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从实变数函数到复变数函数
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作者 朱树德 《经济经纬》 1987年第1期71-74,共4页
一、实一元函数和复一元函数由于复变函数最初伴随着实变函数共存于数学分析领域,故复变函数许多基本概念与定理和实变函数的相类似。比如复一元函数(以下简称复变函数)w=f(z)的定义,在形式上,几乎是实一元函数y=f(x)定义的逐字逐句的... 一、实一元函数和复一元函数由于复变函数最初伴随着实变函数共存于数学分析领域,故复变函数许多基本概念与定理和实变函数的相类似。比如复一元函数(以下简称复变函数)w=f(z)的定义,在形式上,几乎是实一元函数y=f(x)定义的逐字逐句的推广。然而复变函数的自变量和因变量都是复数,对象不同了,情况要复杂得多。一个复变函数等价于两个实二元函数的有序组合,即 w=f(z)(?)u=u(x,y),v=v(x,y) 展开更多
关键词 复变函数论 变数 实变数 变函数 基本初等函数 指数函数 对数函数 二元函数 数学分析 函数复合
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Viscoelasto-plastic rheological experiment under circular increment step load and unload and nonlinear creep model of soft rocks 被引量:23
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作者 赵延林 曹平 +2 位作者 王卫军 万文 刘业科 《Journal of Central South University》 SCIE EI CAS 2009年第3期488-494,共7页
The viscoelastic-plastic creep experiments on soft ore-rock in Jinchuan Mine III were performed under circular increment step load and unload. The experimental data were analyzed according to instantaneous elastic str... The viscoelastic-plastic creep experiments on soft ore-rock in Jinchuan Mine III were performed under circular increment step load and unload. The experimental data were analyzed according to instantaneous elastic strain, visco-elastic strain, instantaneous plastic strain and visco-plastic strain. The result shows that instantaneous deformation modulus tends to increase with the increase of creep stress; soft rocks enhance the ability to resist instantaneous elastic deformation and instantaneous plastic deformation during the multi-level of load and unload in the cyclic process. In respect of specimen JC1099, the ratio of visco-elastic strain to visco-plastic strain varies from 3.15 to 6.58, and the ratio has decreasing tendency with stress increase as a whole; creep deformation tends to be a steady state at low stress level; soft rocks creep usually embodies accelerated creep properties at high stress level. With the damaging variable and the hardening function introduced, a nonlinear creep model of soft rocks is established, in which the decay creep is described by the nonlinear hardening function H of viscidity coefficient. The model can describe the accelerated creep of soft rocks since the nonlinear damaging evolvement variable D of deformation parameter of rocks is introduced. Three stages of soft rocks creep can be described with the uniform creep equation in the nonlinear creep model. With this nonlinear creep model applied to the creep experiments of the ore-rock of Jinchuan Mine III, the nonlinear creep model's curves are in good agreement with experimental data. 展开更多
关键词 rheological experiment nonlinear creep damaging HARDENING soft rocks
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Numerical simulation of intelligent compaction for subgrade construction 被引量:9
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作者 MA Yuan LUAN Ying-cheng +1 位作者 ZHANG Wei-guang ZHANG Yu-qing 《Journal of Central South University》 SCIE EI CAS CSCD 2020年第7期2173-2184,共12页
During the compaction of a road subgrade, the mechanical parameters of the soil mass change in real time, but current research assumes that these parameters remain unchanged. In order to address this discrepancy, this... During the compaction of a road subgrade, the mechanical parameters of the soil mass change in real time, but current research assumes that these parameters remain unchanged. In order to address this discrepancy, this paper establishes a relationship between the degree of compaction K and strain ε. The relationship between the compaction degree K and the shear strength of soil(cohesion c and frictional angle φ) was clearly established through indoor experiments. The subroutine UMAT in ABAQUS finite element numerical software was developed to realize an accurate calculation of the subgrade soil compaction quality. This value was compared and analyzed against the assumed compaction value of the model, thereby verifying the accuracy of the intelligent compaction calculation results for subgrade soil. On this basis, orthogonal tests of the influential factors(frequency, amplitude, and quality) for the degree of compaction and sensitivity analysis were carried out. Finally, the ‘acceleration intelligent compaction value’, which is based on the acceleration signal, is proposed for a compaction meter value that indicates poor accuracy. The research results can provide guidance and basis for further research into the accurate control of compaction quality for roadbeds and pavements. 展开更多
关键词 intelligent compaction numerical simulation dynamic change control indicators orthogonal experiment
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Experimental measurement and numerical analysis of fused taper shape for optical fiber coupler 被引量:3
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作者 帅词俊 段吉安 钟掘 《Journal of Central South University of Technology》 EI 2007年第2期251-254,共4页
To find out the effect of the shape of fused taper region on the optical fiber coupler, the fiber couplers were fabricated at different drawing speeds with a six-axes fiber coupler machine. The results, which were obt... To find out the effect of the shape of fused taper region on the optical fiber coupler, the fiber couplers were fabricated at different drawing speeds with a six-axes fiber coupler machine. The results, which were obtained fi'om the shape of fused taper region measured with microscope, show that there is a close correlation between the cone angle and optical performance of fiber coupler. High-performance fiber coupler cannot be obtained until rheological shape is controlled accurately. The numerical analysis model, which was built based on generalized Maxwell viscoelastic theory, is resolved with ANSYS software. The calculated results accord with the experimental data. It can apply a theoretic basis for forecasting the shape of fiber coupler fabricated under the conditions of different technological parameters. 展开更多
关键词 optical fiber coupler fused biconical taper viscoelastic model rheological shape
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Visco-elastoplastic damage constitutive model for compressed asphalt mastic 被引量:1
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作者 曾国伟 杨新华 +1 位作者 白凡 高虎 《Journal of Central South University》 SCIE EI CAS 2014年第10期4007-4013,共7页
In order to describe the three-stage creep behavior of compressed asphalt mastic, a visco-elastoplastic damage constitutive model is proposed in this work. The model parameters are treated as quadratic polynomial func... In order to describe the three-stage creep behavior of compressed asphalt mastic, a visco-elastoplastic damage constitutive model is proposed in this work. The model parameters are treated as quadratic polynomial functions with respect to stress and temperature. A series of uniaxial compressive creep experiments are performed at various stress and temperature conditions in order to determine these parameter functions, and then the proposed model is validated by comparison between the predictions and experiments at the other loading conditions. It is shown that very small permanent deformation at low stress and temperature increases rapidly with elevated stress or temperature and the damage may initiate in the stationary stage but mainly develops in the accelerated stage. Compared with the visco-elastoplastic models without damage, the predictions from the proposed model is in better agreement with the experiments, and can better capture the rate-dependency in creep responses of asphalt mastic especially below its softening point of 47 ℃ 展开更多
关键词 asphalt mastic visco-elastoplastic damage model compressive creep
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