应用数学和力学

2003 Vol. 24, No. 10

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Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅰ)-Micropolar Continua

DAI Tian-min

2003, 24(10): 991-997.

Abstract(2491) PDF(749)

Abstract:
Based on the restudies of existing polar continuum theories rather complete systems of basic balance laws and equations for micropolar continuum theory are presented.In these new systems not only the additional angular momentum,surface moment and body moment produced by the linear momentum,surface f...

Renewal of Basic Laws and Principles for Polar Continuum Theories (Ⅱ)-Micromorphic Continuum Theory and Couple Stress Theory

DAI Tian-min

2003, 24(10): 998-1004.

Abstract(2432) PDF(959)

Abstract:
The purpose is to reestablish the balance laws of momentum,angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory.The desired results for micromorphic continuum mechanics and couple stress theory ...

Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅲ)-Noether’s Theorem

DAI Tian-min

2003, 24(10): 1005-1011.

Abstract(2451) PDF(663)

Abstract:
The existing various couple stress theories have been carefully restudied.The purpose is to propose a coupled Noether.s theorem and to reestablish rather complete conservation laws and balance equations for couple stress elastodynamics.The new concrete forms of various conservation laws of couple st...

Shape Bifurcation of an Elastic Wafer Due to Surface Stress

YAN Kun, HE Ling-hui, LIU Ren-huai

2003, 24(10): 1012-1016.

Abstract(2901) PDF(627)

Abstract:
A geometrically nonlinear analysis was proposed for the deformation of a free standing elastically isotropic wafer caused by the surface stress change on one surface.The link between the curvature and the change in surface stress was obtained analytically from energetic consideration.In contrast to ...

1/3 Subharmonic Solution of Elliptical Sandwich Plates

LI Yin-shan, ZHANG Nian-mei, YANG Gui-tong

2003, 24(10): 1017-1026.

Abstract(2124) PDF(538)

Abstract:
The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components,the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived.A superpositive-iterative ha...

Random-Fuzzy Model for the Ductile/Brittle Transition

LÜ Zhen-zhou, YUE Zhu-feng, FENG Yun-wen

2003, 24(10): 1027-1034.

Abstract(2502) PDF(605)

Abstract:
A large sample of experiments was carried out to study influence of stress triaxiality and temperature on the growth of micro voids and the ductile/brittle transition(DBT)behavior of 40Cr steel.A random-fuzzy model was put forward for the transition.It is assumed that the ductile fracture is control...

Analysis of Chebyshev Pseudospectral Method for Multi-Dimensional Generalized SRLW Equations

SHANG Ya-dong, GUO Bo-ling

2003, 24(10): 1035-1048.

Abstract(2410) PDF(630)

Abstract:
The Chebyshev pseudo-spectral approximation of the homogenous initial boundary value problem for a class of multi-dimensional generalized symmetric of regularized long wave(SRLW)equations is considered.The fully discrete Chebyshev pseudospectral scheme is constructed.The convergence of the approxima...

Mathematical Model of Two-Phase Fluid Nonlinear Flow in Low-Permeability Porous Media With Applications

DENG Ying-er, LIU Ci-qun

2003, 24(10): 1049-1056.

Abstract(2818) PDF(757)

Abstract:
A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters,a mass conservation law and a concept of tur-bulent ellipses.A...

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

JIAN Yong-jun, E Xue-quan, BAI Wei

2003, 24(10): 1057-1068.

Abstract(2798) PDF(604)

Abstract:
In the cylindrical coordinate system,a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder,which is subject to a vertical oscillation.It is assumed that ...

Regularization of Nearly Singular Integrals in the Boundary Element Method of Potential Problems

ZHOU Huan-lin, NIU Zhong-rong, WANG Xiu-xi

2003, 24(10): 1069-1074.

Abstract(2867) PDF(655)

Abstract:
A general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems.For linear elements,the strongly singular and hypersingular integrals of the interior points very close to boundary were categorized into two forms. The facto...

Analytical Solution of a Simply Supported Piezoelectric Beam Subjected to a Uniformly-Distributed Loading

ZHANG Lin-nan, SHI Zhi-fei

2003, 24(10): 1075-1082.

Abstract(2724) PDF(616)

Abstract:
Using the inverse method,the analytical solution of a simply supported piezoelcetric beam subjected to a uniformly distributed loading has been studied.First,the polynomials of stress function and induction function are given.Then,considering the gradient properties of the elastic parameter and the ...

Spectrum Distribution of the Second Order Generalized Distributed Parameter Systems

GE Zhao-qiang, ZHU Guang-tian, MA Yong-hao

2003, 24(10): 1083-1089.

Abstract(2613) PDF(681)

Abstract:
Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space.The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear o...

Numerical Method for the Shape Reconstruction of a Hard Target

YOU Yun-xiang, MIAO Guo-ping

2003, 24(10): 1090-1100.

Abstract(2648) PDF(581)

Abstract:
A nonlinear optimization method was developed to solve the inverse problem of determining the shape of a hard target from the knowlegde of the far-field pattern of the acoustic scattering wave, it was achieved by solving independently an ill-posed linear system and a well-posed minimization problem....