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Modeling the dynamic magneto-mechanical response of magnetic shape memory alloys based on Hamilton's principle: The numerical algorithm

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2023年第1期180卷

作者： Fan, Chengkai Steinmann, Paul Wang, Jiong South China Univ Technol Sch Civil Engn & Transportat Guangzhou 510640 Guangdong Peoples R China South China Univ Technol State Key Lab Subtrop Bldg Sci Guangzhou 510640 Guangdong Peoples R China Univ Erlangen Nurnberg Inst Appl Mech Egerlandstr 5 D-91058 Erlangen Germany Univ Glasgow Glasgow Computat Engn Ctr Glasgow Scotland

This paper is the second part of a variational modeling work on the dynamic magneto mechanical response of magnetic shape memory alloys (MSMA). In the first part of this series work, the governing equations system for modeling the dynamic response of MSMA samples has been derived based on Hamilton's principle, which contains the Maxwell's equations, the magneto-mechanic equations, the evolution equations of internal variables and the twin interface motion criteria. In this paper, we aim to conduct comprehensive numerical simulations on the dynamic magneto-mechanical response of MSMA samples. To solve the governing system, the space-time finite element method is applied and a double-loop iterative numerical algorithm is proposed. By using this algorithm, the independent variables in the governing system and the motion of twin interfaces in the MSMA sample can be determined separately and iteratively. Besides that, a specific discretization of the sample is adopted to simplify the calculation of variant state distribution in the sample. To show the efficiency of the numerical algorithm, the magneto-mechanical response of a MSMA sample in stress-assisted dynamic field loading tests and field-assisted dynamic mechanical loading tests are studied. Based on the numerical results, some global response curves of the MSMA sample are plotted, which show good consistency with the experimental results. Furthermore, the current configuration of the sample and the distributions of some important physical fields in the sample can be simulated. The current work will be helpful for the design of novel actuators or energy harvesters with MSMA.

关键词： Magnetic shape memory alloy Dynamic response numerical algorithm Finite element simulation Mechanism analysis

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A numerical algorithm for damage progression of reinforced concrete bridge piers during air temperature and solar radiation cycles

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ENGINEERING STRUCTURES 2024年 319卷

作者： Zhang, Kai Lei, Jinshan Wang, Zhiyong Yuan, Qiang Cent South Univ Sch Civil Engn Changsha 410075 Peoples R China Natl Engn Res Ctr High Speed Railway Construct Tec Changsha 410075 Peoples R China Anhui Engineer Mat Technol Co Ltd CTCE Grp Hefei 230041 Peoples R China

Reinforced concrete (RC) solid piers are unavoidably affected by air temperature changes and solar radiation during service life. Nevertheless, the deterioration of pier concrete with increased exposure age remains unclear. A novel thermal-mechanical numerical algorithm (finite element model) for characterizing the deterioration characteristics of RC structures under cyclic environmental loads has been suggested. The deterioration of RC pier concrete after 100 years of air temperature and solar radiation cycles is simulated. The numerical results demonstrate that tensile damage of pier concrete during air temperature and solar radiation cycles increases continuously with exposure age. After one year of exposure, the tensile damage value of pier surface concrete increased to 0.201 and further increased to 0.286 and 0.357 as the exposure age grew to 10 and 100 years. Pier concrete tensile damage can be mitigated by using surface short-wave absorption-reducing methods, controlling the thermal properties of concrete, and raising the concrete peak tensile strain. The proposed finite element framework and numerical solutions enable a viable simulation-based method for the analysis of bridge structural long-term deterioration behavior and design of the bridge engineering.

关键词： Reinforced concrete (RC) piers Elastoplastic behavior Environment loading Damage evolution numerical algorithm

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Parameter calibration and numerical algorithm realization of physically visco-hyperelastic constitutive model based on compression experiment of EPDM

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INTERNATIONAL JOURNAL OF IMPACT ENGINEERING 2023年第1期181卷

作者： Xu, Yude Hu, Shuchuan Hu, Meng Lu, Hongyao Liu, Silei Zhang, Wanqing Xue, Zhiqiang Li, Shaozheng Xu, Guoyao Wu, Xuanqing Ren, Zeqi Zhang, Xi Shi, Zixuan Wang, Zhang Tongji Univ Minist Educ Key Lab Rd & Traff Engn Shanghai 201804 Peoples R China Shanghai Key Lab Rail Infrastruct Durabil & Syst S Shanghai 201804 Peoples R China Tongji Univ Coll Transportat Engn Shanghai 201804 Peoples R China Shanghai Univ Engn Sci Sch Urban Rail Transportat Shanghai 201620 Peoples R China Shanghai Shentong Metro Grp Co Ltd Shanghai 201103 Peoples R China Shanghai Marine Diesel Engine Res Inst Shanghai 201108 Peoples R China Shanghai Tunnel Engn & Rail Transit Design & Res I Shanghai 200235 Peoples R China Liaoning Prov Traff Planning & Design Inst Co Ltd Shenyang 110166 Peoples R China

Multi-constitutive models integrated with microstructure parameters are suitable to capture different rubberlike material mechanical characteristics such as large deformation, hysteresis. However, the typical models are less often adopted to analyze realistic engineering problems due to difficult derivation of numerical algorithm which can be embedded into FEM models. Therefore, we take numerical algorithm derivation of physically visco-hyperelastic constitutive model proposed by Yuhai Xiang as an application example to analyze mechanic performance of EPDM (Ethylene Propylene Diene Monomer), which is widely utilized as cushion members of rail structure. After numerical algorithm is derived, static and dynamic compression tests are designed to calibrate mechanical parameters of EPDM. Finally, FEM models integrated with above numerical algorithm and calibration parameters are established to simulate mechanical response under different boundary conditions. In comparison of results between experiments and FEM simulations, accuracy and precision of numerical iteration formula and practicality can meet demands of engineering design and application when deformation and distortion of the FEM model mesh are not severe. We hope our work can supply some inspiration and be expanded to characterize, analyze, simulate and even predict performance of other similar rubberlike materials by applying suitable constitutive models in future.

关键词： Visco-hyperelasticity numerical algorithm nonlinear FEM Parameter calibration EPDM Compression test

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A Rapid and Robust numerical algorithm for Sensitivity Encoding with Sparsity Constraints: Self-Feeding Sparse SENSE

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MAGNETIC RESONANCE IN MEDICINE 2010年第4期64卷 1078-1088页

作者： Huang, Feng Chen, Yunmei Yin, Wotao Lin, Wei Ye, Xiaojing Guo, Weihong Reykowski, Arne Invivo Corp Adv Concept Dev Gainesville FL 32603 USA Univ Florida Dept Math Gainesville FL 32611 USA Rice Univ Dept Computat & Appl Math Houston TX USA Case Western Reserve Univ Dept Math Cleveland OH 44106 USA

The method of enforcing sparsity during magnetic resonance imaging reconstruction has been successfully applied to partially parallel imaging (PPI) techniques to reduce noise and artifact levels and hence to achieve even higher acceleration factors. However, there are two major problems in the existing sparsity-constrained PPI techniques: speed and robustness. By introducing an auxiliary variable and decomposing the original minimization problem into two subproblems that are much easier to solve, a fast and robust numerical algorithm for sparsity-constrained PPI technique is developed in this work. The specific implementation for a conventional Cartesian trajectory data set is named self-feeding Sparse Sensitivity Encoding (SENSE). The computational cost for the proposed method is two conventional SENSE reconstructions plus one spatially adaptive image denoising procedure. With reconstruction time approximately doubled, images with a much lower root mean square error (RMSE) can be achieved at high acceleration factors. Using a standard eight-channel head coil, a net acceleration factor of 5 along one dimension can be achieved with low RMSE. Furthermore, the algorithm is insensitive to the choice of parameters. This work improves the clinical applicability of SENSE at high acceleration factors. Magn Reson Med 64:1078-1088, 2010. (C) 2010 WileyLiss, Inc.

关键词： partially parallel imaging g-factor sparsity constraint prior information compressed sensing numerical algorithm

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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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A simple numerical algorithm for solution of non-linear equations with multiple roots

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COMPUTERS & CHEMISTRY 1998年第5期22卷 429-432页

作者： Aranovich, GL Donohue, MD Johns Hopkins Univ Dept Chem Engn Baltimore MD 21218 USA

A new algorithm is proposed to calculate the behavior of non-linear equations with multiple solutions. Use of this algorithm is demonstrated by calculation of compositions in an adsorbed layer for a vapor that exhibit... 详细信息

关键词： phase transitions phase equilibria non-linear equations multiple roots numerical algorithm adsorption

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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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Fractional Fokker-Planck dynamics: numerical algorithm and simulations

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Physical Review E 2006年第4期73卷 046133-046133页

作者： E. Heinsalu M. Patriarca I. Goychuk G. Schmid P. Hänggi Institut für Physik Universität Augsburg Universitätsstrasse 1 D-86135 Augsburg Germany Institute of Theoretical Physics Tartu University Tähe 4 51010 Tartu Estonia

Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying continuous-time random walk. An efficient numerical algorithm is developed which is applicable for an arbitrary potential. This algorithm is then applied to investigate the fractional current and the corresponding nonlinear mobility in different washboard potentials. Normal and fractional diffusion are compared through their time evolution of the probability density in state space. Moreover, we discuss the stationary probability density of the fractional current values.

关键词： .Fokker-Planck underlying potentials anomalous Brownian minima Tilted probability density time evolution TILTING continuous-time numerical algorithm Fractional diffusion random walk periodic potential substrate potential nonlinear mobility washboard fractional current

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Fast numerical algorithm for a high-precision 6D electromagnetic positioning navigation system

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TURKISH JOURNAL OF PHYSICS 2014年第2期38卷 165-173页

作者： Xiang, Qian Wang, Shiqing Liu, Haifeng Southwestern Inst Phys Chengdu Sichuan Peoples R China Chengdu Univ Technol Engn & Tech Coll Inst Nucl Engn & Technol Leshan Peoples R China

A fast numerical algorithm is proposed for the 6 degrees of freedom electromagnetic navigation system, which can be used to improve surgical operations guided by medical images. Both the rotation transformation technique and optimization technique are adopted in the algorithm. The results from simulations show that the calculating time is improved greatly under the required precision in the surgery. A navigation system based on the algorithm can make the medical device's dimensions miniaturized and the structure simplified and portable. The performance and application scope of the electromagnetic positioning navigation system can be improved.

关键词： Six degrees of freedom electromagnetic positioning navigation numerical algorithm

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