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AN asymptotic method FOR ANALYZING THE STRESS IN A FUNCTIONALLY GRADIENT MATERIAL LAYER ON A SURFACE OF A STRUCTURAL COMPONENT

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Acta Mechanica Solida Sinica 1997年第1期10卷 36-47页

作者： Shen, LX Yu, SW TSING HUA UNIV DEPT ENGN MECHBEIJING 100084PEOPLES R CHINA

A simple and effective method for analyzing the stress distribution in a Functionally Gradient Material(FGM) layer on the su;face of a structural component is proposed in this paper. Generally, the FGM layer is very thin compared with the characteristic length of the structural component, and the nonhomogeneity exists only in the thin layer. Based on these features, by choosing a small parameter I which characterizes the stiffness of the layer relative to the component, and expanding the stresses and displacements on the two sides of the interface according to the parameter lambda, then asymptotically using the continuity conditions of the stresses and displacements on the interface, a decoupling computing process of the coupling control equations of the layer and the structural component is realized. Finally, two examples are given to illustrate the application of the method proposed.

关键词： gradient material layer stress state asymptotic method

asymptotics of the Solution to a Stationary Piecewise-Smooth Reaction-Diffusion-Advection Equation

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Chinese Annals of Mathematics,Series B 2023年第1期44卷 81-98页

作者： Qian YANG Mingkang NI College of Science University of Shanghai for Science and TechnologyShanghai 200093China School of Mathematical Sciences East China Normal UniversityShanghai 200062China Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice Shanghai 200241China

A singularly perturbed boundary value problem for a piecewise-smooth nonlinear stationary equation of reaction-diffusion-advection type is studied.A new class of problems in the case when the discontinuous curve which separates the domain is monotone with respect to the time variable is considered.The existence of a smooth solution with an internal layer appearing in the neighborhood of some point on the discontinuous curve is studied.An efficient algorithm for constructing the point itself and an asymptotic representation of arbitrary-order accuracy to the solution is proposed.For sufficiently small parameter values,the existence theorem is proved by the technique of matching asymptotic expansions.An example is given to show the effectiveness of their method.

关键词： Reaction-Diffusion-Advection equation Internal layer asymptotic method Piecewise-Smooth dynamical system

asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation

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Science China Mathematics 2022年第2期65卷 291-308页

作者： Qian Yang Mingkang Ni School of Mathematical Sciences East China Normal UniversityShanghai 200241China Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice Shanghai 200241China

A piecewise-smooth second-order singularly perturbed differential equation whose right-hand side is a nonlinear function with a discontinuity on some curve is investigated. This is a new class of problems in the case where the degenerate equation has a multiple root on the left-hand side of the curve which separates the domain and an isolated root on the right-hand side of that curve. The asymptotics of a solution with an internal layer near a point on the discontinuous curve and the transition point is constructed. The method to construct the internal layer function is proposed. The behavior of the solution in the internal layer consisting of four zones essentially differs from the case of isolated roots. For sufficiently small parameter values, the existence of a smooth solution with an internal layer from the multiple root of the degenerate equation to the isolated root in the neighborhood of a point on the discontinuous curve is proved. The method can be shown to be effective in the given example.

关键词： reaction-diffusion equation multizonal internal layer asymptotic method piecewise-smooth dynamical system

A class of asymptotic solution for the time delay wind field model of an ocean

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Chinese Physics B 2014年第4期23卷 83-90页

作者：周先春石兰芳莫嘉琪 College of Electronic and Information Engineering Nanjing University of Information Science and Technology (NUIST) Jiangsu Technology and Engineering Center for Meteorological Sensor Network Nanjing University of Information Science and Technology (NUIST) Jiangsu Key Laboratory of Meteorological Observation and Information Processing Nanjing University of Information Science and Technology (NUIST) College of Mathematics and Statistics Nanjing University of Information Science and Technology (NUIST)

A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturba- tion method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-la... 详细信息

关键词： two-layers barotropic time delay model asymptotic method

THE GROWTH OF DIFFERENCE EQUATIONS AND DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 2021年第6期41卷 1911-1920页

作者：陈宗煊张然然蓝双婷陈创鑫 School of Mathematical Sciences South China Normal UniversityGuangzhou510631China Department of Mathematics Guangdong University of EducationGuangzhou510303China School of Mathematics and Systems Sciences Guangdong Polytechnic Normal UniversityGuangzhou510665China College of Computational Sciences Zhongkai University of Agriculture and EngineeringGuangzhou510225China

In this paper,we mainly apply a new,asymptotic method to investigate the growth of meromorphic solutions of linear higher order difference equations and differential equations.We delete the condition(1.6)of Theorems E... 详细信息

关键词： asymptotic method difference equations differential equations

asymptotic Calculation of the Wave Trough Exceedance Probabilities in A Nonlinear Sea

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China Ocean Engineering 2018年第2期32卷 189-195页

作者： WANG Ying-guang State Key Laboratory of Ocean Engineering Shanghai Jiao Tong UniversityShanghai 200240China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration(CISSE) Shanghai 200240China School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China

This paper concerns the calculation of the wave trough exceedance probabilities in a nonlinear sea. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic method. This is a new approach for the calculation of the wave trough exceedance probabilities, and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The proposed asymptotic method has been applied to calculate the wave trough depth exceedance probabilities of a sea state with the surface elevation data measured at the coast of Yura in the Japan Sea. It is demonstrated that the proposed new method can offer better predictions than the theoretical Rayleigh wave trough depth distribution model. The calculated results by using the proposed new method have been further compared with those obtained by using the Arhan and Plaisted nonlinear distribution model and the Toffoli et al.’s wave trough depth distribution model, and its accuracy has been once again substantiated. The research findings obtained from this study demonstrate that the proposed asymptotic method can be readily utilized in the process of designing various kinds of ocean engineering structures.

关键词： wave trough depth second order nonlinear wave model asymptotic method measured data

Subharmonic resonance of single-degree-of-freedom piecewise-smooth nonlinear oscillator

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Acta Mechanica Sinica 2020年第5期36卷 1109-1118,I0003页

作者： Jiangchuan Niu Wenjing Zhang Yongjun Shen Shaopu Yang State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures Shijiazhuang Tiedao UniversityShijiazhuang 050043China School of Mechanical Engineering Shijiazhuang Tiedao UniversityShijiazhuang 050043China

Take the single degree of freedom nonlinear oscillator with clearance under harmonic excitation as an example,the 1/3 subharmonic resonance of piecewise-smooth nonlinear oscillator is investigated.The approximate analytical solution of 1/3 subharmonic resonance of the single-degree-of-freedom piecewise-smooth nonlinear oscillator is presented.By changing the solving process of Krylov-Bogoliubov-Mitropolsky(KBM)asymptotic method for subharmonic resonance of smooth nonlinear system,the classical KBM method is extended to piecewise-smooth nonlinear system.The existence conditions of 1/3 subharmonic resonance steady-state solution are achieved,and the stability of the subharmonic resonance steady-statesolution is also analyzed.It is found that the clearance affects the amplitude-frequency response of subharmonic resonance in the form of equivalent negative stiffness.Through a demonstration example,the accuracy of approximate analytical solution is verified by numerical solution,and they have good consistency.Based on the approximate analytical solution,the infuences of clearance on the critical frequency and amplitude-frequency response of 1/3 subharmonic resonance are analyzed in detail.The analysis results show that the KBM method is an effective analytical method for solving the subharmonic resonance of piecewise-smooth nonlinear system.And it provides an effective reference for the study of subharmonicr esonance of other piecewise-smooth systems.

关键词： Subharmonic resonance Piecewise-smooth system Approximate analytical solution asymptotic method

Influences of Marangoni effect on solidification of curved interfaces with constant curvature

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Applied Mathematics and Mechanics(English Edition) 2008年第2期29卷 145-151页

作者：胡国辉周哲玮 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai Key Laboratory of Mechanics in Energy and Environment Engineering Shanghai 200072P.R.China

The asymptotic method and phase field simulation are applied to study the influences of variation of the surface tension with temperature on the movements of solid-liquid interfaces in the solidification process of spherical and cylindrical nuclei, respectively. Results indicate that Marangoni effect will increase the critical nucleation radius, slow up the movement of interface. The tip speed of dendrite decreases linearly with Marangoni number for melt without convection. The results of phase field simulation are qualitatively in accord with that of asymptotic method.

关键词： solidification phase field simulation Marangoni effect asymptotic method wcrystal growth

AN INCOMPRESSIBLE RUBBER WEDGE UNDER THE TENSION OF A LINE LOAD AT ITS TIP

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Acta Mechanica Solida Sinica 2000年第4期13卷 306-311页

作者： Shi Shouxia Liu Xinhua China Changfeng Sci Technol Ind Grp Co Beijing Inst Remote Sensing Equipment Beijing 100854 Peoples R China

An analysis is made of the stress distribution and the deformationpattern near the apex of an incompressible rubber wedge under thetension of a concentrated force. The asymptotic method for the tipstress field is developed. The problem is treated as a plane straincase. Finally, the FEM numerical results agree with the theoreticalones.

关键词： incompressible rubber wedge asymptotic method nonlinear FEM