应用数学和力学

2014 Vol. 35, No. 9

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Application of Fractional Calculus to Simulate the Isolation Effects of Discontinuous Pile Barriers on Viscoelastic SH Waves

LI Yuan, CHEN Wen, PANG Guo-fei

2014, 35(9): 949-958. doi: 10.3879/j.issn.1000-0887.2014.09.001

Abstract(1300) PDF(1212)

Abstract:
Based on the 3-dimensional (3D) fractional order constitutive equation of viscoelastic body waves, the frequency dispersion characteristics of viscoelastic P- and S-waves were analyzed. Also, the isolation effects of the discontinuous rigid pile barrier and the elastic pile barrier in soft clay on v...

Research on the Configuration of the Deepwater Steel Lazy-Wave Riser Under Effects of Ocean Currents

WANG Jin-long, DUAN Meng-lan, TIAN Kai

2014, 35(9): 959-968. doi: 10.3879/j.issn.1000-0887.2014.09.002

Abstract(1649) PDF(902)

Abstract:
As a kind of improved SCR, the steel lazy-wave riser (SLWR) gained more and more application in the development of deepwater oil and gas field. The configuration of the SLWR is of great significance in its design process. Under ocean current, the configuration and mechanical parameters of the SLWR v...

Convergence of an Adaptive Finite Element Method for 2D Elasticity Problems

LIU Chun-mei, ZHONG Liu-qiang, SHU Shi, XIAO Ying-xiong

2014, 35(9): 969-978. doi: 10.3879/j.issn.1000-0887.2014.09.003

Abstract(1863) PDF(868)

Abstract:
For 2D linear elasticity problems, firstly, a standard adaptive finite element method (AFEM) was developed based on the newest vertex bisection grid refinement, which was marked only according to the error estimators without special treatment of the oscillation terms and intended conformance to the ...

On the Fracture Modeling Method for Crack Tips Penetrating Elastic Interfaces

CHEN Chang-rong

2014, 35(9): 979-985. doi: 10.3879/j.issn.1000-0887.2014.09.004

Abstract(1707) PDF(897)

Abstract:
The theoretical defects of the linear elastic fracture mechanics in modeling crack tips passing through elastic interfaces were analyzed; for an idealized layered material, the cohesive zone model was applied to study the effects of the material cohesive strength ahead of the interface on the behavi...

A Reduced-Order Stabilized CNFVE Extrapolating Model for Non-Stationary Stokes Equations

TENG Fei, LUO Zhen-dong

2014, 35(9): 986-1001. doi: 10.3879/j.issn.1000-0887.2014.09.005

Abstract(1848) PDF(631)

Abstract:
A reduced-order stabilized Crank-Nicolson finite volume element (SCNFVE) extrapolating model with sufficiently high accuracy and few degrees of freedom for non-stationary Stokes equations was established by means of the SCNFVE method and the proper orthogonal decompostion (POD) technique. The error ...

Bifurcations of Solitary Wave Solutions to the Shallow Water Equation of Moderate Amplitude

QIN Yu-yue, DENG Zi-chen, HU Wei-peng

2014, 35(9): 1002-1010. doi: 10.3879/j.issn.1000-0887.2014.09.006

Abstract(1382) PDF(664)

Abstract:
The qualitative behavior and solitary wave solutions to the model equation for shallow water waves of moderate amplitude were studied with the bifurcation method for dynamic systems. The phase portraits of the system were given under different parametric conditions. The implicit expressions of the s...

A Preconditioned Parallel Method for Solving Saddle Point Problems

JIANG Xiao-lin, Lü Quan-yi, XIE Gong-nan

2014, 35(9): 1011-1019. doi: 10.3879/j.issn.1000-0887.2014.09.007

Abstract(1854) PDF(788)

Abstract:
A parallel algorithm with preconditioned modified conjugate gradient method for solving saddle point problems was studied. It is a model that by using iterative method for preconditioning and applying modified conjugate gradient method for solving the problems. Firstly the approximate inverse of the...

D-η-E-Semipreinvex Vector Mappings and Vector Optimization

PENG Zai-yun, LI Ke-ke, ZHANG Shi-sheng

2014, 35(9): 1020-1032. doi: 10.3879/j.issn.1000-0887.2014.09.008

Abstract(1963) PDF(880)

Abstract:
A class of new vector valued generalized convex mappings—D- η -E-semipreinvex mappings, as a true generalization of the E-preinvex mappings and the D-η-semipreinvex mappings, were given. First, several examples were presented to show the existence of the E-semi-invex sets and theD- η -E-semipreinvex...

Approximate Solutions to the Nonlinear Compartmental Model for Extravascular Administration

HU Xiao-hu, TANG San-yi

2014, 35(9): 1033-1045. doi: 10.3879/j.issn.1000-0887.2014.09.009

Abstract(1803) PDF(1097)

Abstract:
The analytical solution to the pharmacokinetics model plays a key role in the design of new drugs, especially in determining the pharmacokinetic parameters. In recent years, the analytical formulae for most of the pharmacokinetics models decided by the nonlinear Michaelis-Menten elimination process,...

Solutions to a Class of Nonlinear Strong-Damp Disturbed Evolution Equations

SHI Juan-rong, SHI Lan-fang, MO Jia-qi

2014, 35(9): 1046-1054. doi: 10.3879/j.issn.1000-0887.2014.09.010

Abstract(1328) PDF(865)

Abstract:
Widely emerging in the fields of mathematics and mechanics, a class of 3rd-order nonlinear strong-damp disturbed partial differential evolution equations were studied. Firstly, a functional homotopic mapping was constructed to express the solution to the evolution equation in a form of power series ...

Dynamics of a Complex-Valued Heat Equation

XIONG Hui, YANG Guang

2014, 35(9): 1055-1062. doi: 10.3879/j.issn.1000-0887.2014.09.011

Abstract(1144) PDF(819)

Abstract:
The Cauchy problem for a parabolic system which was derived from a complexvalued heat equation with inverse nonlinearity was studied. Some criteria for the global existence and quenching of the solutions were provided. Through transformation of the invariant subset of the solution plane, it was pro...

An Interior-Point Method With a New Iterative Scheme

YANG Xi-mei, LIU Hong-wei, ZHANG Yin-kui

2014, 35(9): 1063-1070. doi: 10.3879/j.issn.1000-0887.2014.09.012

Abstract(1221) PDF(770)

Abstract:
A 2nd-order Mehrotra-type predictor-corrector interior-point method was proposed for linear programming, in which the predictor direction and corrector direction were computed with the Newton method and the search direction was obtained through a new form of combination of the predictor direction an...