A SIGNIFICANT IMPROVEMENT ON NEWTON’S ITERATIVE METHOD

ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌ＿ｋｎｏｗｎｔｈａｔｍｕｃｈｉｍｐｒｏｖｅｍｅｎｔｈａｓｂｅｎｍａｄｅｓｉｎｃｅＮｅｗｔｏｎ’ｓｍｅｔｈｏｄｗａｓｃｏｍｅｏｕｔｆｏｒｔｈｅｎｏｎｌｉｎｅａｒａｌｇｅｂｒａｉｃｅｑｕａｔｉｏｎｆ（ｘ）＝０．Ｈｏｗ...     

REMARKS ON THE PAPER“THE EXTINCTION BEHAVIOR OF THE SOLUTIONS FOR A CLASS OF REACTION -DIFFUSION EQUATIONS”

ＴｈｅｆｏｌｌｏｗｉｎｇＬｅｍｍａｓｔａｔｅｄ (ｉｎ :ＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ (ＥｎｇｌｉｓｈＥｄｉｔｉｏｎ) ,2 0 0 1 ,2 2 ( 1 1 ) :1 3 52 -1 3 56)ｗａｓａｐｐｌｉｅｄｔｏｄｅｓｃｒｉｂｅｔｈｅａｓｙｍｐｔｏｔｉｃｂｅｈａｖｉｏｒｓｏｆｓｏｌｕｔｉｏｎｓｏｆａｃｌａｓｓｏｆｒｅａｃｔｉｏｎ＿ｄｉｆｆｕｓｉｏｎｅｑｕａｔｉｏｎ .Ｏｎａｃｃｏｕｎｔｏｆｔｈｅｓｐｅｃｉａｌｐｒｏｐｅｒｔｙｏｆｔｈｅｓｕｐｅｒｓｏｌｕｔｉｏｎ(ｉ.ｅ .,ａｎｏｎｚｅｒｏｓｏｌｕｔｉｏｎ…     

A SYMBOLIC COMPUTATION METHOD TO DECIDE THE COMPLETENESS OF THE SOLUTIONS TO THE SYSTEM OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｓｙｓｔｅｍｏｆｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌａｌｇｅｂｒａｉｃｅｑｕａｔｉｏｎｓ (ＰＤＡＥｓ) :Σ :　Ｐｉ(ｙ1,ｙ2 ,… ,ｙｎ) =0　　 (ｉ =1,2 ,… ,ｒ) ,ｗｈｅｒｅｔｈｅｃｏｅｆｆｉｃｉｅｎｔｓａｒｅｉｎｔｈｅｄｉｆｆｅｒｅｎｔｉａｌｆｉｅｌｄＫｗｉｔｈｃｈａｒａｃｔｅｒｉｓｔｉｃｚｅｒｏ .ＴｈｅｉｍｐｏｒｔａｎｔｑｕｅｓｔｉｏｎｉｓｈｏｗｔｏｓｏｌｖｅｔｈｉｓＰＤＡＥｓｉｎｔｈｅｔｈｅｏｒｙｏｆｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａ…     

A COMPUTATIONAL METHOD FOR THE NAVIER-STOKES EQUATIONS AT ALL SPEEDS

ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｃｏｍｐｕｔａｔｉｏｎｏｆｔｈｅｖｉｓｃｏｕｓｃｏｍｐｒｅｓｓｉｂｌｅｆｌｏｗｓｔｈｅＮａｖｉｅｒ＿Ｓｔｏｋｅｓｅｑｕａｔｉｏｎｓａｒｅｇｅｎｅｒａｌｌｙｒｅｐｒｅｓｅｎｔｅｄｉｎｔｈｅｃｏｎｓｅｒｖａｔｉｏｎｌａｗｆｏｒｍａｓａｈｙｐｅｒｂｏｌｉｃｓｙｓｔｅｍ .Ｌａｃｋｉｎｇｔｈｅｍａｔｈｅｍａｔｉｃａｌｔｏｏｌｔｏａｎａｌｙｚｅｔｈｉｓｎｏｎｌｉｎｅａｒｓｙｓｔｅｍ ,ｔｈｅｎｕｍｅｒｉｃａｌｍｅｔｈｏｄｓｕｓｅｄｉｎｓｏｌｖｉｎｇｔｈｅｎｏｎｌｉｎｅａｒｈｙｐｅ…     

THE AXISYMMETRIC MIXED BOUNDARY-VALUE PROBLEM OF THE VERTICAL VIBRATION OF A RIGID FOUNDATIONON SATURATED LAYERED SOIL SUBGRADE

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｌａｓｔｉｃｈａｌｆ＿ｓｐａｃｅｔｈｅｏｒｙｏｆｆｏｕｎｄａｔｉｏｎｖｉｂｒａｔｉｏｎａｎｄｔｈｅｓｔｕｄｙｏｆｓｏｉｌ＿ｓｔｒｕｃｔｕｒｅｉｎｔｅｒａｃｔｉｏｎｐｒｏｂｌｅｍｈａｖｅｂｅｅｎｔｈｅｓｕｂｊｅｃｔｏｆｉｎｔｅｎｓｉｖｅｒｅｓｅａｒｃｈｉｎｔｈｅｃｉｖｉｌｅｎｇｉｎｅｅｒｉｎｇ .ＳｉｎｃｅＬｕｃｏｅｔａｌ.[1]ｓｕｍｍａｒｉｚｅｄｔｈｅｖｉｂｒａｔｉｏｎｏｆａｃｉｒｃｕｌａｒｒｉｇｉｄｆｏｕｎｄａｔｉｏｎｒｅｓｔｉｎｇｏｎａｎｅｌａｓｔｉｃｈａｌｆ＿ｓ…     

A NEW QUADRILATERAL THIN PLATE ELEMENT BASED ON THE MEMBRANE-PLATE SIMILARITY THEORY

ＩｎｔｒｏｄｕｃｔｉｏｎＢｅｃａｕｓｅｏｆｔｈｅｒｅｑｕｉｒｅｍｅｎｔｏｆｃ1ｃｏｎｔｉｎｕｉｔｙ ,ｉｔｉｓｖｅｒｙｄｉｆｆｉｃｕｌｔｔｏｃｏｎｓｔｒｕｃｔｃｏｎｆｏｒｍｉｎｇＫｉｒｃｈｈｏｆｆｐｌａｔｅｂｅｎｄｉｎｇｅｌｅｍｅｎｔｓ.Ｉｎｏｒｄｅｒｔｏｏｖｅｒｃｏｍｅｔｈｅｄｉｆｆｉｃｕｌｔｙ ,ｍａｎｙａｐｐｒｏａｃｈｅｓｈａｖｅｂｅｅｎｐｒｅｓｅｎｔｅｄ .Ｉｎｔｈｅｓｅａｐｐｒｏａｃｈｅｓ,ｔｈｅｒｅｑｕｉｒｅｍｅｎｔｏｆｃ1ｉｓｒｅｌｅａｓｅｄｏｎｃｏｎｄｉｔｉｏｎｏｆｔｈｅｃｏｎｖｅｒｇｅｎ…     

THE TARGET WAVE PATTERNS OF A REACTION-DIFFUSION PROCESS IN AN IMMOBILIZED ENZYME

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｎｚｙｍｅｉｓａｃｏｎｃｅｎｔｒａｔｅｄａｎｄｓｐｅｃｉｆｉｃａｌｂｉｏ＿ｃａｔａｌｙｓｔ．Ｉｔｓｅｓｅｎｃｅｉｓａｐｒｏｔｅｉｎａｎｄｉｔｓａｐｐｌｉｃａｔｉｏｎｉｓｖｅｒｙｅｘｔｅｎｓｉｖｅ．Ｈｏｗｅｖｅｒｉｔｈａ...     

THE INTERACTION PROBLEM BETWEEN THE ELASTIC LINE INCLUSIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＯｆａｌｌｔｈｅｆｉｂｅｒ＿ｒｅｉｎｆｏｒｃｅｄｃｏｍｐｏｓｉｔｅｍａｔｅｒｉａｌｓ,ｔｈｅｓｈｏｒｔ＿ｆｉｂｅｒｃｏｍｐｏｓｉｔｅｍａｔｅｒｉａｌｎｏｔｏｎｌｙｓｔｒｅｎｇｔｈｅｎｓｔｈｅｍａｔｒｉｘｂｕｔａｖｏｉｄｓｄｅｆｅｃｔｉｏｎｓｏｆｔｈｅｌｏｎｇ＿ｆｉｂｅｒｃｏｍｐｏｓｉｔｅｍａｔｅｒｉａｌａｓｗｅｌｌ.Ｔｈｅｍｉｃｒｏ＿ｍｅｃｈａｎｉｃｓａｂｏｕｔｉｔｓｕｃｈａｓｆｒａｃｔｕｒｅ ,ｆａｔｉｇｕｅａｎｄｄａｍａｇｅｉｓｖｅｒｙｃｏｍｐｌｅｘ .Ｉｎｔｈｅｐｒｅｖｉ…     

A NONLINEAR GALERKIN MIXED ELEMENT METHOD AND A POSTERIORI ERROR ESTIMATOR FOR THE STATIONARY NAVIER-STOKES EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｎｏｎｌｉｎｅａｒＧａｌｅｒｋｉｎｍｅｔｈｏｄｉｓａｍｕｌｔｉ＿ｌｅｖｅｌｓｃｈｅｍｅｔｏｆｉｎｄｔｈｅａｐｐｒｏｘｉｍａｔｅｓｏｌｕｔｉｏｎｆｏｒｔｈｅｄｉｓｓｉｐａｔｉｖｅＰＤＥ (ｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ) .Ｔｈｉｓｍｅｔｈｏｄｃｏｎｓｉｓｔｓｉｎｓｐｌｉｔｔｉｎｇｔｈｅｕｎｋｎｏｗｎｉｎｔｏｔｗｏ (ｏｒｍｏｒｅ)ｔｅｒｍｓ ,ｗｈｉｃｈｂｅｌｏｎｇｔｏｔｈｅｄｉｓｃｒｅｔｅｓｐａｃｅｓｗｉｔｈｄｉｆｆｅｒｅｎｔｍｅｓｈｓｉｚｅ .Ｔｈｅ…     

VIBRATIONS OF STEPPED RECTANGULAR THIN PLATES ON WINKLER’S FOUNDATION

ＩｎｔｒｏｄｕｃｔｉｏｎＭｕｃｈｆａｍｉｌｉａｒｉｎｅｎｇｉｎｅｅｒｉｎｇａｒｅｅｌａｓｔｉｃｆｏｕｎｄａｔｉｏｎｐｌａｔｅｓ,ｓｕｃｈａｓｆｏｕｎｄａｔｉｏｎｂａｓｅｐｌａｔｅｓｉｎｃｉｖｉｌｅｎｇｉｎｅｅｒｉｎｇ,ｈｉｇｈｗａｙｓｕｒｆａｃｅ,ｒ...     

A mechanical model on elastic cavitation in solid under hydrostatic tension

In this paper, a mechanical model is proposed to study cavitation in solids. The material is elastic and obeys Hook's law. Logarithm strain and Cauchy stress in nonlinear elasticity is used. A sphere with a central hole is loaded under hydrostatic tension on surface. In spherical symmetry, closed form solution is got. As radius of the hole tends to zero, a pitchfork bifurcation appears on load-displacement curve. The pitchfork bifurcation indicates that there is a cavitation at center of solid sphere as load reaches a critical value.     

Cavitated bifurcation for composed compressible hyper-elastic materials

The cavitated bifurcation problem in a solid sphere composed of two compressible hyper-elastic materials is examined. The bifurcation solution for the composed sphere under a uniform radial tensile boundary dead-load is obtained. The bifurcation curves and the stress contributions subsequent to the cavitation are given. The right and left bifurcation as well as the catastrophe and concentration of stresses are analyzed. The stability of solutions is discussed through an energy comparison. Project supported by the National Natural Science Foundation of China (No. 19802012).     

Cavity formation at the center of a sphere composed of two compressible hyper-elastic materials

IntroductionHorgan[1] reviewedthecavitatedbifurcationproblemforhyper_elasticmaterials,includinginhomogeneousandanisotropicmaterialsaswellashomogeneousandisotropicmaterials .Forincompressiblematerials,HorganandPence[2 ,3 ] examinedtheeffectofmaterialinhomogeneityontheformationandgrowthofvoidandobtainedananalyticsolutionofthecavitatedbifurcationproblemforasolidspherecomposedoftwoneo_Hookeanmaterials.Thebifurcationmayoccurnotonlytotherightbutalsototheleftforthecomposedsphere .Thestabilitiesofth…     

CAVITATED BIFURCATION FOR INCOMPRESSIBLE HYPERELASTIC MATERIAL

ＩｎｔｒｏｄｕｃｔｉｏｎＣａｖｉｔａｔｉｏｎｐｈｅｎｏｍｅｎｏｎ ,ｔｈｅｓｕｄｄｅｎｆｏｒｍａｔｉｏｎａｎｄｇｒｏｗｔｈｏｆｖｏｉｄｓｉｎｓｏｌｉｄｍａｔｅｒｉａｌｓ,ｈａｓｌｏｎｇａｔｔｒａｃｔｅｄｍｕｃｈａｔｔｅｎｔｉｏｎｂｅｃａｕｓｅｏｆｔｈｅｆｕｎｄａｍｅｎｔａｌｒｏｌｅｉｔｐｌａｙｓｏｎｔｈｅｌｏｃａｌｆａｉｌｕｒｅａｎｄｆｒａｃｔｕｒｅｏｆｍａｔｅｒｉａｌｓ.Ｔｈｅａｐｐｅａｒａｎｃｅｏｆｖｏｉｄｉｎｔｈｅｉｎｔｅｒｉｏｒｏｆｒｕｂｂｅｒｏｒｒｕｂｂｅｒ＿ｌｉｋｅｍａｔｅｒｉａｌｓｗａ…     

QUALITATIVE ANALYSIS OF SPHERICAL CAVITY NUCLEATION AND GROWTH FOR INCOMPRESSIBLE GENERALIZED VALANIS-LANDEL HYPERELASTIC MATERIALS

I. INTRODUCTION In practice, cavity formulation in materials is recognized as precursors to failure. Thus void nucleationand growth in solid materials have a great in?uence on failure mechanism. Gent and Lindley[1] have observed experimentally the phe…     

超弹性材料中的球形空穴分叉

首先给出了超弹性材料球形空穴分叉问题的数学提法；其次给出了修正Ｂｌａｔｚ－Ｋｏ材料球形空穴分叉问题的两个新的精确解，并计算了空穴生成时，空穴附近的应力集中因子和应力间断，最后数值计算了空穴分支解     

温盐双扩散系统的多平衡稳定性

采用数值试验的方法研究了温盐双扩散系统中的多平衡稳定性在系统中引入非线性状态方程、温通量边界条件和变强迫因子在数值模拟中引入边界拟会坐标系,并按照温盐浮力比λ大于1,等于1和小于1将流场分为温度控制场、温盐均势场和盐度控制场得到了四种稳定平衡状态,特别是,大强迫因子和强非线性影响下的四胞环流对称状态．在对称的定常强迫边条件作用下的流场、温度场和盐度场均为对称分布引入温通量边条件后,对称流场在小干扰下失去对称性,发展为非对称分布,并因为干扰位置的不同而造成不同的非对称性,出现了从对称状态到非对称状态的音叉分叉,得到了a-Ras的稳定曲线及分叉图,并解释了分叉的本质     

热超弹性材料中空穴增长的分岔问题

研究了受外加均布拉伸死载荷作用的不可压热超弹性材料中空穴突然快速增长的分岔问题.不同于外载荷较小的情况,不可压热超弹性材料球体中的预存微空在外载荷足够大时可以发生突然的快速增长,可视为一类分岔问题.给出了不同温度场下,不同初始半径的微空的增长曲线.预存微空的增长曲线相应于初始半径的极限是实心球体中空穴突然生成的分岔曲线.讨论了均匀和非均匀,升高或降低的温度场对空穴增长问题的影响;给出了预存微空能够发生突然的快速增长的临界载荷,得到了临界载荷与实心球体中空穴突然生成时的临界载荷之间的关系及临界载荷与温度变化之间的关系.     

Cavitation in hookean elastic membranes

An exact solution to cavitation is found in tension of a class of Cauchy elastic membranes. The constitutive relationship of materials is based on Hookean elastic law and finite logarithmic strain measure. A variable transformation is used in solving the two-point boundary-value problem of nonlinear ordinary differential equation. A simple formula to calculate the critical stretch for cavitation is derived. As the numerical results, the bifurcation curves describing void nucleation and suddenly rapidly growth of the cavity are obtained. The boundary layers of displacements and stresses near the cavity wall are observed. The cata-strophic transition from homogeneous to cavitated deformation and the jumping of stress distribution are discussed. The result of the energy comparison shows the cavitated deformation has lower energy than the homogeneous one, thus the state of cavitated deformation is relatively stable. All investigations illustrate that cavitation reflects a local behavior of materials. Project supported by the National Natural Science Foundation of China (No. 19802012) the Scientific Research Foundation for Returned Overseas Chinese Scholars, and the Scientific Research Foundation for Key Teachers in Chinese Universities.     

BIFURCATION IN A TWO-DIMENSIONAL NEURAL NETWORK MODEL WITH DELAY

IntroductionForunderstandingthedynamicsofneuralnetworks ,thepropertiesofstabilityandbifurcationinasimplifiednon_self_connectionneuralnetwork u1(t) =-μ1u1(t) aF(u2 (t-τ2 ) ) , u2 (t) =-μ2 u2 (t) bG(u1(t-τ1) ) ( 1 )hasbeenstudied .Forexample ,inRef.[1 ]ChenandWustudiedtheexistenceoftheslowlyoscillatingperiodicsolutionbyusingthemethodofdiscreteLiapunovfunction .InRef.[2 ]thesumoftimedelaysτ=τ1 τ2 beingregardedasabifurcationparameter,theexistenceoflocalHopfbifurcationandthepropertiesof…