EDIT0RIAL B0ARD 0F “APPLIED MATHEMATICS AND MECHANICS”

Editor-in-chief: Chien, Wei-zang (钱伟长) Vice Editor-in-chief: Yeh, Kal-yuan (叶开沅)     

ON THE SOLUTION OF NONLINEARTWOPOINT BOUNDARY VALUE PROBLEM──u" g(t.u) = f(t),u(0) = u(2π) = 0

I.IntroductionLetHbearealHilbertspace,XandYtwoclosedsubspacesofHsuchthatH=X$Y,T:H-HaC'mapping,n>1.Assumethatthereexisttwopositiveconstantsniland)liZsuchthatforVueH,Vx6X,VYey'Undertheconditions(l.1),(l.2)and(l.3),ManasevichprovedthatTisaC"diffeomorphismontoH'tl].ThepurposeofthispaperistoimprovetheaboveManasevich'shomeomQrphismtheorem,andthen,itisusedtoproveanexistenceanduniquenessresultforthenonlineartulopointboundaryvalueproblem11.ANonVariationalVersionofaMax-MinPrincipleToimprov…     

THE VELOCITY OF SAND PARTICLES RELATIVE TO WATER AND THE VARIATI0N 0F FLUCTUATION VELOCITY DUE TO THE CONCENTRATION OF SUSPENDED SAND PARTICLES

In this paper.we discuss three fundamental problemsof the theory of suspended sand particles based on thetheory of fluid dynamics.They are:(1)the relative ve-locity of sand particles to the surrounding fluid in theturbulent flow.(2) the variation of the velocity fluc-tuation of the fluid when the suspended sand particlesexist,(3)the profile of the vertical distribution ofthe concentration of the suspended sand particles in two-dimensional uniform steady channel flow and the modifi-cation of usual diffusion theory.The results of our.theoretical analysis are somewhat different from the cor-responding expressions in the textbooks of hydraulicsand river mechanics.     

云纹干涉法同时测定三维位移场(U_0,U_(45),U_(90),ω)

本文介绍了用云纹干涉法同时获得三维位移场——面内位移(U_0,U_(45),U_(90))和离面位移(w)的两种方法:实时观测法和加载波条纹的差载法.前者可一次加载,分别观测各个位移分量条纹图;后者可用一张底板同时记录全部三维位移信息,通过光学滤波分离出各位移分量条纹图。测试方法和计算都很简便,不仅能测静荷,同时也可测动荷,文中还介绍了实验用的仪器,给出了实验结果。     

A NOTE ON BIFURCATIONS OF u″ μ(u-u~k)=0(4≤k∈Z~ )

ＩｎｔｒｏｄｕｃｔｉｏｎＯｎｅｋｉｎｄｏｆｓｔｅａｄｙｓｔａｔｅｒｅａｃｔｉｏｎ＿ｄｉｆｆｕｓｉｏｎｅｑｕａｔｉｏｎｓｉｓｒｅａｄａｓ([1,2],ｅｔｃ),Ｆ(ｕ,μ)=ｕ″ μ(ｕ-ｕｋ)=0(1)ｗｉｔｈｂｏｕｎｄａｒｙｖａｌｕｅｃｏｎｄｉｔｉｏｎｕ(0)=ｕ(π)=0,(2)ｗｈｅｒｅμｉｓａｐａｒａｍｅｔｅｒ,1<ｋ∈Ｚ .ＬｅｔＸ=ｕ∈Ｃ2[0,π]｜ｕ(0)=ｕ(π)=0,Ｙ=Ｃ0[0,π].ＴｈｅｎＦ(ｕ,μ)ｉｓａｍａｐｆｒｏｍＸ×ＲｏｎｔｏＹ.Ｗｅｄｅｆｉｎｅｉｎｎｅｒｐｒｏｄｕｃｔｓｏｎｔｈｅｓｅｓｐａｃｅｓｂｙ〈ｕ,ｖ〉=∫π0ｕ(ξ)ｖ(…     

复合材料单层的横向拉伸原地强度和0°/90°/O°叠层板张开型裂纹经典解的研究

本文:(1)用傅立叶变换和Copson的对偶积分方程法,求得了0°/90°/0°叠层板90°层内张开型裂纹问题的经典解;(2)应用所得解,对石墨/环氧叠层板中90°层的断裂特性和横向拉伸原地强度进行了定量研究。 结果表明,这类叠层板的应力强度因子不同于90°的单向层,它随0°层的厚度b、模量E_L或G_(LT)的增加而减小,也随90°层的厚度减小而减小,这就导致了叠层效应,并提高了90°层的横向原地强度。这里的理论计算与D.L.Flaggs的试验结果一致。     

Proximal point algorithm with errors for generalized strongly nonlinear quasivariational inclusions

I.IntroductionLetHbeaHibertspaceendowedwithanorm11'11andaninnerproduct',.)andC(H)bethefamilyofallnonemptycompactsubsetsofH.LetT,A:H~C(H)besetvaluedmappings,g:H~Hbeasingle-valuedmappingand9:HxH~RU{ ac}besuchthatforeachfixedyeH,9.,y):H~RUt co}isaproperconvexlowersemicontinuousfunctiononHandg(H)ndomag'Y)#oforeachyeH,ThentheproblemoffindingxeH,ueT(x)andveA(x)suchthatg(x)edomag',x)and(u~v,y~g(x))39(g(x)'x)~9(y'x)(VYeH)(l.l)iscalledthegeneralizedstronglynonlinearquasivariationalinclusio…     

EDITORIAL BOARD OF “APPLIED MATHEMATICS AND MECHANICS”

Editor-in-chief: Chien, Wei-zang (钱伟长) Vice Editor-in chief: Yeh, Kal-yuan (叶开源) Executive Editors: Wang, Zhi-zhong (王志忠) ; Xu, Yin-ge (徐尹格) Zhang, Lu-kun (张录坤)     

EDITORIAL BOARD OF "APPLIED HATHEMATICS AND MECHANICS

Editor-in-chief: Chien, Wei-zang (钱伟长) Vice Editor-in chief: Yeh, Kai-yuan (叶开源) Executive Editors: Wang, Zhi-zhong (王志忠); Xu, Yin-ge (徐尹格) Zhang, Lu-kun (张录坤)     

EDITORIAL COMMITTEE OF “APPLIED MATHEMATICS AND MECHANICS”

Editor-in-chief: Chien, Wei-zang (钱伟长) Vice Editor-in-chief: Yeh, Kai-yuan (叶开沅) Standing Members:Guo Zhong-heng (郭仲衡) Yang Gui-tong (杨佳通) Chen Zhi-da (陈至达) Tan Hao-sheng (谈镐生) Zhou Heng (周恒) Li Hao (李灏) Chu Chao-hsiang (朱兆祥) Wu Xue-mou (吴学谋) Hsueh Dah-wei (薛大为) Loo Wen-da (卢文达) Ouyang Chang (欧阳鬯)     

APPLIED MATHEMATICS AND MECHANICS

Honorary Editor-in-Chief: CHIEN Wei-zang(钱伟长) (President of Shanghai University) Editor-in-Chief: ZHOU Zhe-wei(周哲玮) Vice Editors-in-Chief: YEH Kai-yuan(叶开沅) , GUO Xing-ming(郭兴明) Executive Editors:WU Cheng-ping(吴承平), ZHANG Lu-kun(张禄坤)     

EDITORIAL COMMITTEE OF “APPLIED MATHEMATICS AND MECHANICS”

Editor-in-chief: Chien, Wei-zang (钱伟长) Vice Editor-in-chief: Yeh, Kai-yuan (叶开沅) Standing Members:Guo Zhong-heng (郭仲衡) Yang Gui-tong (杨佳通) Chen Zhi-da (陈至达) Tan Hao-sheng (谈镐生) Zhou Heng (周恒) Li Hao (李灏) Chu Chao-hsiang (朱兆祥) Wu Xue-mou (吴学谋) Hsueh Dah-wei (薛大为) Loo Wen-da (卢文达) Ouyang Chang (欧阳鬯)     

K0超固结结构性黏土的本构模型

K₀固结黏土在自然界广泛分布, 其通常同时具有超固结性与天然结构性, 而K₀超固结性又与K₀正常固结性质存在很大差异. 为了有效的描述K₀超固结性质, 在结构性模型基础上, 做了如下三点改进, 使得原模型拓展为同时考虑K₀超固结特性与天然结构性影响的本构模型. (1)引入相对应力比来描述屈服面, 并引入初始各向异性转轴参量ξ来表达初始各向异性对屈服面在p-q空间的位置影响. (2)基于给定的屈服面方程, 推导得到变相应力比参量, 并将变相应力比引入到统一硬化参数中, 利用统一硬化参数可以有效描述初始各向异性固结黏土在剪切加载下的剪缩与剪胀, 应变硬化及软化现象. (3)引入反映结构性胶结强度性质的胶结参量p_e, 并给出p_e随塑性偏应变的衰减演化方程, 利用胶结参量可描述结构性黏土的剪胀特性. 预测与试验结果对比表明, 所提的K₀超固结结构性模型可有效描述K₀超固结黏土的刚度提高效应, 黏土的包辛格效应, 结构性黏土胶结强度的损失现象以及结构性黏土的应变软化现象. 证明了所提模型的适用性以及合理性.      

EDITORAL COMMITTEE OF "APPLIED MATHEMATICS AND MECHANICS

Editor-in-chief: Chien, Wei-zang (钱伟长) Vice Editor-in-chief: Yeh, Kai-yuan (叶开沅) Standing Members:Guo Zhong-heng (郭仲衡) Yang Gui-tong (杨佳通) Chen Zhi-da (陈至达) Tan Hao-sheng (谈镐生) Zhou Heng (周恒) Li Hao (李灏) Chu Chao-hsiang (朱兆祥) Wu Xue-mou (吴学谋) Hsueh Dah-wei (薛大为) Loo Wen-da (卢文达) Ouyang Chang (欧阳鬯)     

EDITORIAL COMMITTEE OF "APPLIED MATHEMATICS AND MECHANICS

Editor-in-chief: Chien, Wei-zang (钱伟长) Vice Editor-in-chief: Yeh, Kai-yuan (叶开沅) Standing Members:Guo Zhong-heng (郭仲衡) Yang Gui-tong (杨佳通) Chen Zhi-da (陈至达) Tan Hao-sheng (谈镐生) Zhou Heng (周恒) Li Hao (李灏) Chu Chao-hsiang (朱兆祥) Wu Xue-mou (吴学谋) Hsueh Dah-wei (薛大为) Loo Wen-da (卢文达) Ouyang Chang (欧阳鬯)     

正交各向异性材料热弹性问题的三维无网格法计算模型及应用

建立了正交各向异性材料热弹性问题的三维无网格伽辽金(Element Free Galerkin, EFG)法计算模型。利用该计算模型对三维复合材料汽轮机叶轮和轴承座进行了热弹性分析,对比了材料方向角及热导率因子、热膨胀系数因子和拉压弹性模量因子不同组合情况下轴承座的最大热变形总位移和当量应力值,讨论了材料方向角及上述正交各向异性因子对热变形和当量应力的影响规律,并与各向同性材料进行了对比。结果表明:三维EFG模型的热变形总位移和当量应力相对误差范数分别比有限元法小0.1215%和0.1359%;材料方向角同时影响热变形的大小和方向,但对当量应力方向影响不大;正交各向异性材料因子主要影响热变形和当量应力的大小。在考虑热-机械载荷作用下的三维复合材料零件结构设计中,当以刚度或强度为主要需求时,材料方向角、热导率因子、热膨胀系数因子、拉压弹性模量因子分别在(45°~60°,8:1:4~10:1:5,(1/6):(1/5):1~(1/5):(1/4):1,(7/5):1:(9/5)~(3/2):1:2)或(0°~10°,(1/10):1:(1/5)~(1/8):1:(1/4),(1/5):1:(1/6)~(1/4):1:(1/5),1:(1/5):(1/10)~1:(1/4):(1/8))范围内取值能有效降低轴承座等结构的热变形和当量应力。     

On the Solution of Elliptic Equation (sum from k-0 to n) akΔkφ=0 and Its Application in Mechanics

In this paper, the solution of elliptic equation (sum from k-0 to n) a_kΔ^kφ=0 is discussedin detail by the method of separation of variables in complex field. The general solution which can be used in the approximation to the boundary conditions of the practical problems is presented. Two practical examples in mechanics are given.     

Algorithm of solutions for mixed-nonlinear variational-like inequalities in reflexive banach space

I.IntroductionLetDbeanonemptyconvexsubsetofaBanachspaceB,BbethetopologicaldualspaceofBand(u,v)bethepairingbetweenneBandr6B.LetT,A:D~B'and9:DxD-Bbethreemappingsandf:D~(-ac, ac1beareal-valuedfunction.Inthispaper,weshallinvestigatethemixednonlinearvariationalinequalityproblemMNna(T,A,9,f,D):FinduEDsuchthatSpecialCases.(l)f-0,thentheproblem(l.l)isequivalenttofindingueDsuchthatTheproblem(l.2)isthestronglynonlinearvariational-likeinequalityproblemstudiedbyNoorllJwhicharisesnaturallyincon…     

EDITORIAL COMMITTEE OF “APPLIED MATHEMATICS AND MECHANICS”

Editor-in-chief:ChienWeizang(钱伟长)ViceEditor-in-chief:YehKaiyuan(叶开沅)StandingMembers:YangGuitong(杨桂通)ChenZhida(陈至达)TanHaosheng(谈镐生)ZhouHeng(周恒)LiHao(李灏)ChuChaohsiang(朱兆祥)WuXuemou(吴学谋)HsuchDahwei(薛大为)LooWenda(卢文达)OuyangChang(欧阳■)GuoYouzhong(郭友中)Members:BianYingui(卞荫贵)ChenDapeng(陈大鹏)ChenLou(陈洛)ChenZhida(陈至达)ChengGengdong(程耿东)ChienWeizang(钱伟长)ChinYuanshun(#iCNJ)ChouHuanwen(ffi@Z)ChouLi(mN)ChuChaohsiang($)6#)DaiShiqiang(atd…     

EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LINARD SYSTEM

IntroductionInthispaper,weconsidertheexistenceofsolutionsoffollowingboundaryvalueproblemonreallineforLi啨ｎａｒｄｓｙｓｔｅｍ :u″-f(u)u′ g(u) =0 ,u(-∞ ) =0 ,　u( ∞ ) =1 ,(1 )wheref:R →Randg :R →RarefunctionsofclassC1.Amotivationforourresearchisconne