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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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    A novel triple periodic minimal surface-like plate lattice and its data-driven optimization method for superior mechanical properties

    Yanda WANGYanping LIANZhidong WANGChunpeng WANG...
    217-238页
    查看更多>>摘要：Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment,along with the advances in additive manufacturing(AM)technologies.In this work,a novel design of plate lattice structures described by a parametric model is proposed to enrich the design space of plate lattice structures with high connectivity suitable for AM processes.The parametric model takes the basic unit of the triple periodic minimal surface(TPMS)lattice as a skeleton and adopts a set of generation parameters to de-termine the plate lattice structure with different topologies,which takes the advantages of both plate lattices for superior specific mechanical properties and TPMS lattices for high connectivity,and therefore is referred to as a TPMS-like plate lattice(TLPL).Fur-thermore,a data-driven shape optimization method is proposed to optimize the TLPL structure for maximum mechanical properties with or without the isotropic constraints.In this method,the genetic algorithm for the optimization is utilized for global search capability,and an artificial neural network(ANN)model for individual fitness estimation is integrated for high efficiency.A set of optimized TLPLs at different relative densities are experimentally validated by the selective laser melting(SLM)fabricated samples.It is confirmed that the optimized TLPLs could achieve elastic isotropy and have superior stiffness over other isotropic lattice structures.
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    Parametric resonance of axially functionally graded pipes conveying pulsating fluid

    Jie JINGXiaoye MAOHu DINGLiqun CHEN...
    239-260页
    查看更多>>摘要：Based on the generalized Hamilton's principle,the nonlinear governing equa-tion of an axially functionally graded(AFG)pipe is established.The non-trivial equi-librium configuration is superposed by the modal functions of a simply supported beam.Via the direct multi-scale method,the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method(DQEM).The influence of Young's modulus gradient on the parametric reso-nance is investigated in the subcritical and supercritical regions.In general,the pipe in the supercritical region is more sensitive to the pulsating excitation.The nonlinearity changes from hard to soft,and the non-trivial equilibrium configuration introduces more frequency components to the vibration.Besides,the increasing Young's modulus gradi-ent improves the critical pulsating flow velocity of the parametric resonance,and further enhances the stability of the system.In addition,when the temperature increases along the axial direction,reducing the gradient parameter can enhance the response asymme-try.This work further complements the theoretical analysis of pipes conveying pulsating fluid.
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    Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

    Runqing CAOZilong GUOWei CHENHuliang DAI...
    261-276页
    查看更多>>摘要：Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincaré maps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.
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    Tuning mechanical behaviors of highly entangled hydrogels with the random distribution of mobile entanglements

    Jinlong LIUDi LUBin CHEN
    277-294页
    查看更多>>摘要：Highly entangled hydrogels exhibit excellent mechanical properties,includ-ing high toughness,high stretchability,and low hysteresis.By considering the evolu-tion of randomly distributed entanglements within the polymer network upon mechanical stretches,we develop a constitutive theory to describe the large stretch behaviors of these hydrogels.In the theory,we utilize a representative volume element(RVE)in the shape of a cube,within which there exists an averaged chain segment along each edge and a mobile entanglement at each corner.By employing an explicit method,we decouple the elasticity of the hydrogels from the sliding motion of their entanglements,and de-rive the stress-stretch relations for these hydrogels.The present theoretical analysis is in agreement with experiment,and highlights the significant influence of the entanglement distribution within the hydrogels on their elasticity.We also implement the present de-veloped constitutive theory into a commercial finite element software,and the subsequent simulations demonstrate that the exact distribution of entanglements strongly affects the mechanical behaviors of the structures of these hydrogels.Overall,the present theory provides valuable insights into the deformation mechanism of highly entangled hydrogels,and can aid in the design of these hydrogels with enhanced performance.
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    Dynamic characteristics of multi-span spinning beams with elastic constraints under an axial compressive force

    Xiaodong GUOZhu SULifeng WANG
    295-310页
    查看更多>>摘要：A theoretical model for the multi-span spinning beams with elastic con-straints under an axial compressive force is proposed.The displacement and bending angle functions are represented through an improved Fourier series,which ensures the continuity of the derivative at the boundary and enhances the convergence.The exact characteristic equations of the multi-span spinning beams with elastic constraints under an axial compressive force are derived by the Lagrange equation.The efficiency and ac-curacy of the present method are validated in comparison with the finite element method(FEM)and other methods.The effects of the boundary spring stiffness,the number of spans,the spinning velocity,and the axial compressive force on the dynamic character-istics of the multi-span spinning beams are studied.The results show that the present method can freely simulate any boundary constraints without modifying the solution pro-cess.The elastic range of linear springs is larger than that of torsion springs,and it is not affected by the number of spans.With an increase in the axial compressive force,the attenuation rate of the natural frequency of a spinning beam with a large number of spans becomes larger,while the attenuation rate with an elastic boundary is lower than that under a classic simply supported boundary.
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    Analysis of piezoelectric semiconductor fibers under gradient temperature changes

    Shuangpeng LIRuoran CHENGNannan MAChunli ZHANG...
    311-320页
    查看更多>>摘要：Piezoelectric semiconductors(PSs)possess both semiconducting properties and piezoelectric coupling effects,making them optimal building blocks for semiconductor devices.PS fiber-like structures have wide applications in multi-functional semiconduc-tor devices.In this paper,a one-dimensional(1D)theoretical model is established to describe the piezotronic responses of a PS fiber under gradient temperature changes.The theoretical model aims to explain the mechanism behind the resistance change caused by such gradient temperature changes.Numerical results demonstrate that a gradient temperature change significantly affects the physical fields within the PS fiber,and can induce changes in its surface resistance.It provides important theoretical guidance on the development of piezotronic devices that are sensitive to temperature effects.
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    A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints

    Lei WANGYingge LIUJuxi HUWeimin CHEN...
    321-336页
    查看更多>>摘要：A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geo-metric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific prob-lem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit as-sembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analy-sis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.
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    Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field

    Haiyang WUJiangfeng LOUBiao ZHANGYuntong DAI...
    337-354页
    查看更多>>摘要：Self-oscillating systems abound in the natural world and offer substantial potential for applications in controllers,micro-motors,medical equipments,and so on.Currently,numerical methods have been widely utilized for obtaining the characteristics of self-oscillation including amplitude and frequency.However,numerical methods are burdened by intricate computations and limited precision,hindering comprehensive in-vestigations into self-oscillating systems.In this paper,the stability of a liquid crystal elastomer fiber self-oscillating system under a linear temperature field is studied,and analytical solutions for the amplitude and frequency are determined.Initially,we estab-lish the governing equations of self-oscillation,elucidate two motion regimes,and reveal the underlying mechanism.Subsequently,we conduct a stability analysis and employ a multi-scale method to obtain the analytical solutions for the amplitude and frequency.The results show agreement between the multi-scale and numerical methods.This re-search contributes to the examination of diverse self-oscillating systems and advances the theoretical analysis of self-oscillating systems rooted in active materials.
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    Deep bed filtration model for cake filtration and erosion

    L.I.KUZMINAY.V.OSIPOVA.R.PESTEREV
    355-372页
    查看更多>>摘要：Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media.Two main types of particle deposition,namely,cake filtration at the inlet and deep bed filtration throughout the entire porous medium,are studied by different models.A unified approach for the transport and deposition of particles based on the deep bed filtration model is proposed.A variable suspension flow rate,proportional to the number of free pores at the inlet of the porous medium,is considered.To model cake filtration,this flow rate is introduced into the mass balance equation of deep bed filtration.For the cake filtration without deposit erosion,the suspension flow rate decreases to zero,and the suspension does not penetrate deep into the porous medium.In the case of the cake filtration with erosion,the suspension flow rate is nonzero,and the deposit is distributed throughout the entire porous medium.An exact solution is obtained for a constant filtration function.The method of characteristics is used to construct the asymptotics of the concentration front of suspended and retained particles for a filtration function in a general form.Explicit formulae are obtained for a linear filtration function.The properties of these solutions are studied in detail.
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    Effects of multiple shapes for steady flow with transformer oil+Fe3O4+TiO2 between two stretchable rotating disks

    M.RAHMANM.TURKYILMAZOGLUZ.MUSHTAQ
    373-388页
    查看更多>>摘要：In this study,we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks.The steady flow of hybrid nanofluids with transformer oil as the base fluid and Fe3O4+TiO2 as the hybrid nanofluid is considered.Several shapes of Fe3O4+TiO2 hybrid nanofluids,including sphere,brick,blade,cylinder,and platelet,are studied.Every shape exists in the same volume of a nanoparticle.The leading equations(partial differential equations(PDEs))are transformed to the nonlinear ordinary differential equations(ODEs)with the help of similarity transformations.The system of equations takes the form of ODEs depending on the boundary conditions,whose solutions are computed numerically by the bvp4c MATLAB solver.The outputs are compared with the previous findings,and an intriguing pattern is discovered,such that the tangential velocity is increased for the rotation parameter,while it is decreased by the stretching values because of the lower disk.For the reaction rate parameter,the concentration boundary layer becomes shorter,and the activation energy component increases the rate at which mass transfers come to the higher disk but have the opposite effect on the bottom disk.The ranges of various parameters taken into account are Pr=6.2,Re=2,M=1.0,φ1=φ2=0.03,K=0.5,S=-0.1,Br=0.3,Sc=2.0,α1=0.2,γ=0.1,En=2.0,and q=1.0,and the rotation factor K is within the range of 0 to 1.
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