2018 Vol. 39, No. 12

Display Method:
Understanding of GUO Yonghuai From the Collected Works of GUO Yonghuai
2018, 39(12): 1323-1330. doi: 10.21656/1000-0887.390293
Abstract(1211) HTML (120) PDF(688)
The Collected Works of GUO Yonghuai vividly reproduces a great deal of the academic characteristics and the spiritual outlook of GUO Yonghuai. They are respectively “the PLK method, the upper critical Mach number and shock waves” of “applied mathematics, fluid mechanics and gas dynamics”, and “the combination of enthusiasm and sobriety, the pioneering spirit and the constant perfection” of “the rigorous scholarship, the superhuman courage with insight and the taking great pains”. At just the 50-year anniversary of his heroic sacrifice for P.R. China, we are more deeply touched in reading the Collected Works of GUO Yonghuai again and should always cherish the memory of GUO Yonghuai.
Computation of High-Order Moments of Structural Dynamic Characteristics Based on Polynomial Chaos Expansion
WAN Huaping, TAI Yonggan, ZHONG Jian, REN Weixin
2018, 39(12): 1331-1342. doi: 10.21656/1000-0887.390165
Abstract(1102) HTML (71) PDF(811)
Uncertainty of structural parameters leads to uncertainty of structural dynamic characteristics. Quantification of uncertainty of dynamic characteristics provides accurate dynamic information for structural dynamic analysis. Statistical moments (e.g., mean and variance) mainly represent the uncertainty of structural dynamic properties. The MonteCarlo simulation (MCS) requires a large number of model evaluations to ensure the convergence of the results, which hinders its application to the largescale, complex engineering structures. The polynomial chaos expansion (PCE) surrogate model was used to replace the computationally expensive finite element model (FEM), and then the statistical moments of structural dynamic characteristics were efficiently calculated. The presented PCEbased method only needs a small set of model runs before the model formulation and subsequently does not require the FEM for calculations of the statistical moments. Therefore, the issue of the high computational cost associated with the computations of dynamic characteristic statistical moments was solved. The method is suitable for parameters with arbitrary probability distribution and has high computational efficiency in calculating the highorder statistical moments. Finally, the effectiveness of the developed method was verified through an example of an aluminum plate.
A Cumulative Residual Entropy Method in Selection of Random Load Distributions
YANG Yu, LIANG Yingjie, CHEN Wen
2018, 39(12): 1343-1350. doi: 10.21656/1000-0887.390157
Abstract(686) HTML (77) PDF(675)
A cumulative residual entropy method was proposed to select the most suitable statistical distribution for the random load based on the Lévy stable distribution. In this method, the cumulative distribution and the tail distribution of the water level were fitted with the candidate distributions, and the cumulative residual entropy and the corresponding relative distances between the estimated distribution and the real distribution were respectively calculated, where the smaller the relative distance is, the more accurate the candidate distribution will be. The proposed method was validated by the upstream and downstream water levels of the Yongji 2nd sluice gate. The results show that, the Lévy stable distribution has the highest accuracy compared with the normal and the extreme value type I distributions in describing the heavy tail of the water level. The relative distances between the cumulative entropy and the cumulative residual entropy reveal that the fitting errors of the Lévy stable distribution are the smallest. Thus, based on the Lévy stable distribution, the cumulative residual entropy method is effective in selection of the distribution of the random load, which provides new ideas for the selection of random load distributions, and helps accurately calculate the reliability of engineering structures.
Analysis of Shear Lag Effects in Box Girders Based on Abstract Warping Displacement Functions
YAO Xiaodong, ZHANG Yuanhai
2018, 39(12): 1351-1363. doi: 10.21656/1000-0887.390142
Abstract(732) HTML (68) PDF(587)
In view of the shear lag problem in thin-walled box girders, based on the abstract warping displacement functions, the form of the control differential equation was studied. The basic form of the shear lag warping displacement function was constructed. The correction coefficient of the boundary constraint influence on the flanges was introduced, and then the control differential equation of shear lag was deduced under the energy variational principle. According to the finite element results, the value of the boundary constraint correction coefficient for the flanges was determined. A simply supported box girder with flanges was calculated and analyzed under uniform and concentrated loads, respectively. The analytical results are in good agreement with the finite element results. Moreover, the flange stresses are less than the corresponding top plate stresses. The comparison verifies the correctness of the proposed analytical method.
Construction of General Analytic Functions With Finite Stress Concentration for Mono-Material Cracks and Bi-Material Interface Cracks
2018, 39(12): 1364-1376. doi: 10.21656/1000-0887.390030
Abstract(844) HTML (88) PDF(674)
The constructing methods for finite stress concentration analysis near the crack tip were summarized. The stress functions for plane problems with cracks were expressed with irrational or exponential functions. For the mono-material crack, with the crack length as the parameter, the direct weighted integration of the irrational-function-type analytic function was conducted to avoid stress singularity at the crack tip, and construct the finite stress concentration functions and the wedge-type opening displacement functions. The indirect integration of the exponential-function-type analytic function was suitable for the interface crack problem, but put the stress distribution within the integral interval into positive-negative inversion and irrational opening displacement shape, which can be improved through combining selection and superposition of different weight functions. The basic solutions for the central cracks and the symmetrical edge cracks were given in 6 stress states of plane stretching, shearing and bending, etc. The reason why the analytic function can avoid the stress singularity at the crack tip was given.
Contact Stress Analysis of Composite Launching Electromagnetic Rails
TIAN Zhenguo, AN Xueyun
2018, 39(12): 1377-1389. doi: 10.21656/1000-0887.380185
Abstract(750) HTML (102) PDF(780)
During the launching process of electromagnetic rails, the armature slides along the rails, and high-temperature friction occurs on the rail-armature interface, so the rail is liable to damages due to wear, erosion and strength loss. Thus, copper-based composite materials are used to enhance the strength and ablation resistance of the inner surface of the rail. The steel-copper composite electromagnetic rails were studied. While electrified, the armature and the rails constituted a closed loop, and a strong magnetic field formed between the rails, then the armature moved along the rails under the pushing force from the magnetic field. In this process, due to the interaction between the current and the magnetic field, a repulsive force acted between the 2 rails. At the same time, the armature was greatly heated by the strong current, and the thermal expansion of the armature brought extrusive forces on the lateral rails. According to this force condition, the composite rails were simplified as a mechanical model of double-layer beams under a uniformly distributed load and a rigid stamp force. The forces by the armature on the rail surface were solved and the stress state of the composite layers was obtained with the basic equations in the elastic half plane. Hence, the polynomial fitting of the copper-steel interfacial stress was got with the MATLAB software. The boundary conditions of the copper layer surface were determined, the local stresses of the copper layer surface were analyzed, and the relationships between the stress and the loading voltage, as well as the thickness ratios of composite layers, were acquired. The results provide a foundation for the strength design of composite launching electromagnetic rails.
Fracture Analysis on Multiferroic Composite Plates Under Concentrated Forces
2018, 39(12): 1390-1399. doi: 10.21656/1000-0887.390013
Abstract(826) HTML (115) PDF(858)
The fracture mechanics model was established for the interfacial fracture problem of a multiferroic composite plate under concentrated force on the outer face. The Fourier integral transform and Green’s functions were employed to obtain the Cauchy-type singular integral equations, which were further discretized into algebraic equations through the Labatto-Chebyshev collocation. The algebraic equations were numerically solved to determine the stress intensity factor (SIF). Analysis of the numerical results indicates that, the thickness of the piezoelectric layer, the crack length and the concentrated force location are 3 major factors to influence the stress intensity factor at the crack tip. The effects of physical and geometric parameters on the stress intensity factor in this model provide theoretical references for the anti-fracture optimal design of related composite materials in engineering.
Research on a Rumor Spreading Model With Media Coverage
ZHAO Min, CHEN Wenxia, SONG Qiankun
2018, 39(12): 1400-1409. doi: 10.21656/1000-0887.390137
Abstract(1042) HTML (79) PDF(941)
Combined with the impacts of positive media coverage and negative publicity, a new rumor spreading model was provided. With the stability theory for ordinary differential equations, the existence and global stability of the equilibrium point between rumor spreading and no rumor were discussed for the model, respectively. The correctness of the theoretical analysis was verified through numerical simulation. The research results provide corresponding countermeasures and suggestions for the governmental management in public opinion monitoring and crisis decision making.
Convergence of the Generalized Alternating Direction Method of Multipliers for a Class of Nonconvex Optimization Problems
2018, 39(12): 1410-1425. doi: 10.21656/1000-0887.380334
Abstract(690) HTML (68) PDF(859)
The generalized alternating direction method of multipliers (GADMM) for the minimization problems of the sum of 2 functions with linear constraints was considered, where one function was convex and the other can be expressed as the difference of 2 convex functions. For each subproblem in the GADMM, the linearization technique in the convex function difference algorithm was employed. Under the assumptions that the associated functions satisfy the Kurdyka-ojasiewicz inequality, the sequence generated with the GADMM converges to a critical point of the augmented Lagrangian function, while the penalty parameter in the augmented Lagrangian function is sufficiently large. At last, the convergence rate of the algorithm was established.
A Dynamic Differential Game Pricing Model for the Natural Gas Triopoly Market Based on Innovation Drive
LI Shengquan, LONG Denggao, ZHANG Rong
2018, 39(12): 1426-1442. doi: 10.21656/1000-0887.390164
Abstract(744) HTML (61) PDF(554)
The triopoly market of natural gas manufacturers was studied, and a dynamic differential game pricing model was established based on the cost reduction resulting from knowledge innovation and the response lag in the price reduction decision. Model analyses indicate that, when the period of knowledge innovation remains constant, enterprises can reduce costs by adjusting the input and output intensities of knowledge innovation and implement price strategies accordingly. With the variation of the input and output intensities of knowledge innovation, the Hopf bifurcation and a single Nash equilibrium point will emerge in the system. With continuous increases of the input and output intensities, the system will reach and maintain an equilibrium; with continuous decreases of the input and output intensities, the system will yield a periodic solution, the range of the periodic motion will expand, and the market will fall into a chaotic competitive state. Numerical simulations confirm the theoretically derived results. This study provides a reference for the natural gas manufacturers within the triopoly market to effectively implement innovationdriven strategies.