By considering the tightening process, a three-dimensional elastic finite element analysis is conducted to explore the mechanism of bolt self-loosening under transverse cyclic loading. According to the geometrical features of the thread, a hexahedral meshing is implemented by modifying the node coordinates based on cylinder meshes and an ABAQUS plug-in is made for parametric modeling. The accuracy of the finite element model is verified and validated by comparison with the analytical and experimental results on torque-tension relationship. And, then, the fastening states acquired by different means are compared. The results show that the tightening process cannot be replaced by a simplified method because its fastening state is different from the real process. With combining the tightening and self-loosening processes, this paper utilizes the relative rotation angles and velocities to investigate the slip states on contact surfaces instead of the Coulomb friction coefficient method, which is used in most previous researches. By contrast, this method can describe the slip states in greater detail. In addition, the simulation result reveals that there exists a creep slip phenomenon at contact surface, which causes the bolt self-loosening to occur even when some contact facets are stuck.

In this article, a combined approach of the radial integration boundary element method (RIBEM) and the precise integration method is presented for solving transient heat conduction problems with variable thermal conductivity. First, the system of ordinary differential equations on the boundary integral equation can be obtained by the RIBEM. Then, the precise integration method is adopted to solve the system of ordinary differential equations. Finally, three numerical examples are presented to demonstrate the performance of the present method. The results show that the present approach can obtain satisfactory performance even for very large time-step size.

The expensive computational cost is always a major concern for reliability-based design optimization (RBDO) of complex problems. The performance of RBDO can be lowered by the inaccuracy of reliability analysis (RA) which is caused by multiple local optimums and multiple design points in highly non-linear space. In order to reduce the computational burden and guarantee the accuracy of RA (and thus to improve the RBDO performance), a global RBDO algorithm by adopting an improved constraint boundary sampling (GRBDO-ICBS) method is proposed. Specifically, the GRBDO-ICBS method first narrows the concerned search region by using a Kriging-based global search. The accuracies of the design points are verified by the expected risk function (ERF), and the corresponding inaccurate design points are added into training samples to update Kriging. Then a multi-start gradient-based sequential RBDO is carried out, which tries to find out all multiple design points in the concerned search region. The performance of GRBDO-ICBS is demonstrated by four examples. All results have shown that the proposed method can achieve similar accuracy as Monte Carlo simulation (MCS)-based RBDO but with a much lower computational cost.