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Analytical solution of axisymmetric contact problem about indentation of a circular indenter into a soft functionally graded elastic layer 认领 引用 被引量：2
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作者 Sergey Volkov Sergey Aizikovich +1 位作者 Yue-Sheng Wang Igor Fedotov 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2013年第2期196-201,共6页
The paper addresses a contact problem of the theory of elasticity,i.e.,the penetration of a circular indenter with a flat base into a soft functionally graded elastic layer.The elastic properties of a functionally gra... The paper addresses a contact problem of the theory of elasticity,i.e.,the penetration of a circular indenter with a flat base into a soft functionally graded elastic layer.The elastic properties of a functionally graded layer arbitrarily vary with depth,and the foundation is assumed to be elastic,yet much harder than a layer.Approximated analytical solution is constructed,and it is shown that the solutions are asymptotically exact both for large and small values of characteristic dimensionless geometrical parameter of the problem.Numerical examples are analyzed for the cases of monotonic and nonmonotonic variations of elastic properties.Numerical results for the case of homogeneous layer are compared with the results for nondeformable foundation. 展开更多
关键词 Contact problems·Indentation·Functionally graded layer
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Neural boundary shape functions in physics-informed neural networks for discontinuous and high-frequency problems 认领 引用
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作者 P.T.NGUYEN K.A.LUONG J.H.LEE 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2026年第2期423-442,共20页
Physics-informed neural networks(PINNs)have been shown as powerful tools for solving partial differential equations(PDEs)by embedding physical laws into the network training.Despite their remarkable results,complicate... Physics-informed neural networks(PINNs)have been shown as powerful tools for solving partial differential equations(PDEs)by embedding physical laws into the network training.Despite their remarkable results,complicated problems such as irregular boundary conditions(BCs)and discontinuous or high-frequency behaviors remain persistent challenges for PINNs.For these reasons,we propose a novel two-phase framework,where a neural network is first trained to represent shape functions that can capture the irregularity of BCs in the first phase,and then these neural network-based shape functions are used to construct boundary shape functions(BSFs)that exactly satisfy both essential and natural BCs in PINNs in the second phase.This scheme is integrated into both the strong-form and energy PINN approaches,thereby improving the quality of solution prediction in the cases of irregular BCs.In addition,this study examines the benefits and limitations of these approaches in handling discontinuous and high-frequency problems.Overall,our method offers a unified and flexible solution framework that addresses key limitations of existing PINN methods with higher accuracy and stability for general PDE problems in solid mechanics. 展开更多
关键词 physics-informed neural network(PINN) boundary shape function(BSF) strong-form approach energy approach discontinuity high-frequency problem
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The Asymptotic Distribution of General Divisor Problem Associated to Dedekind Zeta Function over Certain Sequences 认领 引用
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作者 HUA Guodong 《数学进展》 CSCD 北大核心 2026年第2期292-314,共23页
Let Kj/Q,1≤j≤ν,ν≥2 be quadratic fields with pairwise coprime discriminants Dj,and let τkjKj(n)be the divisor function associated to Dedekind zeta function SKj(s).In this paper,we consider a multid... Let Kj/Q,1≤j≤ν,ν≥2 be quadratic fields with pairwise coprime discriminants Dj,and let τkjKj(n)be the divisor function associated to Dedekind zeta function SKj(s).In this paper,we consider a multidimensional general divisor problem related to the τkjKj(n)involving several number fields over square integers,by establishing the corresponding asymptotic formula.As an application,we also obtain the asymptotic formula of variance of these coefi icients. 展开更多
关键词 non-normal cubic field Dekekind zeta function divisor problem
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Green’s Functions of a Class of Sturm-Liouville Problems with Eigenparameters in Boundary Conditions 认领 引用
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作者 XIAO Lu MU Dan ZHANG Ruifan 《数学理论与应用》 2025年第1期94-106,共13页
In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hil... In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem. 展开更多
关键词 Sturm-Liouville problem Eigenparameter-dependent boundary condition Green’s function
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An inverse problem in film/substrate indentation:extracting both the Young's modulus and thickness of films 认领 引用 被引量：3
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作者 Yin Zhang Feifei Gao +1 位作者 Zhiyue Zheng Zhihai Cheng 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2018年第6期1061-1071,共11页
In an indentation test,the effective Young's modulus of a film/substrate bilayer heterostructure varies with the indentation depth,a phenomenon known as the substrate effect.In previous studies investigating this,... In an indentation test,the effective Young's modulus of a film/substrate bilayer heterostructure varies with the indentation depth,a phenomenon known as the substrate effect.In previous studies investigating this,only the Young's modulus of the film was unknown.Once the effective Young's modulus of a film/substrate structure is determined at a given contact depth,the Young's modulus of the film can be uniquely determined,i.e.,there is a one-to-one relation between the Young's modulus of the film and the film/substrate effective Young's modulus.However,at times it is extremely challenging or even impossible to measure the film thickness.Furthermore,the precise definition of the layer/film thickness for a two-dimensional material can be problematic.In the current study,therefore,the thickness of the film and its Young's modulus are treated as two unknowns that must be determined.Unlike the case with one unknown,there are infinite combinations of film thickness and Young's modulus which can yield the same effective Young's modulus for the film/substrate.An inverse problem is formulated and solved to extract the Young's modulus and thickness of the film from the indentation depth-load curve.The accuracy and robustness of the inverse problem-solving method are also demonstrated. 展开更多
关键词 Indentation test Film Substrate Inverse problem
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An New Area Function for Sharp Indenter Tips in Nanoindentation 认领 引用 被引量：4
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作者 刘东旭 张泰华 《Chinese Journal of Aeronautics》 EI CAS 2004年第3期159-164,共6页
A new area function is introduced and applied to a Berkovich tip in order tocharacterize the contact projected area between an indenter and indented material. The function canbe related directly to tip-rounding, there... A new area function is introduced and applied to a Berkovich tip in order tocharacterize the contact projected area between an indenter and indented material. The function canbe related directly to tip-rounding, thereby having obviously physical meaning. Nanoindentationexperiments are performed on a commercial Nano Indenter XP^R system. The other two area functionsintroduced by Oliver and Pharr and by Thurn and Cook respectively are involved in this paper forcomparison. By comparison from experimental results among different area functions, the indenter tipdescribed by the proposed area function here is very close to the experimental indenter. 展开更多
关键词 Indentation indenter contact area area function tip-rounding
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Quality-guaranteed Dubins Path Planning for USV Based on Mixed-integer Piecewise linear Programming for Addressing the Extended Minimum-time Intercept Problem 认领 引用 被引量：1
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作者 Xing Zhou Kelin Zhu +3 位作者 Shuang Liu Zhaoqing Li Wenxin Zhang Kang Du 《哈尔滨工程大学学报（英文版）》 CSCD 2026年第1期216-227,共12页
During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive... During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h2/(4√2),where h is the piecewise length. 展开更多
关键词 Minimum-time intercept problem Dubins vehicle Mixed-integer piecewise-linear program Linearization Approximate error trigonometric function USV
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A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function 认领 引用 被引量：2
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作者 GENG Jie ZHANG Mingwang ZHU Dechun 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2024年第1期29-37,共9页
In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear ... In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method. 展开更多
关键词 interior-point algorithm weighted linear complementarity problem full-Newton step kernel function iteration complexity
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Solving the Optimal Control Problems of Nonlinear Duffing Oscillators By Using an Iterative Shape Functions Method 认领 引用 被引量：2
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作者 Cheinshan Liu Chunglun Kuo Jiangren Chang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2020年第1期33-48,共16页
In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,wh... In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data. 展开更多
关键词 Nonlinear Duffing oscillator optimal control problem Hamiltonian formulation shape functions method iterative algorithm
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EXISTENCE OF POSITIVE SOLUTIONS FOR p-LAPLACIAN SINGULAR BOUNDARY VALUE PROBLEMS OF FUNCTIONAL DIFFERENTIAL EQUATION 认领 引用 被引量：6
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作者 SongChangxiu WengPeixuan 《Applied Mathematics(A Journal of Chinese Universities)》 2005年第1期51-58,共8页
In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
关键词 p-Laplacian operator functional differential equation boundary value problem positive solution fixed point theorem in cones.
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EXTENSION OF SMOOTHING FUNCTIONS TO SYMMETRIC CONE COMPLEMENTARITY PROBLEMS 认领 引用 被引量：2
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作者 Liu Yongjin Zhang Liwei Liu Meijiao 《Applied Mathematics(A Journal of Chinese Universities)》 2007年第2期245-252,共8页
The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity proble... The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0. 展开更多
关键词 symmetric cone complementarity problem smoothing function Euclidean Jordan algebra non-interior continuation method
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On the Variational Problems of the Functionals with Derivatives of Higher Orders and Undetermined Boundary 认领 引用 被引量：1
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作者 老大中 谈天民 《Journal of Beijing Institute of Technology》 EI CAS 2007年第1期116-121,共6页
According to the necessary condition of the functional taking the extremum, that is its first variation is equal to zero, the variational problems of the functionals for the undetermined boundary in the calculus of va... According to the necessary condition of the functional taking the extremum, that is its first variation is equal to zero, the variational problems of the functionals for the undetermined boundary in the calculus of variations are researched, the functionals depend on single argument, arbitrary unknown functions and their derivatives of higher orders. A new view point is posed and demonstrated, i.e. when the first variation of the functional is equal to zero, all the variational terms are not independent to each other, and at least one of them is equal to zero. Some theorems and corollaries of the variational problems of the functionals are obtained. 展开更多
关键词 calculus of variations functional variational problems derivatives of higher orders undetermined boundary
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Fekete-SzegProblems for Certain Classes of Meromorphic Functions Using q-Derivative Operator 认领 引用 被引量：1
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作者 Huo TANG H.M.ZAYED +1 位作者 A.O.MOSTAFA M.K.AOUF 《Journal of Mathematical Research with Applications》 CSCD 2018年第3期236-246,共11页
In this paper,we introduce two subclasses Eq*(φ)and∑*q,a(φ)of meromorphic functions f(z)for which qzDqf(z)/f(z)〈φ(z)and-(1-a/q)qzDqf(z)+azqDq[zDqf(z)]/(1-a/q)f(z)-azDqf(z)〈φ(z),a∈C/(0,1],0〈q〈1,respectively.S... In this paper,we introduce two subclasses Eq*(φ)and∑*q,a(φ)of meromorphic functions f(z)for which qzDqf(z)/f(z)〈φ(z)and-(1-a/q)qzDqf(z)+azqDq[zDqf(z)]/(1-a/q)f(z)-azDqf(z)〈φ(z),a∈C/(0,1],0〈q〈1,respectively.Sharp bounds for the Fekete-Szeg5 functional lal-tta21 of the above classes are obtained.Also,we consider some applications of the results obtained to functions defined by q-Bessel function. 展开更多
关键词 analytic function meromorphic function Fekete-Szego problem q-derivative operator q-Bessel function
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New exact penalty function for solving constrainedfinite min-max problems 认领 引用
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作者 马骋 李迅 +1 位作者 姚家晖 张连生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第2期253-270,共18页
This paper introduces a new exact and smooth penalty function to tackle constrained min-max problems. By using this new penalty function and adding just one extra variable, a constrained rain-max problem is transforme... This paper introduces a new exact and smooth penalty function to tackle constrained min-max problems. By using this new penalty function and adding just one extra variable, a constrained rain-max problem is transformed into an unconstrained optimization one. It is proved that, under certain reasonable assumptions and when the penalty parameter is sufficiently large, the minimizer of this unconstrained optimization problem is equivalent to the minimizer of the original constrained one. Numerical results demonstrate that this penalty function method is an effective and promising approach for solving constrained finite min-max problems. 展开更多
关键词 min-max problem constrained optimization penalty function
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FORCED OSCILLATIONS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FUNCTIONAL PARTIAL DIFFERENTIAL EQUATIONS 认领 引用
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作者 靳明忠 董莹 李崇孝 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1996年第9期889-900,共12页
In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish... In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities. 展开更多
关键词 higher order functional partial differential equation boundary value problems forced oscillation
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Functional analyses of the problems in non-English majors' writings 认领 引用 被引量：1
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作者 LI Sh un-ying 《US-China Foreign Language》 2010年第9期38-41,共4页
Problems in generating and organizing ideas, in coherence and language competence are common in non-English majors＇ writings, which decrease non-English majors＇ ability to use English as a tool to realize its pragma... Problems in generating and organizing ideas, in coherence and language competence are common in non-English majors＇ writings, which decrease non-English majors＇ ability to use English as a tool to realize its pragmatic functions and meta-functions. The exam-centered objective, the product-oriented approach, the inefficient mode of instruction, the ineffective feedback and the lack of creativity in teaching are responsible for the problems in non-English majors＇ writings. To avoid those problems, teachers need to improve their ways of instruction. 展开更多
关键词 problems in non-English majors＇ writings causes of those problems a functional perspective
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Solving frictional contact problems by two aggregate-function-based algorithms 认领 引用
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作者 Suyan He Hongwu Zhang Xingsi Li 《Acta Mechanica Sinica》 SCIE EI CAS 2005年第5期467-471,共5页
Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problem... Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased 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. 展开更多
关键词 Frictional contact problem. Linear complementarity problem .Aggregate function ~ Interior pointalgorithm ~ Smoothing algorithm
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Merit functions for nonsmooth complementarity problems and related descent algorithm 认领 引用
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作者 DU Shou-qiang GAO Yan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE 2010年第1期78-84,共7页
Under some assumptions, the solution set of a nonlinear complementarity problem coincides with the set of local minima of the corresponding minimization problem. This paper uses a family of new merit functions to deal... Under some assumptions, the solution set of a nonlinear complementarity problem coincides with the set of local minima of the corresponding minimization problem. This paper uses a family of new merit functions to deal with nonlinear complementarity problem where the underlying function is assumed to be a continuous but not necessarily locally Lipschitzian map and gives a descent algorithm for solving the nonsmooth continuous complementarity problems. In addition, the global convergence of the derivative free descent algorithm is also proved. 展开更多
关键词 Nonsmooth complementarity problem merit function nonsmooth continuous map descent algorithm.
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Majorization and Fekete-Szegö Problems for Multivalent Meromorphic Functions Associated with the Mittag-Leffler Function 认领 引用
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作者 LONG Pin-hong GANGADHARAN Murugusundaramoorthy +1 位作者 HAN Hui-li WANG Wen-shuai 《Chinese Quarterly Journal of Mathematics》 2022年第2期111-123,共13页
The main object of this present paper is to investigate the problem of majorization of certain class of multivalent meromorphic functions of complex order involving Mittag-Leffler function. Meanwhile, for this subclas... The main object of this present paper is to investigate the problem of majorization of certain class of multivalent meromorphic functions of complex order involving Mittag-Leffler function. Meanwhile, for this subclass the corresponding coefficient estimates and some Fekete-Szegö type inequalities are obtained. Moreover we point out some new or known consequences of our main results. 展开更多
关键词 Meromorphic function Majorization problem Hadamard product(convolution) Mittag-Leer function Fekete-Szegöinequality
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A Class of Inverse Boundary Value Problems for (λ,1) Bi-Analytic Functions 认领 引用
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作者 LIN Juan 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2023年第3期185-191,共7页
In this paper,a class of inverse boundary value problems for(λ,1)bi-analytic functions is given.Using the method of Riemann boundary value problem for analytic functions,the conditions of solvability and the expressi... In this paper,a class of inverse boundary value problems for(λ,1)bi-analytic functions is given.Using the method of Riemann boundary value problem for analytic functions,the conditions of solvability and the expression of the solutions for the inverse problems are obtained. 展开更多
关键词 inverse problem Riemann boundary value problem (λ,k)bi-analytic functions canonical function
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