应用数学和力学

Elasticity Solution of Clamped-Simply Supported Beams With Variable Thickness

XU Ye-peng, ZHOU Ding, Y. K. Cheung

2008, 29(3): 253-262.

Abstract(3784) PDF(865)

Abstract:
The stress and displacement distributions of continuously varying thickness beams with one end clamped and the other end simply supported under static loads are studied. By introducing the unit pulse functions and Dirac functions, the clamped edge can be made equivalent to the simply supported one by adding the unknown horizontal reactions. According to the governing equations of plane stress problem, the general expressions of displacements, which satisfy the governing differential equations and the boundary conditions at two ends of the beam, can be deduced. The unknown coefficients in the general expressions were then determined by using the Fourier sinusoidal series expansion along the upper and lower boundaries of the beams and using the condition of zero displacements at the clamped edge. The solution obtained has excellent convergence property. The numerical results being compared with those obtained from the commercial software ANSYS, excellent accuracy of the present method is demonstrated.

Thermal Buckling of Axisymmetrically Laminated Cylindrically Orthotropic Shallow Spherical Shells Including Transverse Shear

ZHU Yong-an, WANG Fan, LIU Ren-huai

2008, 29(3): 263-271.

Abstract(3006) PDF(869)

Abstract:
The nonlinear thermal buckling of symmetrically laminated cylindrically orthotropic shallow spherical shell under temperature field and uniform pressure including transverse shear is studied by using the modified iteration method. And the analytic formulas for determining the critical buckling loads under different temperature fields were obtained. The effect of transverse shear deformation and different temperature fields on critical buckling loads were discussed in a numerical example.

Generalized Constrained Multiobjective Games in Locally FC-Uniform Spaces

DING Xie-ping, Lee Chin-san, YAO Jen-chih

2008, 29(3): 272-280.

Abstract(2758) PDF(790)

Abstract:
A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff functions get their values in an infinite-dimensional space. By using a Himmelberg type fixed point theorem in locally FC-uniform spaces, some existence theorems of weak Pareto equilibria for the generalized constrained multiobjective games are established in locally FC-uniform spaces, which improve, unify and generalize the corresponding results in recent literatures.

Modified Laguerre Spectral and Pseudospectral Methods for Nonlinear Partial Differential Equations in Multiple Dimensions

XU Cheng-long, GUO Ben-yu

2008, 29(3): 281-300.

Abstract(3023) PDF(654)

Abstract:
The Laguerre spectral and pseudospectral methods for multiple-dimensional nonlinear partial differential equations are investigated. Some results on the modified Laguerre orthogonal approximation and interpolation were established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods were proposed for two-dimensional Logistic equation. The stability and convergence of suggested schemes were proved. Numerical results demonstrate the high accuracy of these approaches.

Control of Flight Forces and Moments by the Flapping Wings of a Model Bumble-bee

WU Jiang-hao, SUN Mao

2008, 29(3): 301-315.

Abstract(2904) PDF(644)

Abstract:
The control of flight forces and moments by the flapping wings of a model bumble-bee is studied using the method of computational fluid dynamics. Hovering flight was taken as the reference flight: wing kinematic parameters are varied with respect to their values at hovering flight. Moments about (and forces along) x, y, z axes that pass the center of mass were computed. Changing stroke amplitude (or wingbeat frequency) mainly produces a vertical force. Changing mean stroke angle mainly produces a pitch moment. Changing wing angle of attack, when down-and up-strokes having equal change, mainly produces a vertical force, and when down-and up-strokes having opposite changes, mainly produces a horizontal force and a pitch moment. Changing wing rotation timing, when dorsal and ventral rotations having the same timing, mainly produces a vertical force, and when dorsal and ventral rotations having opposite timings, mainly produces a pitch moment and a horizontal force. Changing rotation duration has very small effect on the forces and moments. Anti- symmetrically changing stroke amplitude (or wingbeat frequency) of the contralateral wings mainly produces a roll moment. Anti- symmetrically changing the angles of attack of the contralateral wings, when down-and up-stroke having equal change, mainly produces a roll moment, and when down-and up-stroke having opposite changes, mainly produces a yaw moment. Anti- symmetrically changing wing rotation timing of the contralateral wings, when dorsal and ventral rotations having the same timing, mainly produces a roll moment and a side force, and when dorsal and ventral rotations having opposite timings, mainly produces a yaw moment. Vertical force and moments about the three axes can be separately controlled by separate kinematic variables. Very fast rotation can be achieved with moderate changes in wing kinematics.

Numerical Investigations on the Dynamic Process of the Muzzle Flow

JIANG Xiao-hai, FAN Bao-chun, LI Hong-zhi

2008, 29(3): 316-324.

Abstract(2348) PDF(733)

Abstract:
The integrative process of the quiescent projectile accelerated by high-pressure gas to shoot out at a supersonic speed and fly out of the range of precursor flow field was simulated numerically. The calculation method was based on ALE equations and second-order precision Roe method adopting chimera grids and dynamic mesh. From the predicted results, the coupling and interaction among the precursor flow field, propellant gas flow field and high-speed projectile were discussed in detail. And the shock-vortex interaction, shockwave reflection, shock-projectile interaction together with shock diffraction and shock focusing were demonstrated clearly to explain the effect on the acceleration of the projectile.

Difference Inversion Model of a Wave Equation

WANG De-ming

2008, 29(3): 325-330.

Abstract(2931) PDF(635)

Abstract:
For calculating the coefficient function of a wave equation, a numerical iterative model was derived from difference method and a perturbation assumption. The method has solved the disaccordant problem of numerical precision between direct problem model and inverse problem model, and its serial problems, in old method. Numerical simulation calculation shows that the method is feasible and effective.

Vibration of an Infinite Inhomogeneous Trasversely Isotropic Viscoelastic Medium With a Cylindrical Hole

D. P. Acharya, Indrajit Roy, P. K. Biswas

2008, 29(3): 331-341.

Abstract(2961) PDF(480)

Abstract:
The influences of higher order viscoela sticity and the inhomo geneities of the transversely isotropic elastic parameters on the disturbances in an infinite medium, caused by the presence of a transient radial force or twist on the surface of a cylindrical hole with circular cross section are investigated. Following Voigt's model for higher order viscoelasticity the nonvanishing stress components valid for a transversely isotropic and higher or derviscoelastic solid medium were deduced in terms of radial displacement component. Considering the power law variation of elastic and viscoelastic parameters, the stress equation of motion was developed. Solving this equation under suitable boundary conditions due to transient forces and twists radial displacement and relevant stress components were found out in terms of modified Bessel functions. The problem for the presence of transient radial force was numerically analysed. Modulations of displacement and stresses due to different order of viscoelasticity and inhomogeneity were graphically depicted. The numerical study of the disturbance caused by the presence of twist on the surface may be similarly done and is not pursued.

“Final All Possible Steps” Approach for Accelerating Stochastic Simulation of Coupled Chemical Reactions

ZHUO Wen, PENG Xin-jun, LIU Xiang, YAN Zheng-lou, WANG Yi-fei

2008, 29(3): 342-350.

Abstract(2375) PDF(725)

Abstract:
A modified accelerated stochastic simulation method for chemically reacting systems, called the "final all possible steps" (FAPS) method is developed. The reliable statistics of all species were obtained in any time during the time course with fewer simulation times. Moreover, the FAPS method can be incorporated into the leap methods, which makes the simulation of larger systems more efficient. Numerical results indicate that the proposed methods can be applied to a wide range of chemically reacting systems with a high-precision level and a significant improvement can be obtained on efficiency over the existed methods.

Elastic-Plastic Deformation of Sandwich Rod on the Elastic Basis

GU Yu

2008, 29(3): 351-360.

Abstract(2891) PDF(558)

Abstract:
The problem about bending of the three-layer elastic-plastic rod located on the elastic base, with a compressibly physical nonlinear core, was studied. The mechanical response of the designed three-layer elements consisting of two bearing layers and a core was examined. The complicated problem about curving of the three-layer rod located on the elastic base was solved. Convergence of the proposed method of elastic solutions was examined to convince that the solution is acceptable. The calculated results indicate that the plasticity and physical nonlinearity of materials have a great influence on the deformation of the sandwich rod on the elastic basis.

Darboux Transformation of Generalized Coupled KdV Soliton Equation and Its Odd-Soliton Solutions

LIU Ping

2008, 29(3): 361-368.

Abstract(3095) PDF(706)

Abstract:
Based on the resulting Lax pairs of generalized coupled KdV soliton equation, a new Darboux transformation with multi-parameters for generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem. By using Darboux transformation, the generalized odd-soliton solutions of ceneralized coupled KdV soliton equation are given and presented in determinant form. As an application, the first two cases are given.

Analysis of the Exercise Boundary of an American Interest Rate Option

YI Fa-huai, PENG Xin-ling, CHEN Ying-shan

2008, 29(3): 369-378.

Abstract(2741) PDF(602)

Abstract:
By applying the variational inequality technique, the behavior of the exercise boundary of the american-style interest rate option is analyzed under the assumption that the interest rates obey a mean-reverting random walk as given by the Vasicek model. The monotonicity, boundedness and C^∞-smoothness of the exercise boundary are proved.

2008 Vol. 29, No. 3