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Summary
The extended Kalman filter (EKF) is a powerful tool used to assess structural damage in the time domain. A method combining EKF and l2‐norm regularization, such as Tikhonov regularization, is found to improve the solution of ill‐posed inverse problems. However, the l2‐norm regularization process may lead to an over‐smooth damage identification solution, which is contradictory to the sparse and concentrated distribution of local damages. This paper presents a new damage identification algorithm based on EKF with l1‐norm regularization via free vibration responses. The l1‐norm regularization item is used to enhance the identification accuracy of local damages while restraining the interference of measurement noise. Afterward, the constrained minimization problem is solved by EKF endowed with a pseudomeasurement equation. The numerical and experimental examples confirm that the proposed algorithm shows good robustness and excellent accuracy of damage identification with the unknown initial structural state.
A numerical study on the role of microstructure in the thermomechanical behavior of shape memory alloy (SMA) composites under uniaxial tension is performed. The simulation is based on the micromechanics model established recently by the authors. The influence of the shape and volume fraction of SMA on the overall behavior of the composite as well as on the internal stress and strain evolution is investigated. The strengthening effect of SMA on ductile matrix is illustrated. The obtained results demonstrate several interesting features of the new composite and may serve as a quantitative basis for the microstructure design of this composite in the future.
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