Due to the complexity involved and limited study on the topic, the equivalent static method, adopted in the current codes for structural design of bridges under ship collisions, does not take into account the dynamic amplification effect correctly. In this article, impact factor method is proposed to estimate the response of bridge’s piers and foundations, as a better alternative of the equivalent static method. Through refined numerical simulations of ship-rigid wall collisions for nine typical ships under various impact velocities, 81 impact force time-histories are obtained. The period-dependent impact factor is defined, and empirical function of it is proposed and parameters in the empirical function are determined by the 81 sample impact force time-histories. Finally, both impact factor method and dynamic time-history method are used to estimate the responses of piers and foundations of two example bridges, and the precision of impact factor method is discussed.

Far-infrared (FIR) is considered to be an ideal method to promote fatigue recovery due to its high permeability and strong radiation. In this paper, we report a flexible and wearable graphene heating device to help fatigue recovery of human exercise by using its high FIR divergence property. This study compares two different fatigue recovery methods, graphene far-infrared heating device hot application and natural recovery, over a 20 min recovery time among the male colleges’ exhaustion exercise. Experimental results show that the achieved graphene device holds excellent electro-thermal radiation conversion efficiency of 70% and normal total emissivity of 89%. Moreover, the graphene FIR therapy in our work is more energy-efficient, easy to use, and wearable than traditional fatigue recovery methods. Such an anti-fatigue strategy offers new opportunities for enlarging potential applications of graphene film in body science, athletic training recovery, and wearable devices.

Moment method is famous for its calculation efficiency. Moments of the performance function are obtained by point estimates based on Hermite Integration. The reliability index and probability of failure can be obtained using existing standardization function or existing distribution systems. The precision of moment method increases monotonously with the increasing number of estimating points. The performance functions with non-differentiable points are frequently encountered when elasto-plastic behavior dominates for a structure under loading. Thus the accuracy and efficiency of moment method should be addressed for performance functions with non-differentiable points. In this paper, an example of structural performance functions is presented to show the existence of non-differentiable points. Two example performance functions are used to verify the accuracy and efficiency of moment method. The MCS method is employed to obtain the accurate results of probability of failure. The relative errors of probability of failure from moment method are obtained through a comparison with the results from MCS method. The fluctuation of the relative errors with the number of estimate points is also presented. The required number of estimate points for performance functions with non-differentiable points is discussed through the above two examples. Finally, criteria to determine the estimate points for performance functions with non-differentiable points are proposed and verified the applicability.