Search

In this paper, we present a preconditioned general two-step modulus-based iteration method to solve a class of linear complementarity problems. Its convergence theory is proved when the system matrix A is an H+-matrix by using classical and new results from the theory of splitting. Numerical experiments show that the proposed methods are superior to the existing methods in actual implementation.

A novel dual proof mass accelerometer is proposed by introducing mode localization in two electrostatically coupled resonators. The levering mechanism is utilized to amplify the inertial force applied axially to the two weakly coupled resonators. The dynamic model considering the electrostatic and mechanical nonlinearities is established and solved by the method of multiple scales, and also is validated by the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). The linear and nonlinear sensitivities depicted as the difference of relative shift of amplitude ratio are investigated as well as the main influencing factors. It has been found that linear sensitivity is up to 4 orders of magnitude higher than that expressed by the difference of relative frequency shift. Also, the nonlinear sensitivity is further increased by 1.47 times comparing to the linear sensitivity. Moreover, the resolution is also greatly improved when the sensor is driven beyond its critical amplitude. Finally, the effect of the electrostatic coupling on the sensing performances is explored, and the optimal coupling voltage is theoretically identified at the limit of mode aliasing.

A detailed FE model for analysis of overturning of concrete box-girder bridge with single-column piers was developed and the failure process was discussed in the presented paper. The result shows that the reason for overturning failure is the non-uniform compression deformation of the loading-side bearing caused by the eccentric external load, which then leads to a large rotating angel of supper structure. Once the friction force between Teflon plate and steel plate in the bearing cannot carry the diagonal component caused by the gravity load and external load, the sliding failure occurs. Based on the simplified mechanical analysis, the condition that bridge overturning occurs is that the tangent value of the rotating angle of box girder is greater than the friction coefficient between Teflon plate and steel plate in rubber bearing.

Longitudinal crack in bottom flange is one of the most common defects in concrete box girder bridges. This paper focuses on the influence of the longitudinal cracks on the mechanical properties of box girder using numerical method. Smear crack model and strain softening model was employed to simulate cracking process. Parameter analysis was also carried out to study the effect of length, crack depth and amounts of cracks in bottom flange. The results indicate longitudinal cracks in one span have a significant effect on the transverse stress and deflection, but have little effect on the other spans. The negative effects of longitudinal cracks increase with the crack length and depth. When the crack length is up to 10% of the girder span, the deflection of the span amplifies to 13%. Compared with the length and depth, the amounts of cracks don’t have much influence on the deformation of girder but affect stress.

A numerical method is proposed to study load and the environment couple effect during the service of a concrete bridge. By studying the corrosion process of reinforcement bars, the strain of the bars is decomposed into two parts, elastic strain and corrosion strain, and their ratio is defined as the corrosion factor. The time-dependent constitution of corrosion of the steel bar is obtained by introducing a nominal elastic module. According to the virtual work principle, the finite element formulation of the reinforcement concrete element is derived, and the computation sequence determined using the time history method is illustrated. The nonlinear finite element program is realized by the Fortran program to numerically solve the problem, which is verified by testing a model of three reinforced concrete beams. The results show that both stiffness matrix and the additional nodal load of the reinforcement concrete element should be considered in the couple effect analysis. The proposed method can be used to predict long-term mechanical properties of concrete bridges.

Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system and the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of beams generated by Gaussian mirror resonator passing through FRFT optical systems have been studied in detail, and some typical numerical examples are given to compare the results obtained by the approximate analytical method with those by the numerical integral method, and it is shown that our method can significantly improve the numerical calculation efficiency. Further, the results indicate that the normalized intensity distributions in the FRFT plane are closely related to the fractional order, truncation parameter and initial beam parameters. The variation period of normalized intensity distributions with p is 2 whatever the value of the truncation parameter δ is.

Based on fixed point theorems for monotone and mixed monotone operators in a normal cone, we prove that the nonlinear matrix equation X - ∑ i = 1 m A i ∗ X δ i A i = Q ( 0 | δ i | 1 ) always has a unique positive definite solution. A conjecture which is proposed in [X.G. Liu, H. Gao, On the positive definite solutions of the matrix equation X s ± A T X - t A = I n , Linear Algebra Appl. 368 (2003) 83–97] is solved. Multi-step stationary iterative method is proposed to compute the unique positive definite solution. Numerical examples show that this iterative method is feasible and effective.

The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution of T-S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor-corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition, determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T-S wave was studied. The nonlinear nonparallel results of examples compare with data of direct nemerical simulations (DNS) using full Navier-Stokes equations.