect algebra method.The influences of different boundary conditions and noise on sensitivity coefficient are further analysised.Aiming at the functionally gradient Timoshenko beam and higher order shear beam,the damage identification equations is deduced based on the element modal strain energy method.The Tikhonov regularization and genetic algorithm are introduced to solve the damage equations.The effects of damage location,damage degree,gradient index,boundary condition and noise on the results are analyzed.The numerical examples show that the method can effectively identify the damage position and damage degree of the function gradient Timoshenko beam and the higher order beam.The function gradient higher order shear beam is difficult to identify at the boundary.Under different boundary conditions,the cantilever beam is the most difficult to be identified.Under the noise condition,the deviation coefficient of the two beams is small,which indicates that the method has certain anti-noise ability.According to the uncertain factors in engineering practice,the theory of probability and statistics is introduced to identify the damage.Considering the existence of model error and measurement error,structural damage is identified by the change of the probability density of the element before and after the damage.Probabilistic statistical damage identification equations are also an inverse problem solving,which are solved by L-curve method and singular value truncation method respectively.The effects of different damage degree,damage position,gradient index and boundary condition and noise on the recognition result are analyzed.The numerical results show that the L-curve method is more effective than the singular value truncation method.The singular value truncation method is prone to misinterpretation and misjudgment of the two kinds of beams.Probability statistical identification method is better for the uncertainty analysis,the greater the degree of damage,the better the recognition effect,and has a certain anti-noise ability.