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应用数学和力学（英文版）
应用数学和力学（英文版）

周哲玮

月刊

0253-4827

amm@department.shu.edu.cn

021-66135601，66135219

200444

上海市上大路99号

应用数学和力学（英文版）/Journal Applied Mathematics and MechanicsCSCDEISCI
查看更多>>1980年5月由我国著名科学家、上海大学校长钱伟长院士创办。创刊至2002年底，钱伟长院士一直亲自担任主编。2003年改由我校副校长、博导周哲玮教授担任主编。钱伟长院士亲自制定办刊的宗旨是：发表力学、力学中的数学方法和近代力学密切相关的应用数学的创造性学术性论文。所谓创造性学术论文是指具有新思想、新观点、新方法的原创性学术论文。我刊对应的中文版由重庆交通大学主办并出版。英文版由上海大学主办，上海大学出版社出版。国外由德国Springer出版社发行。我刊的读者对象主要是从事与力学和应用数学有关的科研人员、工程技术人员和大专院校师生。被收录的数据库《科学引文索引（扩大版）》（SCIE）、《工程索引》（EI Compendex）、《世界译文索引》、美国《数学评论（MR）》、《应用力学评论（AMR）》、《力学》、《宇航文摘》、《当代数学》、俄罗斯《文摘杂志》力学、数学专辑，德国《数学文摘》及中国《中国力学文摘》、《中国数学文摘》、《中国物理文摘》、中国科技期刊光盘版《中国期刊网》、中国台湾《中文电子期刊服务数据库（CEPS）》、中国西南信息研究中心《中文科技期刊数据库》、中国信息研究所《万方数据库——数字化期刊群》等21种国内外权威文摘刊物及其数据库均收录我刊全文、题录和文摘。《应用数学和力学》被美国力学科学院评为17种国际力学刊物之一。
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    Integrated multi-scale approach combining global homogenization and local refinement for multi-field analysis of high-temperature superconducting composite magnets

    Hanxiao GUOPeifeng GAOXingzhe WANG
    747-762页
    查看更多>>摘要：Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting applications.With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer com-ponents,the thermomechanical characteristics of each component differ considerably un-der extremely low temperatures and strong electromagnetic fields.Traditional numerical models include homogenized orthotropic models,which simplify overall field calculation but miss detailed multi-physics aspects,and full refinement(FR)ones that are thorough but computationally demanding.Herein,we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils.This approach combines a global homogenization(GH)scheme based on the homogenized electromagnetic T-A model,a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A,and a homogenized orthotropic thermoelas-tic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale.We then identify"dangerous regions"at the macroscopic scale and obtain finer details using a local refinement(LR)scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale.The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature,indicating that the present approach is accurate and efficient.The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.
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    Comparison of nonlinear modeling methods for the composite rubber clamp

    Yiming CAOHui MAXumin GUOBingfeng ZHAO...
    763-778页
    查看更多>>摘要：The cubic stiffness force model(CSFM)and Bouc-Wen model(BWM)are introduced and compared innovatively.The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments.By fitting the iden-tified nonlinear coefficients under different excitation amplitudes,the nonlinear vibration responses of the system are predicted.The results show that the accuracy of the BWM is higher than that of the CSFM,especially in the non-resonant region.However,the optimization time of the BWM is longer than that of the CSFM.
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    Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study

    Lele RENWei ZHANGTing DONGYufei ZHANG...
    779-794页
    查看更多>>摘要：The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation ex-citation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an elec-tromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are col-lected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.
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    Kinematic analysis of flexible bipedal robotic systems

    R.FAZELA.M.SHAFEIS.R.NEKOO
    795-818页
    查看更多>>摘要：In spite of its intrinsic complexities,the passive gait of bipedal robots on a sloping ramp is a subject of interest for numerous researchers.What distinguishes the present research from similar works is the consideration of flexibility in the constituent links of this type of robotic systems.This is not a far-fetched assumption because in the transient(impact)phase,due to the impulsive forces which are applied to the sys-tem,the likelihood of exciting the vibration modes increases considerably.Moreover,the human leg bones that are involved in walking are supported by viscoelastic muscles and ligaments.Therefore,for achieving more exact results,it is essential to model the robot links with viscoelastic properties.To this end,the Gibbs-Appell formulation and Newton's kinematic impact law are used to derive the most general form of the system's dynamic equations in the swing and transient phases of motion.The most important issue in the passive walking motion of bipedal robots is the determination of the initial robot configuration with which the system could accomplish a periodic and stable gait solely under the effect of gravitational force.The extremely unstable nature of the sys-tem studied in this paper and the vibrations caused by the impulsive forces induced by the impact of robot feet with the inclined surface are some of the very serious challenges encountered for achieving the above-mentioned goal.To overcome such challenges,an innovative method that uses a combination of the linearized equations of motion in the swing phase and the algebraic motion equations in the transition phase is presented in this paper to obtain an eigenvalue problem.By solving this problem,the suitable initial conditions that are necessary for the passive gait of this bipedal robot on a sloping surface are determined.The effects of the characteristic parameters of elastic links including the modulus of elasticity and the Kelvin-Voigt coefficient on the walking stability of this type of robotic systems are also studied.The findings of this parametric study reveal that the increase in the Kelvin-Voigt coefficient enhances the stability of the robotic system,while the increase in the modulus of elasticity has an opposite effect.
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    Generalized polynomial chaos expansion by reanalysis using static condensation based on substructuring

    D.LEES.CHANGJ.LEE
    819-836页
    查看更多>>摘要：This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.
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    Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

    Yu TANFan PENGChang LIUDaiming PENG...
    837-856页
    查看更多>>摘要：Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical elec-tric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1 continuity.Systematic numerical sim-ulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The elec-tric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.
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    Parallelization strategies for resolved simulations of fluid-structure-particle interactions

    Jianhua QINFei LIAOGuodan DONGXiaolei YANG...
    857-872页
    查看更多>>摘要：Fluid-structure-particle interactions in three spatial dimensions happen in many environmental and engineering flows.This paper presents the parallel algorithms for the hybrid diffuse and sharp interface immersed boundary(IB)method developed in our previous work.For the moving structure modeled using the sharp interface IB method,a recursive box method is developed for efficiently classifying the background grid nodes.For the particles modeled using the diffuse interface IB method,a'master-slave'approach is adopted.For the particle-particle interaction(PPI)and particle-structure interaction(PSI),a fast algorithm for classifying the active and inactive Lagrangian points,which discretize the particle surface,is developed for the'dry'contact approach.The results show that the proposed recursive box method can reduce the classifying time from 52 seconds to 0.3 seconds.Acceptable parallel efficiency is obtained for cases with different particle concentrations.Furthermore,the lubrication model is utilized when a particle approaches a wall,enabling an accurate simulation of the rebounding phenomena in the benchmark particle-wall collision problem.At last,the capability of the proposed computational framework is demonstrated by simulating particle-laden turbulent channel flows with rough walls.
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    Research on modeling and self-excited vibration mechanism in magnetic levitation-collision interface coupling system

    Jinghu TANGChaofeng LIJin ZHOUZhiwei WU...
    873-890页
    查看更多>>摘要：The modeling and self-excited vibration mechanism in the magnetic levitation-collision interface coupling system are investigated.The effects of the con-trol and interface parameters on the system's stability are analyzed.The frequency range of self-excited vibrations is investigated from the energy point of view.The phenomenon of self-excited vibrations is elaborated with the phase trajectory.The corresponding con-trol strategies are briefly analyzed with respect to the vibration mechanism.The results show that when the levitation objects collide with the mechanical interface,the system's vibration frequency becomes larger with the decrease in the collision gap;when the vi-bration frequency exceeds the critical frequency,the electromagnetic system continues to provide energy to the system,and the collision interface continuously dissipates energy so that the system enters the self-excited vibration state.
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    Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams

    N.D.NGUYENT.N.NGUYEN
    891-910页
    查看更多>>摘要：This study presents the Chebyshev polynomials-based Ritz method to ex-amine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal dis-tribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deforma-tions with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Cheby-shev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.
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    A phase-field model for simulating the propagation behavior of mixed-mode cracks during the hydraulic fracturing process in fractured reservoirs

    Dan ZHANGLiangping YIZhaozhong YANGJingqiang ZHANG...
    911-930页
    查看更多>>摘要：A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primar-ily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is estab-lished by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical exper-iments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode Ⅱ fracture toughness value,natural fracture mode Ⅱ toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.
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