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A numerical algorithm for ground reaction curves of circular openings in strain-softening rock masses satisfying the generalized Hoek-Brown criterion

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TUNNELLING AND UNDERGROUND SPACE TECHNOLOGY 2023年第1期134卷

作者： Zhao, Xingdong Li, Yangyang Shi, Jingyu Qu, Qingdong Northeastern Univ Lab Safe Min Deep Met Mine Shenyang 110819 Peoples R China Commonwealth Sci & Ind Res Org CSIRO Kenmore Qld Australia

Based on the self-similarity method, a numerical algorithm for constructing ground reaction curves (GRC) of circular openings in elastic-strain softening rock mass that satisfies the generalized Hoek-Brown failure criterion is proposed. The algorithm is derived from the analysis of the axisymmetric plane strain model, where the far -field and excavation boundary are both axisymmetric stresses. Using the self-similar transformation, the plastic zone of the model was transformed into unit plane ring, which has unit radius at the boundary between the plastic zone and the elastic zone. The unit plane ring was dispersed into multiple concentric rings, for which the Runge-Kutta discrete equations of the stress and deformation were established based on corresponding self-similar governing equations. The equations were solved ring by ring in a successive manner, starting from the outer boundary to the excavation boundary. The comparison with the verified algorithm in literature shows that the results of the different algorithms are in good agreement and the relative errors of the plastic zone radius under various softening parameters are only 1.7%-2.0%. These results verified the correctness and reliability of the proposed new algorithm. Finally, the new algorithm is used to investigate the influence of the Hoek-Brown parameter a on GRC. A discussion of the potential capability of practical applications of this algorithm is also provided.

关键词： Circular openings Ground reaction curve numerical algorithm Elastoplastic analysis

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numerical algorithm for Dynamic Impedance of Bridge Pile-Group Foundation and Its Validation

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algorithmS 2021年第8期14卷 247-247页

作者： Wang, Chenyu Qiao, Hong Wang, Yi Du, Xianting Beijing Univ Civil Engn & Architecture Sch Civil & Transportat Engn Beijing 100044 Peoples R China Tsinghua Univ Dept Civil Engn Beijing 100084 Peoples R China Beijing Jiaotong Univ Sch Civil Engn Beijing 100044 Peoples R China

The characteristics of bridge pile-group foundation have a significant influence on the dynamic performance of the superstructure. Most of the existing analysis methods for the pile-group foundation impedance take the trait of strong specialty, which cannot be generalized in practical projects. Therefore, a project-oriented numerical solution algorithm is proposed to compute the dynamic impedance of bridge pile-group foundation. Based on the theory of viscous-spring artificial boundary, the derivation and solution of the impedance function are transferred to numerical modeling and harmonic analysis, which can be carried out through the finite element method. By taking a typical pile-group foundation as a case study, the results based on the algorithm are compared with those from existing literature. Moreover, an impact experiment of a real pile-group foundation was implemented, the results of which are also compared with those resulting from the proposed numerical algorithm. Both comparisons show that the proposed numerical algorithm satisfies engineering precision, thus showing good effectiveness in application.

关键词： numerical algorithm pile-group foundation bridge dynamic impedance viscous-spring artificial boundary harmonic analysis

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Research and validation on the numerical algorithm of mechanical module in a transient fuel rod performance code for fast reactor

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ANNALS OF NUCLEAR ENERGY 2022年 171卷 108991-108991页

作者： Yang, Guangliang Guo, Zixuan Wang, Peng Wang, Weixiang Liao, Hailong Ding, Tao Chen, Hongli Univ Sci & Technol China Sch Nucl Sci & Technol Hefei 230026 Peoples R China Nucl Power Inst China Sci & Technol Reactor Syst Design Technol Lab Chengdu 610213 Peoples R China

Mechanical performance is an important aspect for the fuel rod performance in LMFR. Operating conditions in LMFR, like large power density, high fast neutron flux and deep burnup, are hash for the fuel rod. The evolution of fuel rod behaviors is complicated and tightly coupled with each other through temperature, stress and burnup. Considering various in-pile behaviors of the fuel rod under fast neutron irradiation, the numerical iterative algorithm based on grid integration was established to deal with the complex nonlinear mechanical problem for the fuel rod in LMFR. Verification and validation have been carried out by comparing results from this algorithm with analytical solutions as well as results from typical code, which are all in good agreement with each other, proving the accuracy and reliability of this algorithm. CO 2022 Elsevier Ltd. All rights reserved.

关键词： In-pile behaviors numerical algorithm Mechanical analysis Fuel rod performance code LMFR

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A numerical algorithm for solving power-exponent type nonlinear inequalities with applications in calculating stabilizing parameters for LTI systems

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IFAC-PapersOnLine 2022年第3期55卷 263-268页

作者： Zhihua Chen Yong Guo Kai Zhang Yongchun Xie Beijing Institute of Control Engineering Beijing 100190 China School of Automation Northwestern Polytechnical University Xi’an 710072 China School of Aeronautics and Astronautics Sichuan University Chengdu 610225 China

The paper proposes a numerical algorithm for finding a solution set of a class of power-exponent type nonlinear inequalities. The proposed numerical algorithm applies specifically to the case when the power-exponent is positive irrational number, which can’t be effectively solved by using the existing methods. Firstly, by introducing a novel concept of margin variable and using the monotonicity of power-exponent function, this paper converts the problem of solving the nonlinear inequalities into a constrained nonlinear optimization (CNO) problem. Then the obtained CNO problem is solved by using the MATLAB function fmincon . Finally, a numerical algorithm to solve this class of inequalities is obtained. The proposed algorithm can find a solution set of the considered inequalities, not just one or few solutions. Further, the derived algorithm can be easily used to calculate the stabilizing parameter ranges for LTI systems based on the Routh-Hurwitz criterion. Moreover, an example of calculating the stabilizing parameters of a LTI system and an example of solving power-exponent type nonlinear inequalities are provided to show the effectiveness of the proposed algorithm.

关键词： Power-Exponent Function Nonlinear Inequalities Solution Set numerical algorithm LTI Systems Stabilizing Parameters State Feedback Control Constrained Nonlinear Optimization Margin Variable

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numerical algorithm for the Solutions of Fractional Order Systems of Dirichlet Function Types with Comparative Analysis

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FUNDAMENTA INFORMATICAE 2019年第2期166卷 111-137页

作者： Abu Arqub, Omar Univ Jordan Fac Sci Dept Math Amman 11942 Jordan

The aim of this article is to introduce the reproducing kernel algorithm for obtaining the numerical solutions of fractional order systems of Dirichlet function types. The algorithm provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the n-term of exact solutions, numerical solutions of linear and nonlinear time-fractional equations of homogeneous and nonhomogeneous function type are studied from mathematical viewpoint. Convergence analysis, error estimations, and error bounds for the present algorithm are also discussed. The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such systems compared with other numerical methods.

关键词： Reproducing kernel theory Boundary value problems numerical algorithm Fractional order system Dirichlet function types Comparative analysis

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Fractional modeling of plankton-oxygen dynamics under climate change by the application of a recent numerical algorithm

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PHYSICA SCRIPTA 2021年第12期96卷 124044-124044页

作者： Kumar, Pushpendra Suat Erturk, Vedat Banerjee, Ramashis Yavuz, Mehmet Govindaraj, V Natl Inst Technol Puducherry Dept Math Karaikal 609609 India Ondokuz Mayis Univ Dept Math TR-55200 Atakum Samsun Turkey Natl Inst Technol Dept Elect Engn Silchar India Necmettin Erbakan Univ Dept Math & Comp Sci TR-42090 Konya Turkey Univ Exeter Coll Engn Math & Phys Sci Dept Math Penryn TR10 Cornwall England

This research work is dedicated to studying the dynamics of a coupled plankton-oxygen model in the framework of three non-linear differential equations. As we know that the ocean dynamics have a firm impact on the global climate change and on the creation of the environment. Also, it is recorded that about 70% of the environmental oxygen is manufactured in the oceans due to the photosynthetic bustling of phytoplankton. All the same, the rate of oxygen manufacture based on the temperature of the water and hence can be dominance by global warming. To study the proposed Oxygen-Phytoplankton-Zooplankton system, we use a very recent fractional numerical algorithm. We discuss the existence of the solution for the given model problem because in the case of fractional-order models, the proof of solution existence always becomes an important task. After that, we perform many novel 2-D and 3-D graphs by using Mathematica and Python software to fulfill the requirements of the numerical simulations. We use a generalised form of the well known Liouville-Caputo fractional derivative. Given numerical algorithm is very recent, short, easy, and reliable to use or to apply to the non-linear dynamical models. The main motive of this research work is to study the Plankton-Oxygen dynamics under the climate change by using the proposed fractional-order model with capturing the memory effects and discuss some novel results for the literature on such ecological topics.

关键词： phytoplankton oxygen depletion global warming mathematical model new generalised Caputo fractional derivative numerical algorithm

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One-dimensional continuously distributed sensors for thermophysical fields: Method of measurement, model, and numerical algorithm

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MEASUREMENT 2021年 186卷 110082-110082页

作者： Evdokimov, Yu. K. Denisov, E. S. Fadeeva, L. Yu. Kazan Natl Res Tech Univ Kazan Russia

Continuously distributed sensors (CDS) disclose a principally new way to provide space distribution measurements for different physical fields, such as temperature, velocity and light intensity fields. The design of onedimensional CDS and corresponding pulse measurement method are proposed. The numerical algorithm implementing the pulse measurement method are obtained based on inverse operator problem reduced to the optimal control of parabolic partial differential equation coefficients. The algorithm has been numerically studied for two methods of regularization: Tikhonov and iterative. The results of the numerical simulations show that for the low level of the experimental noise (0.1-0.5%) the proposed algorithm is able to restore the space distribution of the measuring physical field with 0.6-4% accuracy. It is shown that appropriative choice of materials for microfilm CDS allows to obtain the electrical relaxation time within the range 10(-2)-10(-5) s, within which the physical fields under measurement could be considered as quasistatic.

关键词： Continuously distributed sensors Pulse method numerical algorithm Measurement of physical fields Inverse operator problem Methods of regularization

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numerical evaluation on the effective thermal conductivity of the composites with discontinuous inclusions: Periodic boundary condition and its numerical algorithm

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2019年 134卷 735-751页

作者： Tian, Wenlong Qi, Lehua Chao, Xujiang Liang, Junhao Fu, M. W. Northwestern Polytech Univ Sch Mech Engn Xian 710072 Shaanxi Peoples R China Hong Kong Polytech Univ Dept Mech Engn Hung Hom Hong Kong Peoples R China Northwestern Polytech Univ Sch Mat Sci & Engn Xian 710072 Shaanxi Peoples R China

Boundary condition plays an important role in prediction of the effective thermal conductivity of composites. In this research, the periodic boundary condition and the representative volume element (RVE) based finite element (FE) homogenization method are adopted to evaluate the effective thermal conductivities of the composites reinforced by the spherical, ellipsoidal and cylindrical inclusions, and the emphases are on the numerical implementation algorithm and validation of the periodic boundary condition. The heat flux continuity of the node pairs on the opposite surfaces of the RVEs of the composites is analyzed and the effective thermal conductivity of the composites are homogenized. The results show that the heat flux continuity of the node pairs on the opposite surfaces of the RVEs of the composites can be guaranteed by the proposed numerical implementation algorithm for the periodic boundary condition, and that the predicted effective thermal conductivities of the composites agree well with those determined by the Lewis-Nielsen model and the experimental tests. Therefore, the RVE based FE homogenization method with the periodic boundary condition can accurately evaluate the effective thermal conductivity of the composites with discontinuous inclusions. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： FE homogenization Heat flux continuity numerical algorithm Periodic boundary condition Thermal conductivity

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A numerical algorithm for Nuclear Reaction in Deuterium-Tritium Plasma

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FUSION SCIENCE AND TECHNOLOGY 2019年第4期75卷 317-323页

作者： Pan, Dongmei Zhao, Zijia Chen, Zhong Lv, Zhongliang Li, Junhan Univ Sci & Technol China Sch Nucl Sci & Technol Hefei 230027 Anhui Peoples R China Natl Univ Def Technol Coll Liberal Arts & Sci Changsha 230027 Hunan Peoples R China Southwest Sci & Technol Univ Sch Natl Def Sci & Technol Mianyang 621000 Sichuan Peoples R China

Rates of neutron production in deuterium-tritium (D-T) plasmas below the temperature of 100keV have been widely studied with analytical cross sections based on nuclear physics. In the present work, a new algorithm of numerical simulation using the latest nuclear database ENDF/B-VII, discrete ordinate (S-N) method, and Monte Carlo methods was developed to describe nuclear reactions in D-T plasma. Compared with the method that used analytical cross section, this new method can predict the nuclear reaction in plasma to several hundreds of kilo-electron-volts and has the potential to give information about directionality of the neutron flux and other interesting nuclear reactions, if needed.

关键词： Deuterium-tritium plasma neutron source nuclear database numerical algorithm

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A numerical algorithm based on a new kind of tension B-spline function for solving Burgers-Huxley equation

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numerical algorithmS 2019年第4期82卷 1121-1142页

作者： Alinia, N. Zarebnia, M. Univ Mohaghegh Ardabili Dept Math Ardebil *** Iran

In this paper, a numerical algorithm based on a new kind of tension B-spline, named hyperbolic-trigonometric tension B-spline method, is applied for solving Burgers-Huxley equation. This method is generated over the space span {sin(tau t), cos(tau t), sinh(tau t), cosh(tau t), 1, t, ..., t(n-5)}, n >= 5, where tau is the tension parameter. Properties of it are the same in most of the properties of the usual polynomial B-splines and benefit from some other advantages, as well. Therefore, in this paper, we apply three methods consisting of trigonometric method, hyperbolic tension B-spline method, and our new hyperbolic-trigonometric tension B-spline method, to solve Burgers-Huxley equation. The convergence analysis is discussed. Then, we use some numerical examples to illustrate the accuracy and implementation of the proposed algorithm.

关键词： Burgers-Huxley equation Tension B-spline Hyperbolic-trigonometric Collocation method numerical algorithm

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