This paper proposes a new force-displacement model for superelastic shape memory alloy (SMA) springs under complex loading and unloading. For the SMA wires used to make superelastic springs, a new multilinear constitutive model based on a modification of the 1D Motahari model is developed. In the modified model, the stress-strain relation curves are changed to fit the experimental results. Furthermore, the established force-displacement relationship of the springs considers the impact of not only the torque but also the moment on the cross sections of the SMA wires. Afterwards, a series of tension tests are performed on four NiTi helical spring specimens under various loading conditions. From the numerical simulations and experimental results, it is shown that, compared with the force-displacement curves for the SMA springs simulated by the Motahari model, those simulated by the proposed model can better approximate the experimental results. The new model inherits the advantage of simple computation of the multilinear constitutive model and can predict the force-displacement relation for superelastic SMA springs very well. Furthermore, due to the self-sensing properties of the SMA springs, the new model is very significant for establishing a new strategy for measuring the displacements or forces of SMA springs under complex loading and unloading.

With the quick development of transportation in China, long span cable-stayed bridges have been widely constructed to cross large rivers and deep canyons attribute to their unique structural forms and mechanical properties. For large-scale cable-stayed bridges, how to determine their basic dynamic characteristics or modal data is an important issue on the dynamic analysis of bridge structures. Noting the uncertainty of structural parameters or geometric shape, it is also of significance to find out the statistic dynamic characteristics of uncertain long span cable-stayed bridges. At the present paper, different from traditional low order perturbation stochastic approach, a high order perturbation stochastic FEM called as recursive stochastic finite element method was employed, which is a good practical approximation method compared to the Monte Carlo simulation method. Taking Edong Yangtze River Bridge as a research objective, the recursive stochastic finite element method was employed to solve the modal data of large span cable-stayed bridge with random parameters. Firstly, in the non-orthogonal polynomial presentation, natural frequencies and mode shapes of the random cable-stayed bridge were expressed. Then coefficients of the non-orthogonal polynomial expansion are able to be determined through high order perturbation technique. On the basis of the coefficients obtained, the probability density functions and statistic characteristics of the modal data were straightforward to implement. In accordance with detailed analyzations and discussions on the basic dynamic characteristics of the cable-stayed bridge, it can be found that the randomness of sectional flexural stiffness of the deck beam and bridge towers is very sensitive to many modes of Edong Yangtze River Bridge. However, the elastic stiffness simulating the pile-soil interaction has less influence on the in-plane modes.

This paper proposes a new type of energy dissipation brace system that is composed of superelastic Nitinol shape memory alloy (SMA) helical springs to reduce seismic responses of a frame structure. To investigate the earthquake-resistant effectiveness of the proposed brace system, a 2-story steel frame structural model was fabricated, and four SMA springs were trained in the laboratory. To describe the nonlinear force-displacement relationship of the SMA helical springs under general dynamic load, a mathematical model was developed based on a stress-strain relationship of SMA material, and the model agreed well with the test results. A numerical simulation model of the 2-story frame with the new energy dissipation brace system was then established to obtain the responses of the frame subjected to an earthquake. To verify the effectiveness of the numerical model, a series of vibration table experiments were carried out. The experimental results have very good agreement with the numerical simulation results, and the proposed brace system can effectively suppress structural vibrations. Compared with the steel spring brace and the viscous damper brace, the new energy dissipation brace can provide better vibration reduction effects, simultaneously reducing the displacement and acceleration responses of the frame. Considering its abilities of energy dissipation as well as fully recentering, the Nitinol SMA spring brace system has a great potential for frame structural vibration reduction.

This paper proposes a new damage identification approach for beam structures with stochastic parameters based on uncertain static measurement data. This new approach considers not only the static measurement errors, but also the modelling error of the initial beam structures as random quantities, and can also address static damage identification problems with relatively large uncertainties. First, the stochastic damage identification equations with respect to the damage indexes were established. On this basis, a new homotopy analysis algorithm was used to solve the stochastic damage identification equations. During the process of solution, a static condensation technique and a L1 regularization method were employed to address the limited measurement data and ill-posed problems, respectively. Furthermore, the definition of damage probability index is presented to evaluate the possibility of existing damages. The results of two numerical examples show that the accuracy and efficiency of the proposed damage identification approach are good. In comparison to the first-order perturbation method, the proposed method can ensure better accuracy in damage identification with relatively large measurement errors and modelling error. Finally, according to the static tests of a simply supported concrete beam, the proposed method successfully identified the damage of the beam.