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Novel implementation of homogenization method to predict effective properties of periodic materials 被引量:50
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作者 Geng-Dong Cheng Yuan-Wu Cai Liang Xu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2013年第4期550-556,共7页
Representative volume element (RVE) method and asymptotic homogenization (AH) method are two widely used methods in predicting effective properties of pe- riodic materials. This paper develops a novel implementa- ... Representative volume element (RVE) method and asymptotic homogenization (AH) method are two widely used methods in predicting effective properties of pe- riodic materials. This paper develops a novel implementa- tion of the AH method, which has rigorous mathematical foundation of the AH method, and also simplicity as the RVE method. This implementation can be easily realized using commercial software as a black box, and can use all kinds of elements available in commercial software to model unit cells with rather complicated microstructures, so the model may remain a fairly small scale. Several examples were car- fled out to demonstrate the simplicity and effectiveness of the new implementation. 展开更多
关键词 Effective property ~ periodic material - Homog-enization ~ RVE method
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Two-scale finite element method for piezoelectric problem in periodic structure 被引量:2
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作者 邓明香 冯永平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第12期1525-1540,共16页
The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-sc... The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented. 展开更多
关键词 two-scale method PIEZOELECTRICITY periodic structure finite element method homogenization constant
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Construction of doubly-periodic solutions to nonlinear partial differential equations using improved Jacobi elliptic function expansion method and symbolic computation 被引量:7
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作者 赵雪芹 智红燕 张鸿庆 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第10期2202-2209,共8页
Some doubly-periodic solutions of the Zakharov-Kuznetsov equation are presented. Our approach is to introduce an auxiliary ordinary differential equation and use its Jacobi elliptic function solutions to construct dou... Some doubly-periodic solutions of the Zakharov-Kuznetsov equation are presented. Our approach is to introduce an auxiliary ordinary differential equation and use its Jacobi elliptic function solutions to construct doubly-periodic solutions of the Zakharov-Kuznetsov equation, which has been derived by Gottwald as a two-dimensional model for nonlinear Rossby waves. When the modulus k →1, these solutions reduce to the solitary wave solutions of the equation. 展开更多
关键词 Jacobi elliptic function method doubly-periodic solutions Zakharov-Kuznetsov equation
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Re-study on Recurrence Period of Stokes Wave Train with High Order Spectral Method 被引量:4
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作者 陶爱峰 郑金海 +1 位作者 MEE Mee Soe 陈波涛 《China Ocean Engineering》 SCIE EI 2011年第4期679-686,共8页
Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process an... Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schrodinger equation (NLS). However, NLS has limitations on the narrow band and the weak nonlinearity. The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral (HOS) method, which can be applied for the direct phase- resolved simulation of the nonlinear wave train evolution. It is found that the Stiassnie and Shemer's formula should be modified in the cases with most unstable initial conditions, which is important for such topics as the generation mechanisms of freak waves. A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details. 展开更多
关键词 Benjamin-Feir instability High Order Spectral (HOS) method recurrence period nonlinear wave-wave interaction
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Finding Periodic Solutions of Ordinary Differential Equations by the Homotopy Method 被引量:1
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作者 王国铭 吕显瑞 黄庆道 《Northeastern Mathematical Journal》 CSCD 2004年第3期369-378,共10页
As an important aspect of applications, it is discussed how to find periodic solutions for ordinary differential equations. By using the homotopy method, a global method for finding those solutions is proposed.
关键词 homotopy method finding periodic solution global convergence comparison principle
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Synthesis and Optimization of Almost Periodic Antennas Using Floquet Modal Analysis and MoM-GEC Method 被引量:1
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作者 Nader Ben Latifa Taoufik Aguili 《Journal of Electromagnetic Analysis and Applications》 2019年第1期1-16,共16页
This paper presented a new Floquet analysis used to calculate the radiation for 1-D and 2-D coupled periodic antenna systems. In this way, an accurate evaluation of mutual coupling can be proven by using a new mutual ... This paper presented a new Floquet analysis used to calculate the radiation for 1-D and 2-D coupled periodic antenna systems. In this way, an accurate evaluation of mutual coupling can be proven by using a new mutual interaction expression that was based on Fourier analysis. Then, this work indicated how Floquet analysis can be used to study a finite array with uniform amplitude and linear phase distribution in both x and y directions. To modelize the proposed structures, two formulations were given in a spectral and spatial domain, where the Moment (MoM) method combined with a generalized equivalent circuit (GEC) method was applied. Radiation pattern of coupled periodic antenna was shown by varying many parameters, such as frequencies, distance and Floquet states. The 3-D radiation beam of the coupled antenna array was analyzed and compared in several steering angles θs and coupling values dx. The simulation of this structure demonstrated that directivity decreased at higher coupling values. The secondary lobs in the antenna radiation pattern affected the main lobe gain by energy dispersal and considerable increasing of side lobe level (SLL) may be achieved. Therefore, the sweeping of the radiation beam in several steering directions affected the electromagnetic performance of the antenna system: the directivity at the steering angle θs = π&#8260;3 was more damaged and had 19.99 dB while the second at θs = 0 had about 35.11 dB. This parametric study of coupled structure used to concept smart periodic antenna with sweeping radiation beam. 展开更多
关键词 periodIC ANTENNAS FLOQUET Theory MOMENT method GEC method
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Improving Wilson-θ and Newmark-β Methods for Quasi-Periodic Solutions of Nonlinear Dynamical Systems 被引量:1
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作者 G. Liu Z. R. Lv Y. M. Chen 《Journal of Applied Mathematics and Physics》 2018年第8期1625-1635,共11页
Quasi-periodic responses can appear in a wide variety of nonlinear dynamical systems. To the best of our knowledge, it has been a tough job for years to solve quasi-periodic solutions, even by numerical algorithms. He... Quasi-periodic responses can appear in a wide variety of nonlinear dynamical systems. To the best of our knowledge, it has been a tough job for years to solve quasi-periodic solutions, even by numerical algorithms. Here in this paper, we will present effective and accurate algorithms for quasi-periodic solutions by improving Wilson-θ and Newmark-β methods, respectively. In both the two methods, routinely, the considered equations are rearranged in the form of incremental equilibrium equations with the coefficient matrixes being updated in each time step. In this study, the two methods are improved via a predictor-corrector algorithm without updating the coefficient matrixes, in which the predicted solution at one time point can be corrected to the true one at the next. Numerical examples show that, both the improved Wilson-θ and Newmark-β methods can provide much more accurate quasi-periodic solutions with a smaller amount of computational resources. With a simple way to adjust the convergence of the iterations, the improved methods can even solve some quasi-periodic systems effectively, for which the original methods cease to be valid. 展开更多
关键词 Wilson-θ method Newmark-β method QUASI-periodIC Solution PREDICTOR-CORRECTOR Algorithm
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Finding Periodic Solutions of High Order Duffing Equations via Homotopy Method
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作者 YANG XUE Xu Xu 《Communications in Mathematical Research》 CSCD 2009年第3期193-203,共11页
This paper presents a detailed analysis of finding the periodic solutions for the high order Duffing equation x^(2n) + g(x) = e(t) (n ≥ 1). Firstly, we give a constructive proof for the existence of periodi... This paper presents a detailed analysis of finding the periodic solutions for the high order Duffing equation x^(2n) + g(x) = e(t) (n ≥ 1). Firstly, we give a constructive proof for the existence of periodic solutions via the homotopy method. Then we establish an efficient and global convergence method to find periodic solutions numerically. 展开更多
关键词 high order Duffing equation periodic solution homotopy method
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A two-scale method for identifying mechanical parameters of composite materials with periodic configuration 被引量:9
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作者 J.Z. Cui X.G. Yu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第6期581-594,共14页
In this paper, a two-scale method (TSM) is presented for identifying the mechanics parameters such as stiffness and strength of composite materials with small periodic configuration. Firstly, a formulation is briefl... In this paper, a two-scale method (TSM) is presented for identifying the mechanics parameters such as stiffness and strength of composite materials with small periodic configuration. Firstly, a formulation is briefly given for two-scale analysis (TSA) of the composite materials. And then a two-scale computation formulation of strains and stresses is developed by displacement solution with orthotropic material coefficients for three kinds of such composites structures, i.e., the tension column with a square cross section, the bending cantilever with a rectangular cross section and the torsion column with a circle cross section. The strength formulas for the three kinds of structures are derived and the TSM procedure is discussed. Finally the numerical results of stiffness and strength are presented and compared with experimental data. It shows that the TSM method in this paper is feasible and valid for predicting both the stiffness and the strength of the composite materials with periodic configuration. 展开更多
关键词 Two-scale method STIFFNESS STRENGTH Composite materials Small periodic configuration
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A New Kind of Iteration Method for Finding Approximate Periodic Solutions to Ordinary Diferential Equations
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作者 Wu Dong-xu Wang Cai-ling +1 位作者 Xu Xu Li Yong 《Communications in Mathematical Research》 CSCD 2013年第4期297-304,共8页
In this paper, a new kind of iteration technique for solving nonlinear ordinary differential equations is described and used to give approximate periodic solutions for some well-known nonlinear problems. The most inte... In this paper, a new kind of iteration technique for solving nonlinear ordinary differential equations is described and used to give approximate periodic solutions for some well-known nonlinear problems. The most interesting features of the proposed methods are its extreme simplicity and concise forms of iteration formula for a wide range of nonlinear problems. 展开更多
关键词 iteration method approximate periodic solution ordinary differentialequation
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Study of the emissivity of rough surfaces periodic using the method of coupled waves analysis (CWA) compared with method of geometrical optics approximation (GOA)
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作者 Taoufik Ghabara 《Natural Science》 2011年第1期57-64,共8页
We present in this paper a numerical study of the validity limit of the geometrical optics approximation compared with a differential method which is established according to rigorous formalisms based on the electroma... We present in this paper a numerical study of the validity limit of the geometrical optics approximation compared with a differential method which is established according to rigorous formalisms based on the electromagnetic theory. The precedent studies show that this method is adapted to the study of diffraction by periodic rough surfaces. We determine by two methods the emissivity of gold and tungsten for surfaces with a rectangular or sinusoidal profile, for a wavelength equal to 0.55 microns. The monochromatic directional emissivity of these surfaces clearly depends on the angle of incidence, the surface profile, height, period and the nature of the material. We perform our calculations by a method of coupled wave analysis (CWA) and a geometric optics method (GOA). The latter method is theoretically valid only when the dimensions of the cavities are very large compared to the wavelength, while the CWA is theoretically correct whatever these dimensions. The main purpose of this work is to investigate the validity limit of GOA compared with CWA. The obtained results for a fixed height of the grating, allowed us to delimit the validity domain of the optic geometrical approximation for the treated cases. Finally, the agreement between the emissivity calculated by the differential method and that given on the basis of the homogenization theory is satisfactory when the period is much smaller than the wavelength. 展开更多
关键词 periodIC Roughness Differential method (CWA) Geometric Optics APPROXIMATION (GOA) HOMOGENIZATION Theory Emissivity.
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Exponentially-Fitted 2-Step Simpson’s Method for Oscillatory/Periodic Problems
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作者 Ashiribo Senapon Wusu Bosede Alfred Olufemi Akanbi Moses Adebowale 《Journal of Applied Mathematics and Physics》 2016年第2期368-375,共8页
Following a six-step flow chart, exponentially-fitted variant of the 2-step Simpson’s method suitable for solving ordinary differential equations with periodic/oscillatory behaviour is constructed. The qualitative pr... Following a six-step flow chart, exponentially-fitted variant of the 2-step Simpson’s method suitable for solving ordinary differential equations with periodic/oscillatory behaviour is constructed. The qualitative properties of the constructed methods are also investigated. Numerical experiments on standard problems confirming the theoretical expectations regarding the constructed methods compared with other existing standard methods are also presented. Our results unify and improve the existing classical 2-step Simpson’s method. 展开更多
关键词 Exponentially-Fitted Simpson method OSCILLATORY periodIC ODE
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Existence of Periodic Solutions for Odd Order Ordinary Differential Equations via the Homotopy Method
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作者 刘停战 于波 《Northeastern Mathematical Journal》 CSCD 2004年第2期135-138,共4页
This paper deals with the problems of finding periodic solutions for the third order ordinary differential equations of the form (1) where T is a fixed positive number and f satisfies some additional conditions which ... This paper deals with the problems of finding periodic solutions for the third order ordinary differential equations of the form (1) where T is a fixed positive number and f satisfies some additional conditions which will be stated later.The periodicity problem has been one of main topics in the qualitative theory of ordinary 展开更多
关键词 homotopy method finding periodic solution odd order ordinary differential equations global convergence
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ANALYSIS OF OPEN MICROSTRIP STRUCTURES BY USING DIAKOPTIC METHOD OF LINES COMBINED WITH PERIODIC BOUNDARY CONDITIONS
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作者 Zhu Hanqing Fang Dagang Long Yi(Department of Electronic Engineering, Nanjing University of Science and Technology, Nanjing 210094) 《Journal of Electronics(China)》 1998年第1期90-96,共7页
This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch curre... This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch current excited by plane wave. Impedance matrix elements are computed by using fast Fourier transform(FFT), and reduced equation is solved by using diakoptic technique. Consequently, the computing time is reduced significantly. The convergence property of simulating open structure by using PBC and the comparison of the computer time between using PBC and usual absorbing boundary condition (ABC) show the validity of the method proposed in this paper. Finally, the resonant frequency of a microstrip patch is computed. The numerical results obtained are in good agreement with those published. 展开更多
关键词 OPEN MICROSTRIP structures method of LINES periodIC BOUNDARY conditions Fast FOURIER transform Diakoptic technique
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An asymptotic solving method for the periodic solution of a class of disturbed nonlinear evolution equation
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作者 姚静荪 林万涛 +1 位作者 杜增吉 莫嘉琪 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第12期37-41,共5页
A class of disturbed evolution equation is considered using a simple and valid technique. We first introduce the periodic traveling-wave solution of a corresponding typical evolution equation. Then the approximate sol... A class of disturbed evolution equation is considered using a simple and valid technique. We first introduce the periodic traveling-wave solution of a corresponding typical evolution equation. Then the approximate solution for an original disturbed evolution equation is obtained using the asymptotic method. We point out that the series of approximate solution is convergent and the accuracy of the asymptotic solution is studied using the fixed point theorem for the functional analysis. 展开更多
关键词 period solution traveling wave evolution equation asymptotic method
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Hybrid PMM-MoM Method for the Analysis of Finite Periodic Structures
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作者 Shan Zhao Naiqian Zhang +1 位作者 Dong Li Jianxun Su 《Open Journal of Applied Sciences》 2012年第4期175-178,共4页
In this paper, a hybrid method (hybrid PMM-MoM method) is presented for the effective and accurate analysis of finite periodic structures. This method divides a finite periodic structure into two parts. The inner part... In this paper, a hybrid method (hybrid PMM-MoM method) is presented for the effective and accurate analysis of finite periodic structures. This method divides a finite periodic structure into two parts. The inner part of an approximate infinite periodic structure is analyzed by periodic method of moment (PMM);the outer part is then analyzed by method of moments (MoM). For the finite periodic structures, the accuracy of the new method is much better than that of the pure PMM, and is almost the same as that of pure MoM. Because pure PMM uses the periodic boundary conditions, it takes much less memory resources and computation time. For hybrid PMM-MoM method, because the inner part is calculated by PMM, the calculation work concentrates on the outer part. Consequently, compared with the exact MoM, the new method saves much more memory resources and computation time, which provides a drastic reduction of unknowns. 展开更多
关键词 HYBRID method PMM-MoM INFINITE periodIC Structures RCS
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Second-order two-scale computational method for ageing linear viscoelastic problem in composite materials with periodic structure
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作者 Yang ZHANG Junzhi CUI Yufeng NIE 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第2期253-264,共12页
The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elasti... The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elastic case. However, the correspon- dence principle becomes invalid when the materials exhibit ageing. To deal with this problem, a second-order two-scale (SOTS) computational method in the time domain is presented to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. First, in the time domain, the SOTS formulation for calcu- lating the effective relaxation modulus and displacement approximate solutions of the ageing viscoelastic problem is formally derived. Error estimates of the displacement ap- proximate solutions for SOTS method are then given. Numerical results obtained by the SOTS method are shown and compared with those by the finite element method in a very fine mesh. Both the analytical and numerical results show that the SOTS computational method is feasible and efficient to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. 展开更多
关键词 second-order two-scale (SOTS) method ageing VISCOELASTICITY composite material periodic structure
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利用Periodic Fourier法研究橡胶混凝土隔振基础对轨道振动的影响 被引量:1
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作者 金浩 刘维宁 +1 位作者 周顺华 孙晓静 《噪声与振动控制》 CSCD 2015年第3期144-148,共5页
地下铁道轨道减振措施研究是一个受到持续关注的问题,本文创新性地引入橡胶混凝土隔振基础这一概念。并利用Peiodic-Fourier方法,探讨了橡胶混凝土隔振基础物理参数对钢轨振动位移的影响。研究结果表明:(1)高频激励荷载引起的钢轨位移... 地下铁道轨道减振措施研究是一个受到持续关注的问题,本文创新性地引入橡胶混凝土隔振基础这一概念。并利用Peiodic-Fourier方法,探讨了橡胶混凝土隔振基础物理参数对钢轨振动位移的影响。研究结果表明:(1)高频激励荷载引起的钢轨位移比低频激励荷载引起的钢轨位移小;(2)橡胶混凝土隔振基础刚度越大,相应的共振频率越大,但引起的钢轨振动位移越小;(3)橡胶混凝土隔振基础阻尼越大,相应的共振频率越小,且引起的钢轨振动位移也越小。 展开更多
关键词 振动与波 橡胶混凝土 地下铁道 减振 periodic-Fourier方法 钢轨位移
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基于“玄府-络脉-经筋”理论探析恢复期面瘫的针药结合治疗
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作者 张新昱 鞠庆波 《中西医结合慢性病杂志》 2026年第1期64-68,共5页
面瘫是一种常见的神经系统疾病,主要以患侧面部肌肉瘫痪、口眼歪斜等为临床表现。面瘫恢复期(发病16 d~6个月)是正邪交争的关键阶段。本病病位在头面部经络,其恢复期的病机与玄府、络脉、经筋的功能失调密切相关,三者相互关联,共同导致... 面瘫是一种常见的神经系统疾病,主要以患侧面部肌肉瘫痪、口眼歪斜等为临床表现。面瘫恢复期(发病16 d~6个月)是正邪交争的关键阶段。本病病位在头面部经络,其恢复期的病机与玄府、络脉、经筋的功能失调密切相关,三者相互关联,共同导致面部肌肉功能障碍。针对恢复期面瘫的病理特点,提出以通调玄府、疏通络脉、调理经筋为核心的治疗原则。临证以针灸配合中药为主,常选用辛味药和虫类药以祛风通络,并结合经筋透刺法,通过激活神经末梢、改善局部循环及抑制炎症反应,促进面部气血运行和肌肉功能恢复,治疗效果显著。基于“玄府-络脉-经筋”理论,为恢复期面瘫提供了中医治疗思路,强调通补结合、调和气血,未来需进一步优化疗法以提升临床疗效。 展开更多
关键词 玄府 络脉 经筋 面瘫恢复期 透刺法
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Penalty model for delay of bidding section construction period in South-to-North Water Diversion Eastern Route Project from perspective of programs 被引量:2
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作者 Jing-chun FENG Ya-fang REN +2 位作者 Zhong-nan DUAN Zhan-jun LIU Hai-yang LI 《Water Science and Engineering》 EI CAS 2012年第3期350-360,共11页
According to the multi-project and program management theory, this paper analyzes the program generation principle and establishes a program based on progress goals. On the basis of the present situation of calculatio... According to the multi-project and program management theory, this paper analyzes the program generation principle and establishes a program based on progress goals. On the basis of the present situation of calculation of penalty for delay of the bidding section construction period with the critical path method, we studied the effects of contractor-induced delay of the bidding section construction period in detail, including the effects on the construction period of the bidding section itself, the earliest start times of the next bidding section and other subsequent bidding sections, and the construction period of the program, and then constructed a penalty model for delay of the bidding section construction period from the perspective of programs. Using the penalty model, we conducted a practical analysis of penalty for delay of the construction period of the Baoying station program in the South-to-North Water Diversion Project. The model can help determine the amount of penalty for delay of the construction period in bidding sections scientifically and reasonably, 展开更多
关键词 program establishment program management bidding section construction period critical path method (CPM) penaly model South-to-North Water Diversion Project
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