Applied Mathematics and Mechanics was founded in 1980 by CHIEN Wei-zang, a celebrated Chinese scientist in mechanics and mathematics. The current editor in chief is Professor LU Tianjian from Nanjing University of Aeronautics and Astronautics. The Journal was a quarterly in the beginning, a bimonthly the next year, and then a monthly ever since 1985. It carries original research papers on mechanics, mathematical methods in mechanics and interdisciplinary mechanics based on artificial intelligence mathematics. It also strengthens attention to mechanical issues in interdisciplinary fields such as mechanics and information networks, system control, life sciences, ecological sciences, new energy, and new materials, making due contributions to promoting the development of new productive forces.
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2025, Volume 46, Issue 6
publish date：June 01 2025
Display Method:
2025, 46(6): 687-696.
doi: 10.21656/1000-0887.440360
Abstract:
An adaptive power parameter inverse distance weighted (AIDW) reconstruction method to enhance the accuracy of the ghost cell method, was proposed for handling of immersed boundary. The AIDW utilizes the characteristics of the inverse distance weighted interpolation, integrating comprehensive information from the distribution of physical parameters at interpolation nodes with local flow properties to automatically adjust the power parameter value, to improve the reconstruction precision across various flow conditions, particularly in the cases of discontinuities near complex boundaries. Numerical simulations of 2 examples of an inclined shock tube and a cylindrical Couette flow demonstrate advantages of the AIDW in correcting distortions at discontinuous interfaces and in enhancing the accuracy of the physical parameter distribution.
An adaptive power parameter inverse distance weighted (AIDW) reconstruction method to enhance the accuracy of the ghost cell method, was proposed for handling of immersed boundary. The AIDW utilizes the characteristics of the inverse distance weighted interpolation, integrating comprehensive information from the distribution of physical parameters at interpolation nodes with local flow properties to automatically adjust the power parameter value, to improve the reconstruction precision across various flow conditions, particularly in the cases of discontinuities near complex boundaries. Numerical simulations of 2 examples of an inclined shock tube and a cylindrical Couette flow demonstrate advantages of the AIDW in correcting distortions at discontinuous interfaces and in enhancing the accuracy of the physical parameter distribution.
2025, 46(6): 697-708.
doi: 10.21656/1000-0887.450339
Abstract:
The fast singular boundary method was employed to simulate acoustic propagation in infinite domains under subsonic uniform flow. In this approach, a linear combination of the fundamental solutions satisfying the acoustic propagation properties in subsonic flow and the weighting factors was used to compute the sound pressure. The origin intensity factors were used to resolve the singularity of the fundamental solution. A fast direct method, based on recursive skeleton decomposition, was applied to compress the dense matrices generated with the singular boundary method for solving largescale acoustic problems. Finally, the accuracy, convergence, and efficiency of the fast singular boundary method were validated through 2 numerical examples in comparison with analytical solutions, finite element solutions, and existing literature results. The effects of the Mach number and the wave number on acoustic propagation were also investigated.
The fast singular boundary method was employed to simulate acoustic propagation in infinite domains under subsonic uniform flow. In this approach, a linear combination of the fundamental solutions satisfying the acoustic propagation properties in subsonic flow and the weighting factors was used to compute the sound pressure. The origin intensity factors were used to resolve the singularity of the fundamental solution. A fast direct method, based on recursive skeleton decomposition, was applied to compress the dense matrices generated with the singular boundary method for solving largescale acoustic problems. Finally, the accuracy, convergence, and efficiency of the fast singular boundary method were validated through 2 numerical examples in comparison with analytical solutions, finite element solutions, and existing literature results. The effects of the Mach number and the wave number on acoustic propagation were also investigated.
2025, 46(6): 709-716.
doi: 10.21656/1000-0887.450097
Abstract:
In the process of fluid-structure coupling analysis, it is necessary to use appropriate data transfer method to map the node load onto the structural grid. To meet the accuracy requirements of nodal force transfer on complex surfaces, a search algorithm based on the critical dihedral angle criterion and the maximum/minimum influence radius was proposed to determine the interpolation area on the surface. A 3D node force interpolation method based on the principle of minimum potential energy was used to transfer node force data between 2 sets of calculation grids, the consistency of load distributions, resultant forces, and resultant moments after transfer was verified through numerical examples.
In the process of fluid-structure coupling analysis, it is necessary to use appropriate data transfer method to map the node load onto the structural grid. To meet the accuracy requirements of nodal force transfer on complex surfaces, a search algorithm based on the critical dihedral angle criterion and the maximum/minimum influence radius was proposed to determine the interpolation area on the surface. A 3D node force interpolation method based on the principle of minimum potential energy was used to transfer node force data between 2 sets of calculation grids, the consistency of load distributions, resultant forces, and resultant moments after transfer was verified through numerical examples.
2025, 46(6): 717-729.
doi: 10.21656/1000-0887.450199
Abstract:
Curved microchannels exhibit significant advantages in electroosmotic flow and heat transfer, including increased electroosmotic flow velocities and improved heat transfer efficiencies. At the same time, nanofluids have received widespread attention due to their excellent heat transfer performances. However, current research on the electroosmotic flow and heat transfer mechanisms of nanofluids within curved microchannels remains insufficient. Herein, the effects of the geometry of curved microchannels on the electroosmotic flow and heat transfer characteristics of nanofluids in the microchannels were investigated at low zeta potentials and constant wall heat fluxes. The creeping Dean flow was considered, and the velocity field was kept in a straight line distribution due to no centripetal force. The semi-analytic solutions of velocity and temperature were obtained with the Fourier transform method, and the mathematical expression of Nusselt number Nu was derived based on the velocity and temperature solutions. The variation trends of the velocity, the temperature, and Nusselt number Nu with curvature ratio δ, nanoparticle volume fraction φ, and the ratio of the characteristic pressure velocity to the characteristic electroosmotic velocity ur, were analyzed, with the characteristics of the flow and heat transfer phenomena revealed. The results show that, Nusselt number Nu decreases with the pressure velocity and the curvature ratio, and increases with the nanoparticle volume fraction. The work provides an important reference for the design and application of micro and nano fluid devices, and helps to optimize the device performances and applications.
Curved microchannels exhibit significant advantages in electroosmotic flow and heat transfer, including increased electroosmotic flow velocities and improved heat transfer efficiencies. At the same time, nanofluids have received widespread attention due to their excellent heat transfer performances. However, current research on the electroosmotic flow and heat transfer mechanisms of nanofluids within curved microchannels remains insufficient. Herein, the effects of the geometry of curved microchannels on the electroosmotic flow and heat transfer characteristics of nanofluids in the microchannels were investigated at low zeta potentials and constant wall heat fluxes. The creeping Dean flow was considered, and the velocity field was kept in a straight line distribution due to no centripetal force. The semi-analytic solutions of velocity and temperature were obtained with the Fourier transform method, and the mathematical expression of Nusselt number Nu was derived based on the velocity and temperature solutions. The variation trends of the velocity, the temperature, and Nusselt number Nu with curvature ratio δ, nanoparticle volume fraction φ, and the ratio of the characteristic pressure velocity to the characteristic electroosmotic velocity ur, were analyzed, with the characteristics of the flow and heat transfer phenomena revealed. The results show that, Nusselt number Nu decreases with the pressure velocity and the curvature ratio, and increases with the nanoparticle volume fraction. The work provides an important reference for the design and application of micro and nano fluid devices, and helps to optimize the device performances and applications.
2025, 46(6): 730-741.
doi: 10.21656/1000-0887.450123
Abstract:
The density and viscosity of liquid lead-bismuth metal are much larger than those of water, which causes nonnegligible flow induced vibration (FIV) and wear problems of fuel assemblies in the reactor. With the fluid-structure coupled analysis method combining the CFD and the FEM, a rapid analysis method for the turbulent vibration responses of wire-wrapped fuel rods was proposed in view of the spatial periodicity and time periodicity. For the space periodic structure of wire-wrapped fuel rods, a single-span flow field model was established, and the lead-bismuth environment fluid excitation load was obtained based on the CFD analysis. From the frequency domain information of the turbulent excitation force PSD, the equivalent time history extrapolation technique was developed to obtain long-duration loads for vibration analysis. With the nonlinear contact between the wire-wrapped fuel rods considered, an FEM model was established to carry out the vibration analysis. The results show that, the axial flow of liquid lead-bismuth causes turbulent vibrations of fuel rods, with a maximum amplitude of 3.83 μm, which meets the engineering design requirement.
The density and viscosity of liquid lead-bismuth metal are much larger than those of water, which causes nonnegligible flow induced vibration (FIV) and wear problems of fuel assemblies in the reactor. With the fluid-structure coupled analysis method combining the CFD and the FEM, a rapid analysis method for the turbulent vibration responses of wire-wrapped fuel rods was proposed in view of the spatial periodicity and time periodicity. For the space periodic structure of wire-wrapped fuel rods, a single-span flow field model was established, and the lead-bismuth environment fluid excitation load was obtained based on the CFD analysis. From the frequency domain information of the turbulent excitation force PSD, the equivalent time history extrapolation technique was developed to obtain long-duration loads for vibration analysis. With the nonlinear contact between the wire-wrapped fuel rods considered, an FEM model was established to carry out the vibration analysis. The results show that, the axial flow of liquid lead-bismuth causes turbulent vibrations of fuel rods, with a maximum amplitude of 3.83 μm, which meets the engineering design requirement.
2025, 46(6): 742-754.
doi: 10.21656/1000-0887.450237
Abstract:
A tri-stable energy harvester with time-delay feedback control under narrow-band random excitation was proposed. The steady-state responses of the energy harvesting system near the main resonance were obtained with the multi-scale method. Moreover, the 1st-order and 2nd-order nontrivial steady-state moments of the system were derived with the moment method, and their accuracy was also verified through the Monte Carlo simulations. Based on the above steady-state response moments, the effects of system parameters on the performances of the energy harvester were discussed in detail. The results show that, increasing the nonlinear stiffness coefficient can enlarge the working bandwidth of the energy harvester system, while increasing the narrowband random excitation intensity can enhance the output voltage of the energy harvester. The 2nd-order steady-state moments visibly decrease with the piezoelectric coupling term, which indicates that a larger piezoelectric coupling term is beneficial to the miniaturization of energy harvesters. Furthermore, a negative control feedback gain is beneficial to realize the miniaturization design of the energy harvester and increase the power output of the system effectively. The findings provide a theoretical basis for further exploration and optimization of energy harvesting systems.
A tri-stable energy harvester with time-delay feedback control under narrow-band random excitation was proposed. The steady-state responses of the energy harvesting system near the main resonance were obtained with the multi-scale method. Moreover, the 1st-order and 2nd-order nontrivial steady-state moments of the system were derived with the moment method, and their accuracy was also verified through the Monte Carlo simulations. Based on the above steady-state response moments, the effects of system parameters on the performances of the energy harvester were discussed in detail. The results show that, increasing the nonlinear stiffness coefficient can enlarge the working bandwidth of the energy harvester system, while increasing the narrowband random excitation intensity can enhance the output voltage of the energy harvester. The 2nd-order steady-state moments visibly decrease with the piezoelectric coupling term, which indicates that a larger piezoelectric coupling term is beneficial to the miniaturization of energy harvesters. Furthermore, a negative control feedback gain is beneficial to realize the miniaturization design of the energy harvester and increase the power output of the system effectively. The findings provide a theoretical basis for further exploration and optimization of energy harvesting systems.
2025, 46(6): 755-763.
doi: 10.21656/1000-0887.450108
Abstract:
The light-driven self-sustained bending vibration phenomenon of liquid crystal elastomer (LCE) cantilever beams was investigated, and the dynamics model for light-driven vibration was established, with the semi-analytical formula obtained with the method of vibration shape superposition, and the dynamic response laws calculated by the MATLAB software programming. The results show that, the periodic self-sustained vibration responses of the LCE cantilever beam can be realized under the action of constant light, which theoretically and reasonably explains previous experimental phenomena. Furthermore, the bending vibration amplitude of the LCE beam can be controlled through adjustment of the light intensity, the damping coefficient and the thermal relaxation time, and the beam vibration frequency mainly depends on the thermal relaxation time. This work is of significance in the engineering fields of remote light-driven actuators, sensors, soft micro-robots and light energy conversion systems.
The light-driven self-sustained bending vibration phenomenon of liquid crystal elastomer (LCE) cantilever beams was investigated, and the dynamics model for light-driven vibration was established, with the semi-analytical formula obtained with the method of vibration shape superposition, and the dynamic response laws calculated by the MATLAB software programming. The results show that, the periodic self-sustained vibration responses of the LCE cantilever beam can be realized under the action of constant light, which theoretically and reasonably explains previous experimental phenomena. Furthermore, the bending vibration amplitude of the LCE beam can be controlled through adjustment of the light intensity, the damping coefficient and the thermal relaxation time, and the beam vibration frequency mainly depends on the thermal relaxation time. This work is of significance in the engineering fields of remote light-driven actuators, sensors, soft micro-robots and light energy conversion systems.
2025, 46(6): 764-780.
doi: 10.21656/1000-0887.450073
Abstract:
The non-local medium constitutive modeling method based on the spatial fractional derivative was studied, which provides a theoretical guidance for studying the mechanical properties of complex non-local materials. Firstly, the definition of the Chen-Holm fractional-order Laplace operator was extended, to obtain a new-type 0th- to 4th-order spatial fractional derivative operator. Then the constitutive relation of the non-local medium containing the new operator was established based on the strong-weak non-local continuum theory, with some new mechanical elements constructed. Through different combinations of mechanical elements, several types of non-local fractional derivative constitutive models were obtained: the Kelvin model, the Maxwell model and the Zener model. Based on the correlation between the scattered wave equations and the medium constitutive equations, the expressions and physical meanings of the model parameters were determined, and the creep and stress relaxation of some models were studied. Finally, the effectiveness of the non-local Kelvin model was verified by the case study of creep in sand-bearing soft soil.
The non-local medium constitutive modeling method based on the spatial fractional derivative was studied, which provides a theoretical guidance for studying the mechanical properties of complex non-local materials. Firstly, the definition of the Chen-Holm fractional-order Laplace operator was extended, to obtain a new-type 0th- to 4th-order spatial fractional derivative operator. Then the constitutive relation of the non-local medium containing the new operator was established based on the strong-weak non-local continuum theory, with some new mechanical elements constructed. Through different combinations of mechanical elements, several types of non-local fractional derivative constitutive models were obtained: the Kelvin model, the Maxwell model and the Zener model. Based on the correlation between the scattered wave equations and the medium constitutive equations, the expressions and physical meanings of the model parameters were determined, and the creep and stress relaxation of some models were studied. Finally, the effectiveness of the non-local Kelvin model was verified by the case study of creep in sand-bearing soft soil.
2025, 46(6): 781-790.
doi: 10.21656/1000-0887.450207
Abstract:
The transmission eigenvalue problem of exterior inverse scattering in fully coated inhomogeneous media was studied. Firstly, a nonlinear 4th-order formulation was established based on the classical process, and the existence and discreteness were proved by the Lax-Milgram theorem and the Fredholm theory. Next, by means of an equivalent mixed formulation with an auxiliary variable, the problem is transformed into a linear eigenvalue problem, and an appropriate operator was constructed by the Riesz representation theorem and the Rellich-Kondrachov compactness theorem, etc. The compactness and coerciveness of the operators were proved with the Cauchy convergence criterion, the Brezzi theory and the Poincaré inequality.
The transmission eigenvalue problem of exterior inverse scattering in fully coated inhomogeneous media was studied. Firstly, a nonlinear 4th-order formulation was established based on the classical process, and the existence and discreteness were proved by the Lax-Milgram theorem and the Fredholm theory. Next, by means of an equivalent mixed formulation with an auxiliary variable, the problem is transformed into a linear eigenvalue problem, and an appropriate operator was constructed by the Riesz representation theorem and the Rellich-Kondrachov compactness theorem, etc. The compactness and coerciveness of the operators were proved with the Cauchy convergence criterion, the Brezzi theory and the Poincaré inequality.
2025, 46(6): 791-799.
doi: 10.21656/1000-0887.450222
Abstract:
Based on the upper bound theorem of limit analysis, a solution procedure for limit analysis of structures made of rigid-perfectly plastic material was proposed with the cell-based smoothed radial point interpolation method (CS-RPIM). To impose the essential boundary conditions directly, the RPIM was utilized to construct a kinematically admissible velocity field. The plastic incompressibility conditions of plane stress and plane strain problems were treated respectively with 2 different methods. The upper bound problem was formulated mathematically through minimization of the dissipation power subject to a set of equality constraints and this minimization problem can be transformed into a standard 2nd-order cone programming one, which can be easily solved with the primal-dual interior point method. Numerical examples demonstrate that, the proposed method can provide reasonable and satisfactory upper bound limit load multipliers for rigid-perfectly plastic structures. In addition, the computational results are very insensitive to the mesh distortion.
Based on the upper bound theorem of limit analysis, a solution procedure for limit analysis of structures made of rigid-perfectly plastic material was proposed with the cell-based smoothed radial point interpolation method (CS-RPIM). To impose the essential boundary conditions directly, the RPIM was utilized to construct a kinematically admissible velocity field. The plastic incompressibility conditions of plane stress and plane strain problems were treated respectively with 2 different methods. The upper bound problem was formulated mathematically through minimization of the dissipation power subject to a set of equality constraints and this minimization problem can be transformed into a standard 2nd-order cone programming one, which can be easily solved with the primal-dual interior point method. Numerical examples demonstrate that, the proposed method can provide reasonable and satisfactory upper bound limit load multipliers for rigid-perfectly plastic structures. In addition, the computational results are very insensitive to the mesh distortion.
2025, 46(6): 800-808.
doi: 10.21656/1000-0887.450021
Abstract:
An alternating direction implicit (ADI) compact finite difference method (CFDM) was proposed for the numerical solution of the nonlinear nerve conduction equations. The method has 2nd-order accuracy in time and 4th-order accuracy in space, respectively. With the Fourier method and the discrete energy method, the proposed method was proved to be unconditionally linearly stable. In addition, 2 kinds of Richardson extrapolation methods used along with this ADI CFDM, are also developed to get time-space numerical extrapolation solutions with 4th-order or 6th-order accuracy, respectively, and improve the computational efficiency. Numerical results verify the accuracy and efficiency of the proposed method.
An alternating direction implicit (ADI) compact finite difference method (CFDM) was proposed for the numerical solution of the nonlinear nerve conduction equations. The method has 2nd-order accuracy in time and 4th-order accuracy in space, respectively. With the Fourier method and the discrete energy method, the proposed method was proved to be unconditionally linearly stable. In addition, 2 kinds of Richardson extrapolation methods used along with this ADI CFDM, are also developed to get time-space numerical extrapolation solutions with 4th-order or 6th-order accuracy, respectively, and improve the computational efficiency. Numerical results verify the accuracy and efficiency of the proposed method.
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Founded in 1980 ( monthly )
Supervisor：Chongqing Jiaotong University
Founder：CHIEN Weizang
Honorary Chief Editor：ZHONG Wanxie
Editor-in-Chief：LU Tianjian
ISSN 1000-0887
CN 50-1060/O3
