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Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua 被引量:1
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作者 Karan S. Surana Emilio N. Alverio 《Applied Mathematics》 2020年第7期546-578,共33页
Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous... Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper. 展开更多
关键词 Energy methods principle of Virtual Work Calculus of Variations Euler’s Equation mathematical model Classical and Non-Classical Continuum mechanics
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Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation 被引量:3
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作者 Karan S. Surana Sri Sai Charan Mathi 《American Journal of Computational Mathematics》 2020年第2期167-220,共54页
Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived ... Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models. 展开更多
关键词 Plate and Shell mathematical models Energy Functional Thermodynamic Consistency Classical Continuum mechanics Non-Classical Continuum mechanics Internal Rotations Cosserat Rotations principle of Virtual Work
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Dynamic Factor Method of Computing Dynamic Mathematical Model for System Simulation
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作者 老大中 吴娟 +1 位作者 杨策 蒋滋康 《Journal of Beijing Institute of Technology》 EI CAS 2003年第2期143-148,共6页
The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of t... The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of the dynamic mathematical model is researched. By means of theoretical analysis, the error formulas, the error sign criteria and the error relationship criterion of the implicit Euler method and the trapezoidal method are given, the dynamic factor affecting the computational accuracy has been found, the formula and the methods of computing the dynamic factor are given. The computational accuracy of the dynamic mathematical model like this can be improved by use of the dynamic factor. 展开更多
关键词 system simulation dynamic mathematical model computational method dynamic factor ERROR
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Mathematical modelling of a biofilm: The Adomian decomposition method
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作者 Subramanian Muthukaruppan Alagu Eswari Lakshmanan Rajendran 《Natural Science》 2013年第4期456-462,共7页
A mathematical modelling by a biofilm under steady state conditions is discussed. The nonlinear differential Equations in biofilm reaction is solved using the Adomian decomposition method. Approximate analytical expre... A mathematical modelling by a biofilm under steady state conditions is discussed. The nonlinear differential Equations in biofilm reaction is solved using the Adomian decomposition method. Approximate analytical expressions for substrate concentration have been derived for all values of parameters δ and SL. These analytical results are compared with the available numerical results and are found to be in good agreement. 展开更多
关键词 mathematical modeling Simulation Adomian DECOMPOSITION method INITIAL BOUNDARY VALUE Problems
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A two-parameter mathematical model for immobilizedenzymes and Homotopy analysis method
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作者 Rathinasamy Angel Joy Athimoolam Meena +1 位作者 Shunmugham Loghambal Lakshmanan Rajendran 《Natural Science》 2011年第7期556-565,共10页
A two parameter mathematical model was developed to find the concentration for immobilized enzyme systems in porous spherical particles. This model contains a non-linear term related to reversible Michaelies-Menten ki... A two parameter mathematical model was developed to find the concentration for immobilized enzyme systems in porous spherical particles. This model contains a non-linear term related to reversible Michaelies-Menten kinetics. Analytical expression pertaining to the substrate concentration was reported for all possible values of Thiele module φ and α . In this work, we report the theoretically evaluated steady-state effectiveness factor for immobilized enzyme systems in porous spherical particles. These analytical results were found to be in good agreement with numerical results. Moreover, herein we employ new “Homotopy analysis method” (HAM) to solve non-linear reaction/diffusion equation. 展开更多
关键词 mathematical modeling MICHAELIS-MENTEN KINETICS HOMOTOPY Analysis method Reaction/Diffusion Equation EFFECTIVENESS factor
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Mathematical modeling of elastic inverted pendulum control system 被引量:3
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作者 ChaoXU XinYU 《控制理论与应用(英文版)》 EI 2004年第3期281-282,共2页
Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering. The researches concentrate on the rigid finite dimensional models which are described... Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering. The researches concentrate on the rigid finite dimensional models which are described by ordinary differential equations (ODEs) .Complete rigidity is the approximation of practical models ; Elasticity should be introduced into mathematical models in the analysis of system dynamics and integration of highly precise controller. A new kind of inverted pendulum, elastic inverted pendulum was proposed, and elasticity was considered. Mathematical model was derived from Hamiltonian principle and variational methods, which were formulated by the coupling of partial differential equations (PDE) and ODE. Because of infinite dimensional, system analysis and control of elastic inverted pendulum is more sophisticated than the rigid one. 展开更多
关键词 Elastic inverted pendulum Hamiltonian principle Variational methods mathematical model Coupling equation array
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Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core 被引量:3
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作者 M.GRYGOROWICZ E.MAGNUCKA-BLANDZI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第10期1361-1374,共14页
The paper is devoted to mathematical modelling of static and dynamic stability of a simply supported three-layered beam with a metal foam core. Mechanical properties of the core vary along the vertical direction. The ... The paper is devoted to mathematical modelling of static and dynamic stability of a simply supported three-layered beam with a metal foam core. Mechanical properties of the core vary along the vertical direction. The field of displacements is for- mulated using the classical broken line hypothesis and the proposed nonlinear hypothesis that generalizes the classical one. Using both hypotheses, the strains are determined as well as the stresses of each layer. The kinetic energy, the elastic strain energy, and the work of load are also determined. The system of equations of motion is derived using Hamilton's principle. Finally, the system of three equations is reduced to one equation of motion, in particular, the Mathieu equation. The Bubnov-Galerkin method is used to solve the system of equations of motion, and the Runge-Kutta method is used to solve the second-order differential equation. Numerical calculations are done for the chosen family of beams. The critical loads, unstable regions, angular frequencies of the beam, and the static and dynamic equilibrium paths are calculated analytically and verified numerically. The results of this study are presented in the forms of figures and tables. 展开更多
关键词 mathematical modelling dynamic stability metal foam core with variable mechanical property static and dynamic equilibrium path angular frequency
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Mathematical Model and Geometrical Model of Double Pitch ZN-type Worm Gear Set Based on Generation Mechanism 被引量:2
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作者 SHU Linsen CAO Huajun +2 位作者 LI Xianchong ZHANG Chenglong LI Yuxia 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2015年第3期549-555,共7页
The current researches on the tooth surface mathematical equations and the theory of gearing mainly pay attention to the ordinary type worm gear set(e.g., ZN, ZA, or ZK). The research of forming mechanism and three-... The current researches on the tooth surface mathematical equations and the theory of gearing mainly pay attention to the ordinary type worm gear set(e.g., ZN, ZA, or ZK). The research of forming mechanism and three-dimensional modeling method for the double pitch worm gear set is not enough. So there are some difficulties in mathematical model deducing and geometry modeling of double pitch ZN-type worm gear set based on generation mechanism. In order to establish the mathematical model and the precise geometric model of double pitch ZN-type worm gear set, the structural characteristics and generation mechanism of the double pitch ZN-type worm gear set are investigated. Mathematical model of the ZN-type worm gear set is derived based on its generation mechanism and the theory of gearing. According to the mathematical model of the worm gear set which has been developed, a geometry modeling method of the double pitch ZN-type worm and worm gear is presented. Furthermore, a geometrical precision calculate method is proposed to evaluate the geometrical quality of the double pitch worm gear set. As a result, the maximum error is less than 6′10–4 mm in magnitude, thus the model of the double pitch ZN-type worm gear set is available to meet the requirements of finite element analysis and engineering application. The derived mathematical model and the proposed geometrical modeling method are helpful to guiding the design, manufacture and contact analysis of the worm gear set. 展开更多
关键词 double pitch ZN-type worm gear set generation mechanism mathematical model geometrical model
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Mathematical modelling of translational motion of rail-guided cart with suspended payload 被引量:3
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作者 MITREV Rosen 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2007年第9期1395-1400,共6页
In this paper modelling of the translational motion of transportation rail-guided cart with rope suspended payload is considered. The linearly moving cart,driven by a travel mechanism,is modelled as a discrete six deg... In this paper modelling of the translational motion of transportation rail-guided cart with rope suspended payload is considered. The linearly moving cart,driven by a travel mechanism,is modelled as a discrete six degrees of freedom (DOF) dynamic system. The hoisting mechanism for lowering and lifting the payload is considered and is included in the dynamic model as one DOF system. Differential equations of motion of the cart elements are derived using Lagrangian dynamics and are solved for a set of real-life constant parameters of the cart. A two-sided interaction was observed between the swinging payload and the travel mechanism. Results for kinematical and force parameters of the system are obtained. A verification of the proposed model was conducted. 展开更多
关键词 Transportation rail-guided cart Travel mechanism Swinging payload Discrete dynamical model mathematical model
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A Mathematical Model for EstimatingElectroosmosis Effect on Water Displacing Oil Process in Porous Media and Its Application 被引量:1
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作者 Yun Junxian (Chemical Engineering Institute, Dalian University of Technology, DaLian 116012)Zhang Ningsheng Zhang Wei Wu Xinmin(Department of Petroleum Engineering, Xi’an Petroleum Institute, Xi’an 710065) 《Journal of Earth Science》 SCIE CAS CSCD 1999年第3期241-244,共4页
A mathematical model based on Darcy's law and electroosmosis equation in porous media is developed and two parameters named electroosmosis coefficient K, and relative electroosmosis coefficient Kre are used to cal... A mathematical model based on Darcy's law and electroosmosis equation in porous media is developed and two parameters named electroosmosis coefficient K, and relative electroosmosis coefficient Kre are used to calculate the curves of Ke and Krevs. water saturation whick are employed to estimate the effect of electroosmosis on water displacing oil process in sandstone cores. Under the conditions of constant injection rate displacement and constant electrical potential gradient, the method to calculate parameters K. and K. at different water saturation is developed and unsteadystate displacement experin.ental data under the effect of electroosmosis are used to determine the Parameter values. The results show that K, and K, are increased firstly with increasing water saturation and then decreased. This trend shows the inter-relationship between electroosmosis and the water displacing oil process. Finally, application of the model to ECMP mechauics studies and ac-tual reservoirs is analyzed in this peper. 展开更多
关键词 electroosmosis mathematical model electrical-chemical producing method displacement experiment porous media
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STREAMLINE-BASED MATHEMATICAL MODEL FOR CO_2 MISCIBLE FLOODING 被引量:8
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作者 侯健 《应用数学和力学》 EI CSCD 北大核心 2004年第6期635-642,共8页
According to the research theory of improved black oil simulator, a practical mathematical model for CO2 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas... According to the research theory of improved black oil simulator, a practical mathematical model for CO2 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas relative permeability and effective viscosity under the condition of miscible flow. In order to predict the production performance(fast,) streamline method is employed to solve this model as an alternative to traditional finite(difference) (methods.) Based on streamline distribution of steady-state flow through porous media with complex boundary confirmed with the boundary element method (BEM), an explicit total variation diminishing (TVD) method is used to solve the one-dimensional flow problem. At the same time, influences of development scheme, solvent slug size, and injection periods on CO2 drive recovery are discussed. The model has the advantages of less(information) need, fast calculation, and adaptation to calculate CO2 drive performance of all kinds of patterns in a random shaped porous media with assembly boundary. It can be an(effective) tool for early stage screening and reservoir dynamic management of the CO2(miscible) oil field. 展开更多
关键词 混相驱 流线 数学模型 边界元法 提高采收率
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Optimization Mathematical Model of Pile Forces for Offshore Piled Breasting Dolphins 被引量:1
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作者 周锡礽 王乐芹 +1 位作者 王晖 朱福明 《海洋工程:英文版》 EI 2004年第4期567-575,共9页
An optimization mathematical model of the pile forces for piled breasting dolphins in the open sea under various loading conditions is presented. The optimum layout with the well distributed pile forces and the least ... An optimization mathematical model of the pile forces for piled breasting dolphins in the open sea under various loading conditions is presented. The optimum layout with the well distributed pile forces and the least number of piles is achieved by the multiplier penalty function method. Several engineering cases have been calculated and compared with the result of the conventional design method. It is shown that the number of piles can be reduced at least by 10%~20% and the piles' bearing state is improved greatly. 展开更多
关键词 piled breasting dolphin mathematical model multiplier penalty function method optimization design
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Impact of pertinent parameters on foam behavior in the entrance region of porous media:mathematical modeling 被引量:1
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作者 Fereshteh Samimi Zahra Sakhaei Masoud Riazi 《Petroleum Science》 SCIE CAS CSCD 2020年第6期1669-1682,共14页
Foam injection is a promising solution for control of mobility in oil and gas field exploration and development,including enhanced oil recovery,matrix-acidization treatments,contaminated-aquifer remediation and gas le... Foam injection is a promising solution for control of mobility in oil and gas field exploration and development,including enhanced oil recovery,matrix-acidization treatments,contaminated-aquifer remediation and gas leakage prevention.This study presents a numerical investigation of foam behavior in a porous medium.Fractional flow method is applied to describe steady-state foam displacement in the entrance region.In this model,foam flow for the cases of excluding and including capillary pressure and for two types of gas,nitrogen(N2)and carbon dioxide(CO2)are investigated.Effects of pertinent parameters are also verified.Results indicate that the foam texture strongly governs foam flow in porous media.Required entrance region may be quite different for foam texture to accede local equilibrium,depending on the case and physical properties that are used.According to the fact that the aim of foaming of injected gas is to reduce gas mobility,results show that CO2 is a more proper injecting gas than N2.There are also some ideas presented here on improvement in foam displacement process.This study will provide an insight into future laboratory research and development of full-field foam flow in a porous medium. 展开更多
关键词 Foam displacement Entrance region Fractional flow method Foam texture Water saturation mathematical modeling
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Mathematical modeling of the bellows dispersion system of submunitions
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作者 师娇 唐胜景 高峰 《Journal of Beijing Institute of Technology》 EI CAS 2012年第1期23-30,共8页
A mathematical model of the bellows dispersion system is developed by combining the interior ballistic theory with structural dynamics theory to describe the deformation course of bellows. By analyzing the physical mo... A mathematical model of the bellows dispersion system is developed by combining the interior ballistic theory with structural dynamics theory to describe the deformation course of bellows. By analyzing the physical model of the bellows dispersion system, the dispersion course is divided into three stages. For each stage, mathematical model is built and its terminal conditions are given. The numerical simulation is based on the Runge-Kutta method and differential quadrature method. Simulation results of the model agree with those of the model built by only interior ballistics theory. However, this model is congruous with the actual dispersion course and can more easily determine the dispersion time and submunition displacement. 展开更多
关键词 mathematical model differential quadrature method DEFORMATION DISPERSION submu- nitions
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MATHEMATICAL MODELS ARISING FROM A SURVEY OF FERROMAGNETIC MATERIALS UNDER MAGNETISATION
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作者 顾晓安 曾进 沈荣瀛 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第9期1065-1074,共10页
This paper focuses on mathematical models describing the mechanical behavior of ferromagnetic materials under magnetization. Through combination of the electromagnetic field theory with the theory of elastic mechanics... This paper focuses on mathematical models describing the mechanical behavior of ferromagnetic materials under magnetization. Through combination of the electromagnetic field theory with the theory of elastic mechanics, several nonlinear systems of fourth order partial differential equations were deduced. By making further assumption, the first-order approximation of the above equations was established, of which the solutions are good enough for engineering application. 展开更多
关键词 sinusoidal magnetic field ferromagnetic material mechanical behavior mathematical model
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Establishment and Application of A Mathematical Model for Rectangular Billet Continuos Casting
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作者 IJU Qing TIAN Nianyuan +5 位作者 WANG Yingqun WU Xiaodong HOU Wenyi XU Mingxin XIANYU Jintang ZHANG Xiumu(Shanghai Pudong Iron & Steel Co. Ltd.)(Metallurgy Engineering School, USTB, Beijiing 100083, China) 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 1997年第4期10-14,共5页
A two dimension unsteady heat transfer model is established for rectangular billet casting. Solidification process of liquid steel in secondary cooling zone was analyzed using direct difference method. The influence o... A two dimension unsteady heat transfer model is established for rectangular billet casting. Solidification process of liquid steel in secondary cooling zone was analyzed using direct difference method. The influence of operation parameters including casting speed and temperature of liquid steel was investigated. Experimental results have been used for increasing the casting speed. 展开更多
关键词 continuous casting rectangular billed direct difference method mathematical model
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Mathematical Model for Takeoff Simulation of a Wing in Proximity to the Ground
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作者 Omer Kemal Kinaci 《Journal of Marine Science and Application》 CSCD 2016年第2期136-143,共8页
Aircraft flying close to the ground benefit from enhanced efficiency owing to decreased induced drag and increased lift. In this study, a mathematical model is developed to simulate the takeoff of a wing near the grou... Aircraft flying close to the ground benefit from enhanced efficiency owing to decreased induced drag and increased lift. In this study, a mathematical model is developed to simulate the takeoff of a wing near the ground using an Iterative Boundary Element Method (IBEM) and the finite difference scheme. Two stand-alone sub-codes and a mother code, which enables communication between the sub-codes, are developed to solve for the self-excitation of the Wing-In-Ground (WIG) effect. The aerodynamic force exerted on the wing is calculated by the first sub-code using the IBEM, and the vertical displacement of the wing is calculated by the second sub-code using the finite difference scheme. The mother code commands the two sub-codes and can solve for the aerodynamics of the wing and operating height within seconds. The developed code system is used to solve for the force, velocity, and displacement of an NACA6409 wing at a 4° Angle of Attack (AoA) which has various numerical and experimental studies in the literature. The effects of thickness and AoA are then investigated and conclusions were drawn with respect to generated results. The proposed model provides a practical method for understanding the flight dynamics and it is specifically beneficial at the pre-design stages of a WIG effect craft. 展开更多
关键词 wing-in-ground effect ground proximity flightdynamics iterative boundary element method mathematical model takeoff simulation
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Tight gas charging and accumulation mechanisms and mathematical model
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作者 ZHOU Nengwu LU Shuangfang +11 位作者 ZHANG Pengfei LIN Zizhi XIAO Dianshi LU Jiamin ZHU Yingkang LIU Yancheng LIN Liming WANG Min JIANG Xinyu LIU Yang WANG Ziyi LI Wenbiao 《Petroleum Exploration and Development》 SCIE 2023年第6期1411-1425,共15页
The gas-water distribution and production heterogeneity of tight gas reservoirs have been summarized from experimental and geological observations, but the charging and accumulation mechanisms have not been examined q... The gas-water distribution and production heterogeneity of tight gas reservoirs have been summarized from experimental and geological observations, but the charging and accumulation mechanisms have not been examined quantitatively by mathematical model. The tight gas charging and accumulation mechanisms were revealed from a combination of physical simulation of nuclear magnetic resonance coupling displacement, numerical simulation considering material and mechanical equilibria, as well as actual geological observation. The results show that gas migrates into tight rocks to preferentially form a gas saturation stabilization zone near the source-reservoir interface. When the gas source is insufficient, gas saturation reduction zone and uncharged zone are formed in sequence from the source-reservoir interface. The better the source rock conditions with more gas expulsion volume and higher overpressure, the thicker the gas saturation stabilization and reduction zones, and the higher the overall gas saturation. When the source rock conditions are limited, the better the tight reservoir conditions with higher porosity and permeability as well as larger pore throat, the thinner the gas saturation stabilization and reduction zones, but the gas saturation is high. The sweet spot of tight gas is developed in the high-quality reservoir near the source rock, which often corresponds to the gas saturation stabilization zone. The numerical simulation results by mathematical model agree well with the physical simulation results by nuclear magnetic resonance coupling displacement, and reasonably explain the gas-water distribution and production pattern of deep reservoirs in the Xujiaweizi fault depression of the Songliao Basin and tight gas reservoirs in the Linxing-Huangfu area of the Ordos Basin. 展开更多
关键词 tight gas charging and accumulation mechanism mathematical model Xujiaweizi fault depression Songliao Basin Linxing-Huangfu area Ordos Basin
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Mathematical Modeling of Heat Flux Distribution in Raw Cotton Stored in Bunt
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作者 Karimov Abdusamat Ismonovich Ismanov Muhammadziyo 《Engineering(科研)》 2020年第8期591-599,共9页
The scientific article examines the physical and mechanical properties of raw cotton stored in buntings in cotton palaces. Because during the storage of raw cotton in bunts, some of its properties deteriorate, some im... The scientific article examines the physical and mechanical properties of raw cotton stored in buntings in cotton palaces. Because during the storage of raw cotton in bunts, some of its properties deteriorate, some improvements. Therefore, the mathematical modeling of storage conditions of raw cotton in bunts and the physical and mechanical conditions that occur in it is of great importance. In the developed mathematical model, the main factor influencing the physical and mechanical properties of raw cotton is the change in temperature. Due to the temperature, kinetic and biological processes accumulated in the raw cotton in Bunt, it can spread over a large surface, first in a small-local state, over time with a nonlinear law. As a result, small changes in temperature lead to a qualitative change in physical properties. In determining the law of temperature distribution in the raw cotton in Bunt, Laplace’s differential equation of heat transfer was used. The differential equation of heat transfer in Laplace’s law was replaced by a system of ordinary differential equations by approximation. Conditions are solved in MAPLE-17 program by numerical method. As a result, graphs of temperature changes over time in raw cotton were obtained. In addition, the table shows the changes in density, pressure and mass of cotton, the height of the bun. As the density of the cotton raw material increases from the top layer of the bunt to the bottom layer, an increase in the temperature in it has been observed. This leads to overheating of the bottom layer of cotton and is the main reason for the deterioration of the quality of raw materials. 展开更多
关键词 Physical Mechanical Properties The Bunt Parallelepiped The mathematical model Biological System Heat Processes Temperature Coefficient Experiment The Bulk Density Volumetric Density Humidity FIGURE Coordinate Axes The Laplace Differential Equation Transfer Solution Approximate MAPLE
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Mathematical modeling and analytical solution for stretching force of automatic feed mechanism 被引量:1
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作者 魏志芳 陈国光 《Journal of Central South University》 SCIE EI CAS 2008年第S2期389-393,共5页
Load of an automatic feed mechanism is composed of the stretching force of feed belt at the entrance to lower flexible guidance and the friction force between feed belt and flexible guidance. A mathematical model for ... Load of an automatic feed mechanism is composed of the stretching force of feed belt at the entrance to lower flexible guidance and the friction force between feed belt and flexible guidance. A mathematical model for computing the load was presented. An optimization problem was formulated to determine the attitude of the flexible guidance based on the principle that the potential energy stored in the system was the minimum at the equilibrium. Then the friction force was obtained according to the attitude of guide leaves and the moving velocity of the feed belt and the friction factor. Consequently, the load of the automatic feed mechanism can be calculated. Finally, an example was given to compute the load when the horizontal and elevating firing angles of the automation were respectively 45° and 30°. The computing result can be a criterion to determine the designing parameters of automat. 展开更多
关键词 mathematical model load automatic FEED mechanism optimization problem potential energy hoist-feed system
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