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ELASTODYNAMIC SOLUTION OF A non-homogeneous ORTHOTROPIC HOLLOW CYLINDER

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Acta Mechanica Sinica 2002年第6期18卷 621-628页

作者：丁皓江王惠明陈伟球 Department of Civil Engineering. Zhejianq University Hanqzhou China 310027 Department of Mechanics Zhejiang University Hangzhou China 310027 Department of Civil Engineering Zhejiang University Hangzhou China 310027

A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure.

关键词： orthotropic non-homogeneous hollow cylinder elastodynamic

Boundedness of Commutators of θ-Type Calderón-Zygmund Operators on non-homogeneous Metric Measure Spaces

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Chinese Annals of Mathematics,Series B 2019年第4期40卷 585-598页

作者： Chol RI Zhenqiu ZHANG Department of Mathematics Kim Hyong Jik Normal UniversityPyongYangD.P.R of Korea School of Mathematical Sciences and the Key Laboratory of Pure Mathematics and Combinatorics Nankai UniversityTianjin 300071China

Let(X, d, μ) be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions in the sense of Hyt?nen. In this paper, the authors obtain the boundedness of the commutators of θ-type Calderón-Zygmund operators with RBMO functions from L∞(μ) into RBMO(μ) and from Hat1,∞(μ) into L1(μ), *** a consequence of these results, they establish the Lp(μ) boundedness of the commutators on the non-homogeneous metric spaces.

关键词： non-homogeneous space θ-Type Calderón-Zygmund operator Commutator RBMO(μ) space Hat1,∞(μ) space

Activity criterion of pre-existing fabrics in non-homogeneous deformation domain

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Science China Earth Sciences 2010年第8期53卷 1115-1125页

作者： TONG HengMao CAI DongSheng WU YongPing LI XiaoGuang LI XuShen MENG LingJian State Key Laboratory of Petroleum Resources and Prospecting China University of PetroleumBeijing 102249China Zhanjiang Branch of China National Offshore Oil Corporation Zhanjiang 524057China Dagang Branch of China National Petroleum Corporation Tianjin 300280China Exploration and Development Institute Liaohe Oilfield Company of China National Petroleum CorporationPanjin 124010China

The Anderson's model can be applied only to elastic homogeneous deformation and cannot explain complicated phenomena of natural faults, which to a large degree limits the model to practical application. By combing the Coulomb-Mohr Criterion with the sandbox modeling and considering non-homogeneous deformation, mechanisms of how basement pre-existing fabrics control fault formation and evolution are analyzed and a mechanical factor, activation-coefficient (faS) of pre-existing fabrics, is proposed. It is determined by the attitude and mechanical properties of pre-existing fabric, and the stress state (the magnitudes and directions of the three principal stresses). The coefficient has taken the heterogeneity of rocks into account and may serve as a criterion for evaluating the activity of a pre-existing fabric. The Mohr-Coulomb Criterion is expanded to non-homogeneous deformation domain in terms of activation-coefficient (faS) of pre-existing fabrics, the general law of the activity of a pre-existing fabric is predicted, the fault complexity real of rift basin is revealed in theory, and the controlling law of basement pre-existing faults to fault formation and evolution is determined, and checked with sandbox modeling. A new way is provided for in-depth study of faulting.

关键词： Anderson’s model pre-existing fabric non-homogeneous deformation activation-coefficient sandbox modeling

Isogeometric Boundary Element Method for Two-Dimensional Steady-State non-homogeneous Heat Conduction Problem

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Computer Modeling in Engineering & Sciences 2022年第8期132卷 471-488页

作者： Yongsong Li Xiaomeng Yin Yanming Xu School of Architectural Engineering Huanghuai UniversityZhumadian463000China College of Intelligent Construction Wuchang University of TechnologyWuhan430223China

The isogeometric boundary element technique(IGABEM)is presented in this study for steady-state inhomogeneous heat conduction *** physical unknowns in the boundary integral formulations of the governing equations are discretized using non-uniform rational B-spline(NURBS)basis functions,which are utilized to build the geometry of the *** speed up the assessment of NURBS basis functions,the Bezier extraction´approach is *** solve the extra domain integrals,we use a radial integration *** numerical examples show the potential of IGABEM for dimension reduction and smooth integration of CAD and numerical analysis.

关键词： Isogeometric analysis NURBS boundary element method heat conduction non-homogeneous radial integration method

Operational limits of a non-homogeneous dielectric elastomer transducer

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International Journal of Smart and Nano Materials 2017年第4期8卷 214-231页

作者： Anup Teejo Mathew Soo Jin Adrian Koh Department of Mechanical Engineering National University of SingaporeSingaporeSingapore

Operation of a dielectric elastomer(DE)transducer is limited by the way it fails,and any other limits imposed by the *** example,material rupture and dielectric breakdown are two examples of transducer failure,while tension loss is a user-imposed *** instability may or may not result in transducer failure,but is often considered as a boundary to denote the onset of state *** a DE undergoing homogeneous deformation,constructing operational limits on work-conjugate state diagrams are rather ***,for DE subjected to non-homogeneous deformation,the process is more *** present a method to plot the operational boundaries of a DE subject to non-homogeneous deformation,known commonly as the Universal Muscle Actuator or the loudspeaker *** analysis show that tension loss need not be imposed as a hard operational limit,and that there is further operational space for the transducer,post tension *** plotting the operational limits on work-conjugate planes,we determine an optimal inner-to-outer ring ratio and the required pre-stretches that maximize energy conversion.

关键词： Dielectric elastomer non-homogeneous operational limits loudspeaker configuration

The C~α regularity of a class of non-homogeneous ultraparabolic equations

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Science China Mathematics 2009年第8期52卷 1589-1606页

作者： WANG WenDong ZHANG LiQun Institute of Mathematics Academy of Mathematics and Systems ScienceHua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijing 100190China

We obtain the Cα regularity for weak solutions of a class of non-homogeneous ultra- parabolic equation, with measurable coefficients. The result generalizes our recent Cα regularity results of homogeneous ultraparab... 详细信息

关键词： non-homogeneous ultraparabolic equations C α regularity Kruzhkov’s approaches 35K70 35D10 35B65

Thermal Effect on Free Vibration of non-homogeneous Orthotropic Visco-Elastic Rectangular Plate of Parabolically Varying Thickness

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Applied Mathematics 2010年第6期1卷 456-463页

作者： Arun Kumar Gupta Pooja Singhal Department of Mathematics M. S. College

A simple model presented here is to study the thermal effect on vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness having clamped boundary conditions on all the four edges. For non-homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the separation of variables method, the governing differential equation has been solved for vibration of non-homogeneous orthotropic viscoelastic rectangular plate. An approximate frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Results are calculated for time period and deflection at different points, for the first two modes of vibration, for various values of temperature gradients, non-homogeneity constant, taper constant and aspect ratio and shown by graphs.

关键词： Thermal Gradient Vibration non-homogeneous Orthotropic Visco-Elastic Rectangular Plate Variable Thickness

Development of Optimal Maintenance Policies for Offshore Wind Turbine Gearboxes Based on the non-homogeneous Continuous-Time Markov Process

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Journal of Marine Science and Application 2019年第1期18卷 93-98页

作者： Mingxin Li Jichuan Kang Liping Sun Mian Wang College of Shipbuilding Engineering Harbin Engineering University Center for Marine Technology and Engineering University of Lisbon University of California

Gearbox in offshore wind turbines is a component with the highest failure rates during operation. Analysis of gearbox repair policy that includes economic considerations is important for the effective operation of offshore wind farms. From their initial perfect working states, gearboxes degrade with time, which leads to decreased working efficiency. Thus, offshore wind turbine gearboxes can be considered to be multi-state systems with the various levels of productivity for different working states. To efficiently compute the time-dependent distribution of this multi-state system and analyze its reliability, application of the nonhomogeneous continuous-time Markov process(NHCTMP) is appropriate for this type of object. To determine the relationship between operation time and maintenance cost, many factors must be taken into account, including maintenance processes and vessel requirements. Finally, an optimal repair policy can be formulated based on this relationship.

关键词： Maintenance policy non-homogeneous continuous-time Markov process Offshore wind turbine gearboxes Reliability analysis Failure rates System engineering

The Existence of Positive Solutions of p-Laplacian non-homogeneous Multi-point Boundary Value Problems

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Chinese Quarterly Journal of Mathematics 2013年第2期28卷 190-195页

作者： TIAN Ya Department of Mathematics Xingtai University Xingtai 054001 China

We study the following nonlinear m-point p-Laplacian boundary value problem with non-homogenous condition: (Φp(u′)′)+f(t, u, u′)=0, 01, λ>0, ki≥0(i = 1, 2, ··· , m-2), 0 λ*. The proof is based on the Schaude... 详细信息

关键词： p-Laplacian operator non-homogeneous Shauder fixed-point theorem upperlower technics