2016 Vol. 37, No. 3

Display Method:
A Thought about the Development of Applied Mathematics in China
ZHONG Wan-xie
2016, 37(3): .
Abstract(783) PDF(973)
A Nonorthogonal Constitutive Model for Woven Composites Involving Biaxial Tension Coupling
ZHANG Bi-chao, PENG Xiong-qi, HUANG Xiao-shuang
2016, 37(3): 227-234. doi: 10.3879/j.issn.1000-0887.2016.03.001
Abstract(819) PDF(801)
Based on the continuum mechanics theory, a nonorthogonal constitutive model for woven composites involving biaxial tension coupling was developed. The biaxial tension coupling effects of the composite fabric were introduced into a previously built nonorthogonal constitutive model, and the method to identify the material parameters in the constitutive model was provided. In the fitting of experimental data from the uniaxial tensile test, the biaxial tensile test at different stretch ratios and the bias extension test, the model parameters were obtained. The present model was validated through comparison between the numerical results and the experimental data out of a biaxial tensile test and a doubledome stamping test, which indicated that the model was reliable to characterize the highly nonlinear and strongly anisotropic mechanical behaviors of the composite fabric in large deformation. The new model has the merits of accurate results and easy determination of material parameters, making a theoretical foundation for the numerical simulation and optimization of the woven composite forming process in the future.
The Variational Principle for Multi-Layer Timoshenko Beam Systems Based on the Simplified
XU Xiao-jian, DENG Zi-chen
2016, 37(3): 235-244. doi: 10.3879/j.issn.1000-0887.2016.03.002
Abstract(1049) PDF(684)
The mechanical properties of member materials exhibit notable size effects when the characteristic sizes of the members are comparable to their instinct length parameters. A variational formulation of the nanosize multi-layer Timoshenko beam problem was developed via the semi-inverse method within the context of the simplified strain gradient theory. This method was fit for determining all the possible low-order and high-order boundary condtions directly from the governing equations of the system, according to the minimum total potential energy principle. In turn, the Rayleigh solutions of buckling load and free vibration frequencies of the simply supported beam system were given. The numerical simulations indicate the prominent effects of the instinct length parameters and aspect ratios on the free vibration frequencies of the double-layer beam systems. As a possible benchmark for the later numerical studies with the transfer matrix method or the finite element method, the present Rayleigh solutions of buckling load and free vibration frequencies of the multi-layer beam systems will make good sense.
Characterization of the tool-part interaction during the curing of CFRP composites
SUN Liang-liang, WANG Ji-hui, DING An-xin
2016, 37(3): 245-255. doi: 10.3879/j.issn.1000-0887.2016.03.003
Abstract(777) PDF(475)
Experiments with fiber bragg grating (FBG) sensors and the related theoretical model were used to study the toolpart interaction during the curing of carbon fiber reinforced polymer (CFRP) composites. The results show that on the condition of using release agent, the sliding friction and sticking force exist simultaneously between the tool and the part. After curing, temperature drop causes different degrees of deformations in the part and in the tool, therefore the sticking force rises and finally reaches a limit value to trigger the debonding process. The debonding area first occurs at the ends of the part, then moves to the part’s center along the tool’s length direction. The thermal expansion coefficient difference between the part and the tool makes the main cause for the interfacial friction and the part’s deformation.
Numerical research of temperature field during resin transfer molding
SHI Fei, CHENG Xiao-min, ZHANG Tao-jie, DONG Xiang-huai
2016, 37(3): 256-265. doi: 10.3879/j.issn.1000-0887.2016.03.004
Abstract(685) PDF(566)
The temperature field is the most important concern during resin transfer molding of resin-based composite materials. The temperature field deciding the molding process and product quality was investigated through numerical simulation. Some factors influencing the temperature field, such as porosity of the porous media, resin reaction heat, resin injection temperature and resin injection flux, were discussed. In the simulation the 3D 1st-order upwind scheme was applied for spatial discretization, and the implicit scheme was used for time integration. Comparison between the present results and those previous ones proves the correctness and effectiveness of the proposed numerical method. It is also shown that, the resin injection temperature influences the temperature field much more markedly than the other factors, and the factors’ effects on the part near the resin inlet are much weaker than those on the parts far away from the inlet, which means more temperature measure points shall be arranged in the zones far away from the inlet to better detect the real temperature field.
Stress relaxation properties and the prediction models for PTFE membranes
XU Shan-shan, ZHANG Ying-ying, ZHANG Qi-lin
2016, 37(3): 266-276. doi: 10.3879/j.issn.1000-0887.2016.03.005
Abstract(998) PDF(595)
With the PTFE membranes as the research object, the uniaxial stress relaxation tests were carried out respectively under 5 temperatures (23, 40, 50, 60, 70 ℃) and at 4 initial tensile rates (2, 5, 10, 20 N/s), and the effects of these 2 kinds of factors on the stress relaxation properties of the membranes were investigated. The variations of the relaxation moduli were got and several existent viscoelastic constitutive models were used to fit the experimental data. The results show that, the PTFE membranes exhibit obvious stress relaxation behaviors. Both the temperature and the initial tensile rate have significant effects on the stress relaxation characteristics. The membrane stress relaxation rate decreases while the final steady stress increases with the temperature; on the other hand, the final steady stress decreases with the initial tensile rate while the stress relaxation rate keeps almost unaffected. Most of the existent viscoelastic models, esp. the fractional exponent one, make good predictions for the stress relaxation behaviors of the PTFE membranes, while some models work ill due to their poor compositions.
Research on vortex-induced vibration of flexible pipes at different locations in a limited fluid domain
YUE Qian-bei, DONG Ri-zhi, LIU Ju-bao
2016, 37(3): 277-289. doi: 10.3879/j.issn.1000-0887.2016.03.006
Abstract(764) PDF(449)
In view of the vortex-induced vibration of flexible pipes in a limited fluid domain, the flexible pipe was numerically discretized into 3D beam elements and the fluid body was discretized into solid elements. The fluid-structure interaction model and numerical calculation method were set up for the flexible pipe in the limited fluid domain. A special experimental device was designed and machined for the test of flexible pipe vibration in the cylindrical fluid container. In the experiment, the GWT-2B-axis accelerometers were used to monitor the vibration. Comparison between the tested vibration results and the numerical simulation results showed a good degree of agreement. Based on the established model and methods, the vortex-induced vibration mechanism was studied for the flexible pipe at different locations in the cylindrical fluid domain. The results show that, the bigger the deviation angle at which the flexible pipe is located from the inlet velocity is, the easier the fluid elastic instability is to occur and the more intense the flexible pipe vibration is. However, when the flexible pipe is opposite the inlet velocity, the fluid elastic instability is less easy to occur and the flexible pipe vibration is weakened.
Research of pressure wave velocity and response time for oil-gas mixing transportation in large span pipelines
SHI Shuang, JING Jia-qiang, KONG Xiang-wei
2016, 37(3): 290-300. doi: 10.3879/j.issn.1000-0887.2016.03.007
Abstract(671) PDF(488)
Based on the 2-fluid model and the theory of small perturbation, the pressure wave velocity model was put forward for the oil-gas mixing transportation in large span pipelines, and the computer program to solve this model was built. The conclusions based on a practical engineering example are as follow: in the process of multiphase mixing large span transportation, the change of pressure wave velocity is more influenced by the gas phase, even a small amount of mixed gas can affect the pressure wave velocity dramatically. With the increase of mixed gas, the pressure wave velocity decreases and the pressure response time extends. The pressure at the low point is higher than at the high point, so the gas compressibility factor at the low point is smaller than at the high point and the pressure wave velocity at the low point is bigger, meanwhile, the pressure response time at the low point is shorter. Moreover, at the low point of mixed transportation the mixed gas is compressed tremendously, so the pressure wave velocity there changes little and almost remains at a constant value; in contrast, the pressure wave velocity changes easily at the high point.
Numerical simulation of mixing enhancement in T-shaped micromixers
XIAO Shui-yun, LI Ming, YANG Da-yong
2016, 37(3): 301-310. doi: 10.3879/j.issn.1000-0887.2016.03.008
Abstract(747) PDF(619)
To study the effects of different mixing enhancement modes on micromixing, numerical simulations with the finite element method were carried out on the simple T-shaped micromixers, the active T-shaped micromixers with surface heterogeneous Zeta potential and the passive T-shaped micromixers with embedded ribs. The flow fields, velocity fields and concentration fields in the 3 kinds of T-shaped micromixers, as well as the relationships between the mixing efficiency and 2 dimensionless parameters Re and Sc, were investigated. The results show that the mixing efficiency decreases with Sc and Re, fast at first and then slowly. The mixing efficiency in the passive T-shaped micromixer with embedded ribs has large undulation along the microchannel, while that in the active T-shaped micromixer with surface heterogeneous Zeta potential has only gentle undulation, and this undulation will be restrained in the cases of high Re values or low Sc values. The Re value also notably influences the improving effect of different mixing enhancement modes. For relatively lower Re values, the outlet mixing efficiency is improved more evidently in the active mixing enhancement mode with surface heterogeneous Zeta potential; otherwise, for relatively higher Re values, that happens instead in the passive mixing enhancement mode with embedded ribs.
A numerical approximation method for nonlinear dynamic systems based on radial basis functions
LI Yan-ting, XU Xi-bin, ZHOU Shi-liang, XU Ji-qing
2016, 37(3): 311-318. doi: 10.3879/j.issn.1000-0887.2016.03.009
Abstract(1198) PDF(816)
The radial basis functions have the advantages of simple forms and isotropy. A new numerical method for solving the initial-value problems of nonlinear dynamic systems was constructed through combination of the idea of the radial basis function approximation and the weighted residual collocation point method. The advantages and disadvantages of several methods for the numerical solution of nonlinear dynamic systems were analyzed. Some practical numerical examples were given to compare the proposed method with the existing methods. The results show that the present method is easily applicable with good convergence and high accuracy.
Solitary solutions to generalized Schrödinger disturbed coupled systems
SHI Juan-rong, ZHU Ming, MO Jia-qi
2016, 37(3): 319-330. doi: 10.3879/j.issn.1000-0887.2016.03.010
Abstract(649) PDF(536)
A class of generalized nonlinear Schrödinger disturbed coupled systems were studied. Firstly, with a special projection method of undetermined coefficients the solitary exact travelling wave solutions to the corresponding nondisturbed coupled systems were found, which were selected as the initial approximation of the disturbed coupled systems. Next, by means of the homotopy analysis method, a set of homotopy mappings were constructed. Thus, each order of the approximate solutions to the original nonlinear Schrödinger disturbed coupled system was obtained successively with the homotopy analysis method. Finally, through the examples and the perturbation theory, it is shown that the acquired approximate solutions to the generalized nonlinear Schrödinger disturbed coupled systems are simple and valid.