2015 Vol. 36, No. 6

Display Method:
Latest Advancements of the Bridging Model Theory
HUANG Zheng-ming
2015, 36(6): 563-581. doi: 10.3879/j.issn.1000-0887.2015.06.001
Abstract(1024) PDF(1175)
In order to predict the strength of a composite only based on the mechanical properties of its constituent fiber and matrix materials measured independently, 3 challenging problems must be resolved with high success rate. First, internal stresses in the fiber and matrix must be accurately evaluated. Second, efficient failure detection of the composite in terms of the internal stresses, i.e., the micromechanical strength theory, must be achieved. Last but not the least, the input data of in-situ strengths of the matrix, which can hardly be measured through experiments, must be correctly determined according to its original counterparts available independently. Each of these problems is by no means easy to deal with. This is why the prediction of composite strength is extremely difficult. The bridging model, originally established by HUANG Zheng-ming and further developed to a powerful theory, presents a systematic approach towards solving all of the 3 problems. This paper briefly summarizes the theory by focusing on some of the latest advancements. A number of further research topics are also highlighted in the paper.
Random Seismic Analysis of Multi-Supported Pipelines Subjected to Spatially Varying Ground Motions
LI Yu-yin, ZHANG Ya-hui
2015, 36(6): 582-592. doi: 10.3879/j.issn.1000-0887.2015.06.002
Abstract(659) PDF(818)
An analytical method was formulated for the random seismic analysis of multi-supported pipelines subjected to spatially varying ground motions. With the pseudo-excitation method, the stationary random seismic responses were proven to be represented in terms of deterministic responses of pipelines under multi-support harmonic excitations. The harmonic responses were expressed as a series of harmonic functions with undetermined coefficients, which could be solved with the appropriate boundary and compatibility conditions. In comparison with the quasi-static decomposition method, the present method is derived analytically without computation of the structural normal modes and quasi-static components. The high accuracy and efficiency of the present method is verified through its application to an exemplary 6-span pipeline and the comparison of results made with those from the quasi-static decomposition method.
Stochastic Bifurcations in a Duffing System Driven by Additive Dichotomous Noises
WU Juan, XU Yong
2015, 36(6): 593-599. doi: 10.3879/j.issn.1000-0887.2015.06.003
Abstract(635) PDF(758)
The stochastic bifurcations in a Duffing system driven by additive dichotomous noises were investigated. Firstly, the transition probability of the dichotomous noise states was deduced according to its statistical properties and then the dichotomous noise was simulated numerically. Secondly, the stationary joint probability density of the system displacement and speed and the stationary probability density of the displacement were calculated with the 4th-order Runge-Kutta algorithm. Then, through the study of the variation between unimodality and bimodality of the stationary probability density of the system displacement, it is found that specific states and certain intensity values of the additive dichotomous noise may induce stochastic bifurcations. Lastly, it is also observed that stochastic bifurcations may occur with the variations of the system asymmetric parameters.
Shear Deformable Bending of Carbon Nanotubes Based on a New Analytical Nonlocal Timoshenko Beam Model
YIN Chun-song, YANG Yang
2015, 36(6): 600-606. doi: 10.3879/j.issn.1000-0887.2015.06.004
Abstract(904) PDF(827)
According to Hamilton’s principle, a new mathematical model was established and the analytical solutions to the nonlocal Timoshenko beam model (ANT) were obtained based on the nonlocal elastic continuum theory in view of shear deformation and nonlocal effects. The new ANT equilibrium equations and boundary conditions were derived for bending analysis on carbon nanotubes (CNTs) of simply supported, clamped and cantilever types. The ANT deflection solutions demonstrate that the CNT stiffness is enhanced by the presence of nonlocal stress effects, as is predicted by the widely accepted but complicated molecular dynamics model and proved by tests. Furthermore, the new ANT model indicates verifiable bending behaviors of a cantilever CNT with point load at the free end, which depends on the magnitude of nonlocal stress. Therefore, this new model conveniently gives better prediction about the mechanical performances of nanostructures.
Effects of Surface Stresses on Contact Problems of an Elastic Half Plane With a Circular Cavity
OU Zhi-ying, WU Ya-wen
2015, 36(6): 607-615. doi: 10.3879/j.issn.1000-0887.2015.06.005
Abstract(683) PDF(781)
In view of the importance of surface stress in controlling mechanical responses of nanoscale structures, the effects of surface stresses on the elastic field around a circular hole in an elastic half plane were analyzed. The complex variable function method was adopted to derive the fundamental solution to the contact problem. The deformation caused by the uniformly distributed traction on the plane surface and the surface stress along the cavity boundary was analyzed in detail. The results reveal strong sizedependence of the stress field and the surface deformation on the surface stress, and the surface displacement directly above the circular hole was a function of the surface stress.
Numerical Simulation of 3D PTT Droplet Impact Onto Solid Surface With an Improved Smoothed Particle Hydrodynamics Method
XU Xiao-yang, PENG Yan, DENG Fang-an
2015, 36(6): 616-627. doi: 10.3879/j.issn.1000-0887.2015.06.006
Abstract(794) PDF(680)
Based on an improved smoothed particle hydrodynamics (SPH) method, the spreading deformation of 3D PTT droplets impacting onto solid surface was numerically simulated. In order to prevent the fluid particles from crossing the suface, an improved treatment technique for the suface boundary was proposed, which can drastically reduce the consumed CPU time for 3D numerical simulation. Furthermore, an artificial stress term was added to the momentum equation to remove the socalled tensile instability. The dynamic processes of 3D PTT droplets impacting onto solid surface were numerically simulated with the improved SPH method. The different flowing features between the Newtonian and PTT fluid droplets during impacting were discussed. The effects of the elongational parameter on the collision behavior were analyzed in detail. The simulation results demonstrate that the improved SPH method can effectively describe the rheological characteristics of 3D PTT droplets impacting onto solid surface.
Thermal Analysis and Optimization of Structural Parameters for Dry Gas Seal Rings
WANG Yan-zhong, PU Tian-xin, HUANG Rong-yin, NING Ke-yan, HAN Ming
2015, 36(6): 628-638. doi: 10.3879/j.issn.1000-0887.2015.06.007
Abstract(858) PDF(641)
Leakage is the primary failure form of the dry gas seal, while the end face of the seal ring makes the main leaking channel. For some specific conditions, based on the relationships between the structural parameters and the gas film properties of the seal ring, the methods of finite element simulation and orthogonal optimization were used to select a better combination of the seal ring end face structural parameters. In addition, the steady-state heat distribution of the seal ring was simulated. On the basis of that, the thermal deformation of the seal ring was computed to explore the relationships between the material parameters and the sealing properties of the seal ring. The research results show that, except the elastic modulus, the thermal conductivity, Poisson's ratio and thermal expansion coefficient are all in a quasi-linear relationship with the thermal deformation of the seal ring. The work has guiding significance and reference value for the design and optimization of dry gas seal rings.
Study on a Class of Diffusion Models for Dust Plasma in Atmosphere
FENG Yi-hu, SHI Lan-fang, XU Yong-hong, MO Jia-qi
2015, 36(6): 639-650. doi: 10.3879/j.issn.1000-0887.2015.06.008
Abstract(881) PDF(840)
A class of nonlinear diffusion equation initial value problems about dust plasma diffusion in atmosphere were investigated. Firstly, the exact solution to the non-disturbed dust plasma diffusion equation was obtained with the Fourier transformation method. Then a homotopic mapping was introduced and an initial approximate function was chosen to find out successively the arbitrary-order approximate analytic solutions to the disturbed initial value problems according to the homotopic mapping theory again. Next, the fixed point theory was applied to make clear validity of the approximate analytic solutions and determine their respective degrees of approximation. In the 2 examples, simulation curves and tables were given to make comparison between the exact solution and the various-order approximate ones. Finally, the physical sense of the approximate solutions obtained with the homotopic mapping method was analyzed simply and their easy application and high accuracy were examined.
Existence and Hadamard Well-Posedness of Solutions to Generalized Strong Vector Quasi-Equilibrium Problems
ZENG Jing, PENG Zai-yun, ZHANG Shi-sheng
2015, 36(6): 651-658. doi: 10.3879/j.issn.1000-0887.2015.06.009
Abstract(770) PDF(791)
Under the conditions of naturally quasi C-convexity of -f(·,y,u) and upper (-C)-continuity of f, an auxiliary function was constructed and an existence theorem for solutions to generalized strong vector quasi-equilibrium problems (for short, GSVQEPs) was established based on a method of proof other than the traditional ones, without the assumption that the dual of the ordering cone has a weak* compact base. Moreover, a definition of problem sequence convergence was given and the upper semi-continuity of solution set mappings was obtained under some proper conditions. Based on these results, a concept of Hadamard-type well-posedness for GSVQEPs was introduced and the sufficient conditions for that Hadamard well-posedness was proposed.
Bivariate Osculatory Rational Interpolation on Rectangular Grids
2015, 36(6): 659-667. doi: 10.3879/j.issn.1000-0887.2015.06.010
Abstract(823) PDF(739)
The bivariate osculatory rational interpolation is an important element of rational interpolation, and reducing the degrees of the osculatory rational interpolation functions and solving their existence make an important problem. The bivariate osculatory rational interpolation algorithms mostly have conditional feasibility and massive computational complexity with high function degrees. A bivariate osculatory rational interpolation algorithm was obtained on rectangular grids and extended to vector-valued cases, with the method of bivariate Hermite interpolation basis function in view of the error characteristics of bivariate polynomial interpolation. The numerical examples illustrate that, compared to other methods, the feasibility of the presented algorithm is unconditional, the degrees of the related rational functions are lower, and the algorithm has less computational complexity.
Optimality Conditions for Proximal Proper Efficiency in Multiobjective Optimization Problems
LI Xiao-yan, GAO Ying
2015, 36(6): 668-676. doi: 10.3879/j.issn.1000-0887.2015.06.011
Abstract(954) PDF(903)
First, linear scalarization of the proximal proper efficient points to a closed set was presented under the generalized convexity assumption, and the equivalency among the proximal proper efficiency, Benson proper efficiency and Borwein proper efficiency in multiobjective optimization problems was proved. Second, the optimality conditions for multiobjective optimization problems were obtained through application of these results to the problems. Finally, the fuzzy optimality conditions for the proximal proper efficient solutions were given with the proximal subdifferential.