应用数学和力学

2014 Vol. 35, No. 2

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Boundary Knot Method for 2D Transient Heat Conduction Problems

SHI Jin-hong, FU Zhuo-jia, CHEN Wen

2014, 35(2): 111-120. doi: 10.3879/j.issn.1000-0887.2014.02.001

Abstract(1916) PDF(1279)

Abstract:
The boundary knot method (BKM) in conjunction with the dual reciprocity method (DRM) was introduced to solve 2D transient heat conduction problems. With the finite difference scheme applied to deal with the time derivative term, the transient heat conduction equation was converted to a set of nonhomogeneous modified Helmholtz equations. Then the numerical solution to the nonhomogeneous problems was divided into two parts: the particular solution and the homogeneous solution. The DRM with few inner interpolation nodes was employed to get the particular solution, and the BKM with boundaryonly nodes used to obtain the homogeneous solution. Numerical results show that the present combined method has the merits of high accuracy, wide applicability, good stability and rapid convergence, which were appealing to solving transient heat conduction problems.

Calculation of Boltzmann-Rykov Model Equation by Finite Volume Method

WU Jun-lin, LI Zhi-hui, PENG Ao-ping, JIANG Xin-yu

2014, 35(2): 121-129. doi: 10.3879/j.issn.1000-0887.2014.02.002

Abstract(1480) PDF(1137)

Abstract:
A three order precision finite volume scheme was formulated to numerically solve the Boltzmann-Rykov model equation in which rotational energy was considered. This model equation was discretized into a series of equations at each discrete velocity point, and then a high order half-discretization finite volume scheme was used to compute these equations. Three order Runge-Kutta method was introduced for time marching, and central value in each cell was taken to approximate the average collision term. This finite volume scheme was of three order precision in convection term, while positive definiteness of the distribution functions and flux conservation were ensured. Results were compared with those of finite difference method and Riemann exact solution in continuum regime. The good coincidence shows validity of the solving process for the model equation by finite volume method.

A Modified Finite Volume Approximation of 2-Dimensional Diffusion Equation With Discontinuous Coefficients

XU Xiao-lei, FENG Xiu-fang

2014, 35(2): 130-147. doi: 10.3879/j.issn.1000-0887.2014.02.003

Abstract(1376) PDF(777)

Abstract:
A new modified finite volume method was presented to solve the 2-dimensional diffusion equation. Through improvement of the methods for solving the flux function and harmonic average coefficient, a new difference scheme was obtained for the diffusion equation with discontinuous coefficients. This scheme was an implicit difference scheme and was unconditionally stable. Subsequent numerical tests show that the presented method is more accurate than the classical finite volume method.

A Reduced-Order Extrapolating Simulation Model for Unsaturated Soil Water Flow Problem

TENG Fei, LUO Zhen-dong

2014, 35(2): 148-161. doi: 10.3879/j.issn.1000-0887.2014.02.004

Abstract(1225) PDF(980)

Abstract:
A reduced-order extrapolating simulation model with sufficiently high accuracy and fews degress of freedom for the two-dimensional unsaturated soil water flow problem was established by means of the Crank-Nicolson finite volume element (CNFVE) method and POD technique. The error estimates of the reduced-order approximate solutions and the algorithm implementation for the reduced-order extrapolating simulation model were provided. Finally, a numerical example was taker to illustrate that the results of numerical computation are consistent with those of theoretical solutions. Moreover, the advantage of the reduced-order extrapolating simulation model lies in its simpler computation and higher accuracy.

Degeneration and Tranfer of the Displacement-Stress Functions From Poroelastic Layered Media to Elastic Layered Media

DING Bo-yang, CHEN Zhang-long, XU Ting

2014, 35(2): 162-180. doi: 10.3879/j.issn.1000-0887.2014.02.005

Abstract(1167) PDF(1048)

Abstract:
Based on Biot’s dynamic governing equations, through decoupling of the fast and slow dilational waves, the first-order differential simultaneous equations for the displacement-stress propagation were obtained, which satisfy the kinetics of wave propagation in the multilayer poroelastic saturated media. Both the simultaneous equations and the transfer funtions could be degenerated to those for the multilayer single-phase media. With the displacement-stress continuity conditions at the interface between the poroelastic and single-phase media, the interfacial transitional transfer matrix was established by analysis of the propagation of displacement-stress from the poroelastic medium to the single-phase medium. The 4×6 transfer matrix was derived from the 6×6 transitional transfer matrix of the multilayer poroelastic medium and could be combined with the 4×4 transfer matrix of the single-phase medium. Finally, the degenerated results from the presented method were compared with those from the previous classical wave-propagation models to get good consistency between them. The presented method has merits of simpler calculation and clearer physical sense compared with the classical ones.

Steady-State Amplitude-Frequency Characteristics of Axially Buckled Beams Under Strong Transverse Excitation

WANG Hao, CHEN Li-qun

2014, 35(2): 181-187. doi: 10.3879/j.issn.1000-0887.2014.02.006

Abstract(1239) PDF(1098)

Abstract:
A nonlinear vibration analysis was conducted to determine the steady-state response of simply-supported viscoelastic axially buckled beams to harmonic base excitation. Based on the 2-order Galerkin truncation of the governing equation, and in the case of strong excitation, the solvability condition was derived with the multiple-scale method in the presence of 1∶2 internal resonance, to analyze the primary strong external resonance. Various jumping phenomena were revealed in the amplitude-frequency characteristic curves, and the effects of related parameters, especially the axial force, on the phenomena were examined.

Experimental Study and Numerical Simulation of Global Buckling of Pipe-in-Pipe Systems

CHE Xiao-yu, DUAN Meng-lan, ZENG Xia-guang, GAO Pan, PANG Yi-qian

2014, 35(2): 188-201. doi: 10.3879/j.issn.1000-0887.2014.02.007

Abstract(1523) PDF(1584)

Abstract:
Offshore pipelines are usually buried to avoid damage from fishing activities and get thermal insulation. Provided that the pipelines are sufficiently confined in the lateral direction by the passive resistance of the trench walls, they may be liable to upheaval buckling caused by rise in axial force due to temperature changes or other factors. Unless lateral restraint is provided, by trenching the line, for example, lateral buckling will be dominant. The axial compressive force is the primary cause of pipeline buckling. Lateral buckling takes place at a lower axial compressive force than upheaval buckling. The complex structure of the pipe-in-pipe (PIP) system makes global buckling difficult to tackle by theoretical analysis. An experimental study of the global buckling of pipelines was conducted by means of a small-scale model test apparatus. Results were presented for several tests involving both the relationship between the axial force and displacement and the critical axial force. Futhermore, the efficient finite element model was used to simulate the pre-buckling and post-buckling states of the pipeline with the latest tube-to-tube technology. The comparison shows that the numerical simulation results agree well with the experimental ones.

Characterizations and Applications of D-η-Semipreinvex Mappings

PENG Zai-yun, WANG Kun-ying, ZHAO Yong, ZHANG Shi-sheng

2014, 35(2): 202-211. doi: 10.3879/j.issn.1000-0887.2014.02.008

Abstract(1358) PDF(891)

Abstract:
A class of new vector valued generalized convex mappings—D-η-semipreinvex mappings, which was a true generalization of D-preinvex mapping, was given. Firstly, examples were given to show the existence of D-η-semipreinvexmappings and illustrate the differences between D-η-semistrictly semi-preinvex and D-η-semipreinv exmapping. Secondly, a criterion of D-η-semipreinv exity was given, and the relationships among D-η-semipreinvexity, D-η-strict semipreinvexity and D-η-semistrict semipreinvexity were discussed. Finally, an important application of D-η-semistrict semipreinvexity in vector optimization was discussed, then give an example was given to illustrate the result.

Inverse Limit and Lauwerier Attractor(Ⅰ)

GUO Feng, LI Deng-hui, XIE Jian-hua

2014, 35(2): 212-218. doi: 10.3879/j.issn.1000-0887.2014.02.009

Abstract(1338) PDF(871)

Abstract:
A two dimensional Lauwerier mapping was studied and an analytical expression of the strange attractor was obtained. The dynamic properties of the shift map on the inverse limit space of the quadratic mapping were investigated. The projection mapping was established. Then the Lauwerier mapping was studied based on the theory of inverse limit space. It is proved that the Lauwerier mapping restricted to its attractor is topologically semi-conjugate to the shift map on the inverse limit space of the quadratic mapping; therefore the Lauwerier strange attractor is chaotic in the sense of Devaney.

Identification of High-Strain-Rate Material Parameters in Dynamic Johnson-Cook Constitutive Model

LIU Ai-qun, HUANG Xi-cheng

2014, 35(2): 219-225. doi: 10.3879/j.issn.1000-0887.2014.02.010

Abstract(2333) PDF(1457)

Abstract:
The dynamic Johnson-Cook constitutive model is widely used in numerical simulation of materials under dynamic loading. This model is very important in impact dynamics. The method of determining the parameters of heat softening and strain-strengthening in the Johnson- Cook model was proposed based on the strain-hardening parameters obtained from the material experiments including quasi-static uniaxial tension and uniaxial torsion. The material parameters were identified with the optimization algorithm, in which the parameter space was solved through iteration and the optimal point was found to minimize the difference between the model prediction and the experimental data. In the adiabatic heating case, the determination method of the Johnson-Cook model parameter m was demonstrated.

Application of Two-Level Combination Method for Evidence Theory to Structural Damage Detection

LI Yi, YAN Yun-ju

2014, 35(2): 226-232. doi: 10.3879/j.issn.1000-0887.2014.02.011

Abstract(960) PDF(746)

Abstract:
The structural damage identification method based on multiple-source damage information could effectively get over the defects of poor accuracy and high-probability misjudgement with the single-source-based method. The key point of this method lies in the effective fusion processing of the multiple damage data. As an important part of data fusion, the evidence theory is liable to problems of robustness and contrary to common sense, while dealing with high-conflict complex data. The effectiveness of the two-level combination method to improve the evidence theory, was discussed in the case of application to the structural multiple-damage detection.