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Theoretical solution of transient heat conduction problem in one-dimensional double-layer composite medium 被引量:2
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作者 周龙 白敏丽 +1 位作者 吕继组 崔文政 《Journal of Central South University》 SCIE EI CAS 2010年第6期1403-1408,共6页
To make heat conduction equation embody the essence of physical phenomenon under study, dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to ... To make heat conduction equation embody the essence of physical phenomenon under study, dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to dimensionless forms. Then, a theoretical solution model of transient heat conduction problem in one-dimensional double-layer composite medium was built utilizing the natural eigenfunction expansion method. In order to verify the validity of the model, the results of the above theoretical solution were compared with those of finite element method. The results by the two methods are in a good agreement. The maximum errors by the two methods appear when τ(τ is nondimensional time) equals 0.1 near the boundaries of ζ =1 (ζ is nondimensional space coordinate) and ζ =4. As τ increases, the error decreases gradually, and when τ =5 the results of both solutions have almost no change with the variation of coordinate 4. 展开更多
关键词 composite medium transient heat conduction theoretical solution natural eigenfunction expansion method
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Theoretical solution for wave diffraction by wedge or corner with arbitrary reflection characteristics 被引量:1
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作者 Hong Guangwen(Received December 20 1990 acepted June 15, 1991) 《Acta Oceanologica Sinica》 SCIE CAS CSCD 1992年第2期287-303,共17页
An exact analytic solution for wave diffraction by wedge or corner with arbitrary angle (rπ) and reflection coefficients (R0 and Rr) is presented in this paper. It is expressed in two forms-series and integral repres... An exact analytic solution for wave diffraction by wedge or corner with arbitrary angle (rπ) and reflection coefficients (R0 and Rr) is presented in this paper. It is expressed in two forms-series and integral representations, corresponding recurrence relation and asymptotic expressions are also derived. The solution is simplified for some special cases of rπ. For Rr= R0,r= 1/N and Rr≠R0,r = 1/2N, the solution can be reduced to linear superpositions of incident and partially reflected waves, hence a nonlinear solution of forth order for this problem can be obtained by using the author's theory of nonlinear interaction among gravity surface waves. The given solution is related to inhomogeneous Robin boundary conditions, which include the Neumann boundary conditions usually accepted in wave diffraction theory. 展开更多
关键词 WAVE theoretical solution for wave diffraction by wedge or corner with arbitrary reflection characteristics
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Approximate solutions of the Alekseevskii–Tate model of long-rod penetration 被引量:4
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作者 W.J.Jiao X.W.Chen 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2018年第2期334-348,共15页
The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, pe... The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration. 展开更多
关键词 Long-rod penetration Alekseevskii–Tate model theoretical solution Approximate solution Perturbation solution
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Theoretical study of the effect of topographic height and width on generation of internal tides 被引量:1
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作者 曹安州 吕咸青 苗春葆 《Chinese Journal of Oceanology and Limnology》 SCIE CAS CSCD 2014年第6期1421-1434,共14页
Internal tides generated upon two-dimensional Gaussian topographies of different sizes and steepness are investigated theoretically in a numerical methodology.Compared with previous theoretical works,this model is not... Internal tides generated upon two-dimensional Gaussian topographies of different sizes and steepness are investigated theoretically in a numerical methodology.Compared with previous theoretical works,this model is not restricted by weak topography,but provides an opportunity to examine the influence of topography.Ten typical cases are studied using different values of height and/or width of topography.By analyzing the baroclinic velocity fields,as well as their first eight baroclinic modes,it is found that the magnitude of baroclinic velocity increases and the vertical structure becomes increasingly complex as height increases or width decreases.However,when both height and width vary,while parameter s(the ratio of the topographic slope to the characteristic slope of the internal wave ray) remains invariant,the final pattern is influenced primarily by width.The conversion rate is studied and the results indicate that width determines where the conversion rate reaches a peak,and where it is positive or negative,whereas height affects only the magnitude.High and narrow topography is considerably more beneficial to converting energy from barotropic to baroclinic fields than low and wide topography.Furthermore,parameter s,which is an important non-dimensional parameter for internal tide generation,is not the sole parameter by which the baroclinic velocity fields and conversion rate are determined. 展开更多
关键词 internal tide theoretical solution numerical methodology influence of topography
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THEORETICAL ANALYSIS ON HYDRAULIC TRANSIENT RESULTED BY SUDDEN INCREASE OF INLET PRESSURE FOR LAMINAR PIPELINE FLOW
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作者 邓松圣 周绍骑 +2 位作者 廖振方 邱正阳 曾顺鹏 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第6期672-678,共7页
Hydraulic transient, which is resulted from sudden increase of inlet pressure for laminar pipeline flow, is studied. The partial differential equation, initial and boundary conditions for transient pressure were const... Hydraulic transient, which is resulted from sudden increase of inlet pressure for laminar pipeline flow, is studied. The partial differential equation, initial and boundary conditions for transient pressure were constructed, and the theoretical solution was obtained by variable-separation method. The partial differential equation, initial and boundary conditions for flow rate were obtained in accordance with the constraint correlation between flow rate and pressure while the transient flow rate distribution was also solved by variable-separation method. The theoretical solution conforms to numerical solution obtained by method of characteristics (MOC) very well. 展开更多
关键词 laminar flow pipeline flow hydraulic transient theoretical solution
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A simple theoretical approach for analysis of slide-toe-toppling failure
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作者 Hassan Sarfaraz 《Journal of Central South University》 SCIE EI CAS CSCD 2020年第9期2745-2753,共9页
A prevalent kind of failure of rock slopes is toppling instability.In secondary toppling failures,these instabilities are stimulated through some external factors.A type of secondary toppling failure is"slide-toe... A prevalent kind of failure of rock slopes is toppling instability.In secondary toppling failures,these instabilities are stimulated through some external factors.A type of secondary toppling failure is"slide-toe-toppling failure".In this instability,the upper and toe parts of the slope have the potential of sliding and toppling failures,respectively.This failure has been investigated by an analytical method and experimental tests.In the present study,at first,the literature review of toppling failure is presented.Then a simple theoretical solution is suggested for evaluating this failure.The recommended method is compared with the approach of AMINI et al through a typical example and three physical models.The results indicate that the proposed method is in good agreement with the results of AMINI et al’s approach and experimental models.Therefore,this suggested methodology can be applied to examining the stability of slide-toe-toppling failure. 展开更多
关键词 rock slopes slope stability slide-toe-toppling theoretical solution
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THEORETIC SOLUTION OF RECTANGULAR THIN PLATE ON FOUNDATION WITH FOUR EDGES FREE BY SYMPLECTIC GEOMETRY METHOD 被引量:1
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作者 钟阳 张永山 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第6期833-839,共7页
The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firs... The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firstly, the basic equations for elastic thin plate are transferred into Hamilton canonical equations. The symplectic geometry method is used to separate the whole variables and eigenvalues are obtained simultaneously. Finally, according to the method of eigen function expansion, the explicit solution for rectangular thin plate on foundation with the boundary conditions of four edges frees are developed. Since the basic elasticity equations of thin plate are only used and it is not need to select the deformation function arbitrarily. Therefore, the solution is theoretical and reasonable. In order to show the correction of formulations derived, a numerical example is given to demonstrate the accuracy and convergence of the current solution. 展开更多
关键词 elastic foundation rectangular thin plate symplectic geometry method theoretic solution
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STRESS CONCENTRATIONS IN CYLINDRICAL SHELLS WITH LARGE OPENINGS 被引量:3
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作者 Liu Diankui Song Tianshu, Harbin Engineering University, Harbin 150001, China 《Acta Mechanica Solida Sinica》 SCIE EI 1997年第3期220-234,共15页
Based on Donnell's shallow shell equation, a new method is given in this paper to analyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With the method of complex var... Based on Donnell's shallow shell equation, a new method is given in this paper to analyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With the method of complex variable function, a series' of conformal mapping functions are obtained from different cutouts' boundary curves in the developed plane of a cylindrical shell to the unit circle. And, the general expressions for the equations of a cylindrical shell, including the solutions of stress concentrations meeting the boundary conditions of the large openings' edges, are given in the mapping plane. Furthermore, by applying the orthogonal function expansion technique, the problem can be summarized into the solution of infinite algebraic equation series. Finally, numerical results are obtained for stress concentration factors at the cutout's edge with various opening's ratios and different loading conditions. This new method, at the same time, gives a possibility to the research of cylindrical shells with large non-circular openings or with nozzles. 展开更多
关键词 cylindrical shell with large opening theoretical solution for single circular cutout conformal mapping and complex variable method
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Dynamic quasi-continuum model for plate-type nano-materials and analysis of fundamental frequency
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作者 Chunxiao XIA Wenlong XU Guohua NIE 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2021年第1期85-94,共10页
A dynamic quasi-continuum model is presented to analyze free vibration of plate-type cubic crystal nano-materials.According to the Hamilton principle,fundamental governing equations in terms of displacement components... A dynamic quasi-continuum model is presented to analyze free vibration of plate-type cubic crystal nano-materials.According to the Hamilton principle,fundamental governing equations in terms of displacement components and angles of rotations are given.As an application of the model,the cylindrical bending deformation of the structure fixed at two ends is analyzed,and a theoretical formula evaluating the fundamental frequency is obtained by using Galerkin's method.Meanwhile,the solution for the classical continuous plate model is also derived,and the size-dependent elastic modulus and Poisson's ratio are taken in computation.The frequencies corresponding to different atomic layers are numerically presented for the plate-type NaC l nano-materials.Furthermore,a molecular dynamics(MD)simulation is conducted with the code LAMMPS.The comparison shows that the present quasi-continuum model is valid,and it may be used as an alternative model,which reflects scale effects in analyzing dynamic behaviors of such plate-type nano-materials. 展开更多
关键词 plate-type nano-material quasi-continuum model SIZE-DEPENDENT fundamental frequency theoretical solution molecular dynamics(MD)simulation
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A theoretical method for solving shock relations coupled with chemical equilibrium and its applications 被引量:2
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作者 Zijian ZHANG Chihyung WEN +2 位作者 Wenshuo ZHANG Yunfeng LIU Zonglin JIANG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2022年第6期47-62,共16页
In this study,a theoretical method is proposed to solve shock relations coupled with chemical equilibrium.Not only shock waves in dissociated flows but also detonation waves in combustive mixtures can be solved.The gl... In this study,a theoretical method is proposed to solve shock relations coupled with chemical equilibrium.Not only shock waves in dissociated flows but also detonation waves in combustive mixtures can be solved.The global iterative solving process is specially designed to mimic the physical and chemical process in reactive shock waves to ensure good stability and fast convergence in the proposed method.Within each global step,the single-variable equations of normal and oblique shock relations are derived and solved with the Newton iteration method to reduce the complexity of the problems,and the minimization of free energy method of NASA(National Aeronautics and Space Administration)is adopted to solve equilibrium compositions.It is demonstrated that the convergent process is stable and very close to the real chemical-kinetic process,and high accuracy is achieved in the solutions of normal and oblique reactive shock waves.Moreover,the proposed theoretical method has also been applied to many problems associated with reactive shocks,including the stability of oblique detonation wave,bow detonation over a sphere,and shock reflection in dissociated air.The great importance of using chemical equilibrium to theoretically predict the theoretical range of the wedge angle for a standing oblique detonation wave(the standing window of the oblique detonation wave),the stand-off distance of bow detonation wave and the transition criterion of shock reflection in dissociated air with high accuracy have been addressed. 展开更多
关键词 Chemical equilibrium DETONATION Dissociated air Shock relation theoretical solution
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Theoretical study of failure in composite pressure vessels subjected to low-velocity impact and internal pressure 被引量:1
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作者 Roham RAFIEE Hossein RASHEDI Shiva REZAEE 《Frontiers of Structural and Civil Engineering》 SCIE EI CSCD 2020年第6期1349-1358,共10页
A theoretical solution is aimed to be developed in this research for predicting the failure in internally pressurized composite pressure vessels exposed to low-velocity impact.Both in-plane and out-of-plane failure mo... A theoretical solution is aimed to be developed in this research for predicting the failure in internally pressurized composite pressure vessels exposed to low-velocity impact.Both in-plane and out-of-plane failure modes are taken into account simultaneously and thus all components of the stress and strain fields are derived.For this purpose,layer-wise theory is employed in a composite cylinder under internal pressure and low-velocity impact.Obtained stress/strain components are fed into appropriate failure criteria for investigating the occurrence of failure.In case of experiencing any in-plane failure mode,the evolution of damage is modeled using progressive damage modeling in the context of continuum damage mechanics.Namely,mechanical properties of failed ply are degraded and stress analysis is performed on the updated status of the model.In the event of delamination occurrence,the solution is terminated.The obtained results are validated with available experimental observations in open literature.It is observed that the sequence of in-plane failure and delamination varies by increasing the impact energy. 展开更多
关键词 composite pressure vessel low-velocity impact FAILURE theoretical solution progressive damage modeling
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Shock relations in gases of heterogeneous thermodynamic properties
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作者 HU ZongMin ZHOU Kai +2 位作者 PENG Jun LI JinPing JIANG ZongLin 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2017年第7期1050-1057,共8页
Shock relations usually found in literatures are derived theoretically under the assumption of homogeneous thermodynamic properties, i.e., constant ratio of specific heats, γ. However, high temperature effects post a... Shock relations usually found in literatures are derived theoretically under the assumption of homogeneous thermodynamic properties, i.e., constant ratio of specific heats, γ. However, high temperature effects post a strong shock wave may result in thermodynamic heterogeneities and failure to the original shock relations. In this paper, the shock relations are extended to take account of high-temperature effects. Comparison indicates that the present approach is more feasible than other analytical approaches to reflect the influence of γ heterogeneity on the post-shock parameters. 展开更多
关键词 shock wave imperfect gas heterogeneous theoretical solution
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