接触问题的互补变分原理及非线性互补模型

给出了接触问题的互补虚功原理,互补能量原理及变分不等式等变分提法,并讨论了三类提法的关系。其此建立了有限维非线性互补模型并给出解的存在唯一性定理。文中还阐明了有,无摩擦接触问题之间以及二维和三维有摩擦接触问题之间的本质区别。     

A positive interior-point algorithm for nonlinear complementarity problems

1　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＡｌｇｏｒｉｔｈｍＧｉｖｅｎａｆｕｎｃｔｉｏｎｆ:Ｒｎ→Ｒｎ,ｗｈｉｃｈｉｓａｓｓｕｍｅｄｔｏｂｅｃｏｎｔｉｎｕｏｕｓｌｙｄｉｆｆｅｒｅｎｔｉａｂｌｅｉｎａｎｏｐｅｎｓｅｔｃｏｎｔａｉｎｉｎｇＲｎ+,ｔｈｅｎｏｎｌｉｎｅａｒｃｏｍｐｌｅｍｅｎｔａｒｉｔｙｐｒｏｂｌｅｍ ,ｄｅｎｏｔｅｄＮＣＰ (ｆ) ,ｉｓｔｏｆｉｎｄａｖｅｃｔｏｒｘ∈Ｒｎｓｕｃｈｔｈａｔｘ≥ 0 ,　ｆ(ｘ) ≥ 0 ,　ｘＴｆ(ｘ) =0 ,Ｃｌｅａｒｌｙ ,ｔｈｅＮＣＰ (ｆ)ｉｓｅｑｕｉｖａｌｅｎｔｔｏｔｈｅｆｏｌｌｏｗ…     

Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problems in Banach spaces

A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.     

FIXED POINT THEOREMS FOR FUZZY MAPPINGS IN PROBABILISTIC METRIC SPACES

ＦＩＸＥＤ　ＰＯＩＮＴ　ＴＨＥＯＲＥＭＳ　ＦＯＲ　ＦＵＺＺＹ　ＭＡＰＰＩＮＧＳ　ＩＮ　ＰＲＯＢＡＢＩＬＩＳＴＩＣ　ＭＥＴＲＩＣ　ＳＰＡＣＥＳＺｈａｎｇＳｈｉｓｈｅｎｇ（张石生）；ＺｈａｎｇＹｉｎｇ（张颖）；ＹｕａｎＪｉａｗｅｉ（袁家玮）（Ｒｅｃｅｉｖ...     

接触问题的非线性互补－接触柔度法

基于势能互补原理，不引入额外松弛变量，对库仑摩擦定律未做预先线性化近似，提出了三维弹性摩擦接触问题的非线性互补－接触柔度法，收敛性和收敛速率得到了严格理论保证。数值实验结果表明方法可靠、有效、低存储量、高精度     

Hybrid projection method for generalized mixed equilibrium problems, variational inequality problems, and fixed point problems in Banach spaces

A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.     

Hybrid projection method for generalized mixed equilibrium problems,variational inequality problems,and fixed point problems in Banach spaces

A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.     

The perturbation-iterative method applied to the problems of the large deflection of the elastic circular thin plates

In this paper, we present a perturbation-iterative method for solving certain boundary value problems encountered in the nonlinear theory of elastic circular thin plates. At the same time, with this method, we strictly prove the convergence of the solutions for the large deflection equations of circular plates subjected to certain distributed loads.     

解Drucker-Prager塑性问题的二阶锥互补法

基于经典弹塑性理论中多数屈服准则具有凸锥数学结构的事实,将在大规模计算中更具潜力的锥规划法引入弹塑性分析。考虑到弹塑性流动理论有关联与非关联之分,本文提出利用锥型互补法求解弹塑性问题。具体以Drucker-Prager弹塑性模型为例,首先利用最大塑性功耗散原理和圆锥对偶理论等工具,建立了弹塑性本构方程的等价二阶锥互补模型;然后,基于参变量变分原理和有限元技术,建立了弹塑性增量分析的二阶锥线性互补模型;最后,利用一类半光滑Newton算法求解。数值算例表明了本文方法的有效性。     

A linear complementarity model for multibody systems with frictional unilateral and bilateral constraints

The Lagrange-I equations and measure differential equations for multibody systems with unilateral and bilateral constraints are constructed.For bilateral constraints,frictional forces and their impulses contain the products of the filled-in relay function induced by Coulomb friction and the absolute values of normal constraint reactions.With the time-stepping impulse-velocity scheme,the measure differential equations are discretized.The equations of horizontal linear complementarity problems(HLCPs),which are used to compute the impulses,are constructed by decomposing the absolute function and the filled-in relay function.These HLCP equations degenerate into equations of LCPs for frictional unilateral constraints,or HLCPs for frictional bilateral constraints.Finally,a numerical simulation for multibody systems with both unilateral and bilateral constraints is presented.     

Solving frictional contact problems by two aggregate-function-based algorithms

Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-function-based algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms. The project supported by the National Natural Science Foundation of China(10225212, 50178016, 10302007), the National Key Basic Research Special Foundation and the Ministry of Education of China The English text was polished by Ron Marshall.     

Generalized Strongly Nonlinear Quasi-Complementarity Problems

ＧＥＮＥＲＡＬＩＺＥＤＳＴＲＯＮＧＬＹＮＯＮＬＩＮＥＡＲＱＵＡＳＩ－ＣＯＭＰＬＥＭＥＮＴＡＲＩＴＹＰＲＯＢＬＥＭＳＬｉＨｏｎｇ－ｍｅｉ（李红梅）ＤｉｎｇＸｉｅ－ｐｉｎｇ（丁协平）（ＳｉｃｈｕａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ），Ｃｈｅｎｇｄｕ（Ｒｅ...     

GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS IN LOCALLY G-CONVEX SPACES

IntroductionLetX ,YbetwotopologicalspacesandZbeanonemptyset.LetF∶X×X→ 2 Z,A∶X→ 2 XandC∶X→ 2 Zbeset_valuedmappingswhere2 ZdenotesthefamilyofallsubsetsofZ .　　Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅰ ) (inshort,GVQEP(Ⅰ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) ,　　 z∈A( ^x) . ( 1 )　　Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅱ ) (inshort,GVQEP(Ⅱ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) ,　　 z∈A( ^x) . ( 2 )　　…     

NON-INTERIOR SMOOTHING ALGORITHM FOR FRICTIONAL CONTACT PROBLEMS

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.     

Generalized mixed equilibrium problem in Banach spaces

This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-C- nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.     

Global linear and quadratic one-step smoothing newton method for vertical linear complementarity problems

IntroductionLetN ∈Rm0 ×n(m0 ≥n)beaverticalblockmatrixoftype(m1,… ,mn) ,q∈Rm0 beaconstantvectorpartitionedconformablywithN ,thatareN =N1Nn,　q =q1qn,　m0 = ni=1mi,whereNi ∈Rmi×n,qi ∈Rmi,i ∈I =1 ,… ,n .WeconsidertheverticallinearomplementarityproblemVLCP(N ,q)associatedwith (N ,q)offindingavectorx∈Rnsuchthatx≥ 0 ,　si(x) :=Nix+qi ≥ 0 ,　xi∏mij=1sij(x) =0　　 (i∈I) ,wherexi,sij(x)denotetheithcomponentofxandthejthcomponentofsi(x) ,respectively ;∏ mj=1ajdenotesa1…am.Iti…     

Bilevel generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems in reflexive Banach spaces

A new bilevel generalized mixed equilibrium problem(BGMEP) involving generalized mixed variational-like inequality problems(GMVLIPs) is introduced and studied in the reflexive Banach spaces.First,an auxiliary generalized mixed equilibrium problem(AGMEP) is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs.By using a minimax inequality,the existence and the uniqueness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions.By using an au...     

Generalized Riemann problem for gas dynamic combustion

The generalized Riemann problem for gas dynamic combustion in a neighborhood of the origin t > 0 in the (x, t) plane is considered. Under the modified entropy conditions, the unique solutions are constructed, which are the limits of the selfsimilar Zeldovich-von Neumann-Dring (ZND) combustion model. The results show that, for some cases, there are intrinsical differences between the structures of the perturbed Riemann solutions and the corresponding Riemann solutions. Especially, a strong detonation in the...     

Existence results for generalized vector equilibrium problems with applications

By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the generalized vector equilibrium constraints under the mild conditions are also given. The results of this paper unify and improve the corresponding results in the previous literature.     

Fixed point theorems for fuzzy mappings

Fixed point theorems for fuzzy mappings are of fundamental importance in fuzzy mathematical theory and application investigation. This paper pressents some new fixed point theorems for fuzzy mapping, whose results generalize and improve the results of [3] and give a partial answer to the unsolved problem suggested in [1].