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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2024, Volume 45, Issue 3
publish date：March 01 2024
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2024, 45(3): 253-260.
doi: 10.21656/1000-0887.440339
Abstract:
Sound quality is an important measure of the sound performance of acoustic devices. However, the process of optimizing the sound quality requires a collaborative optimization of the responses at multiple frequency points, resulting in poor solvability of the optimization problem. A data-driven acoustic channel topology optimization design method was proposed to enable fast prediction of the acoustic frequency responses in the acoustic-structural system and then optimize the sound quality of acoustic devices with explicit topology optimization techniques. The non-linear relationship between structural geometry parameters, excitation frequencies and acoustic frequency responses was modelled with artificial neural networks. An artificial neural network model for acoustic frequency responses was developed by training a multilayer feedforward network with the structural geometrical parameters in the moving morphable components method and the excitation frequencies as input variables, and the acoustic pressure frequency responses as output variables. The obtained results can effectively reduce the range difference of the sound pressure level (SPL) in the target frequency band from 44.89 dB to 6.49 dB. Compared with the traditional optimization method, the solution speed is about 16.3 times as before, which shows that the current method is effective for the rapid solution of sound quality optimization problems.
Sound quality is an important measure of the sound performance of acoustic devices. However, the process of optimizing the sound quality requires a collaborative optimization of the responses at multiple frequency points, resulting in poor solvability of the optimization problem. A data-driven acoustic channel topology optimization design method was proposed to enable fast prediction of the acoustic frequency responses in the acoustic-structural system and then optimize the sound quality of acoustic devices with explicit topology optimization techniques. The non-linear relationship between structural geometry parameters, excitation frequencies and acoustic frequency responses was modelled with artificial neural networks. An artificial neural network model for acoustic frequency responses was developed by training a multilayer feedforward network with the structural geometrical parameters in the moving morphable components method and the excitation frequencies as input variables, and the acoustic pressure frequency responses as output variables. The obtained results can effectively reduce the range difference of the sound pressure level (SPL) in the target frequency band from 44.89 dB to 6.49 dB. Compared with the traditional optimization method, the solution speed is about 16.3 times as before, which shows that the current method is effective for the rapid solution of sound quality optimization problems.
2024, 45(3): 261-272.
doi: 10.21656/1000-0887.440162
Abstract:
The mussel byssal is a high-performance biological device that provides adhesion between the mussels and solid surfaces in different environments. In recent years, researchers paid increasing attention to the quantitative effects of the composition and macro/microstructure of the mussel byssal on its adhesion performance, with insights for the design of biomimetic adhesive devices. Here, the 3D printing technique was combined with the detachment test and the finite element method to systematically investigate the effects of shapes and geometric parameters on the detachment modes and adhesive properties of biomimetic mussel byssal structures. The results reveal the detachment mechanism of the mussel byssal and show that, the mussel byssal has an optimal thread direction angle resulting in optimal adhesion. The effects of the thread-plaque junction position and the plaque bottom shape on adhesion properties were explored. Furthermore, the simulated complete detachment process of the bundle-like mussel byssal array under vertical traction, and the obtained sawtooth force-displacement curve indicates that, the bundle model has a relatively stable ability to resist detachment. These findings help understand the detachment behavior of the mussel byssal in nature and provide a theoretical guidance for the optimization design of biomimetic adhesive devices.
The mussel byssal is a high-performance biological device that provides adhesion between the mussels and solid surfaces in different environments. In recent years, researchers paid increasing attention to the quantitative effects of the composition and macro/microstructure of the mussel byssal on its adhesion performance, with insights for the design of biomimetic adhesive devices. Here, the 3D printing technique was combined with the detachment test and the finite element method to systematically investigate the effects of shapes and geometric parameters on the detachment modes and adhesive properties of biomimetic mussel byssal structures. The results reveal the detachment mechanism of the mussel byssal and show that, the mussel byssal has an optimal thread direction angle resulting in optimal adhesion. The effects of the thread-plaque junction position and the plaque bottom shape on adhesion properties were explored. Furthermore, the simulated complete detachment process of the bundle-like mussel byssal array under vertical traction, and the obtained sawtooth force-displacement curve indicates that, the bundle model has a relatively stable ability to resist detachment. These findings help understand the detachment behavior of the mussel byssal in nature and provide a theoretical guidance for the optimization design of biomimetic adhesive devices.
2024, 45(3): 273-286.
doi: 10.21656/1000-0887.440146
Abstract:
The existing studies mostly take the occurrence of plastic zones or stress peak point transfer on the contact surface of anchor rock as the criterion for the limit state. However, due to different engineering geological conditions, there are significant differences in the fracture surface alignments of tunnel anchors, and the ultimate bearing capacity of the tunnel-type anchorage (TTA) cannot be accurately derived. To further explore the working process of the TTA under pull-out loading, the power exponential form was used to characterize the shape of the inverse cone damage rupture surface, based on Mindlin's stress solution and the peak shear stress control theory. The interface failure stress distribution was obtained, the equations for the bearing capacities under 2 damage forms were given. Five domestic TTA suspension bridges were taken for example and verification in both damage forms, and the effects of different parameters on the TTA load-bearing capacity were analyzed. The results show that, the main source for the bearing capacity is the cohesive force on the fracture surface, which is more than 50% of the total. The bearing capacity increases linearly with the length and the cohesion force, and grows with the inclination angle at a slowing rate. The bearing capacity would first increase and then decrease with the inclination angle under the interface failure form. These derived results are basically in agreement with those previous experimental and numerical results. The analysis of the proposed analytical displacement curves indicates that, the working process of the TTA has 3 visible stages, and the final failure mode is a combination of the interfacial failure and the inverse cone failure.
The existing studies mostly take the occurrence of plastic zones or stress peak point transfer on the contact surface of anchor rock as the criterion for the limit state. However, due to different engineering geological conditions, there are significant differences in the fracture surface alignments of tunnel anchors, and the ultimate bearing capacity of the tunnel-type anchorage (TTA) cannot be accurately derived. To further explore the working process of the TTA under pull-out loading, the power exponential form was used to characterize the shape of the inverse cone damage rupture surface, based on Mindlin's stress solution and the peak shear stress control theory. The interface failure stress distribution was obtained, the equations for the bearing capacities under 2 damage forms were given. Five domestic TTA suspension bridges were taken for example and verification in both damage forms, and the effects of different parameters on the TTA load-bearing capacity were analyzed. The results show that, the main source for the bearing capacity is the cohesive force on the fracture surface, which is more than 50% of the total. The bearing capacity increases linearly with the length and the cohesion force, and grows with the inclination angle at a slowing rate. The bearing capacity would first increase and then decrease with the inclination angle under the interface failure form. These derived results are basically in agreement with those previous experimental and numerical results. The analysis of the proposed analytical displacement curves indicates that, the working process of the TTA has 3 visible stages, and the final failure mode is a combination of the interfacial failure and the inverse cone failure.
2024, 45(3): 287-294.
doi: 10.21656/1000-0887.440295
Abstract:
High-order continuum models are needed for properly capturing the post-failure mechanical responses of soils involving shear bands. Through analysis on the evolution of shear band in granular soils based on a previously proposed micropolar hypoplastic model, a governing equation for the shear band in the critical state was obtained, which is a special nonlinear ordinary differential equation satisfied by the Cosserat angular velocity. A concise derivation of the governing equation was conducted. The properties of the governing equation, the range of the chief parameter and the approach to the solution were mainly discussed. An energy balance equation was formulated as a complementary condition for the determinant of the problem through analysis on the mechanical properties of the shear band. Then, the complete solutions, including the shear-band thickness factor, the stress distribution, the strain rate components, and the shear velocity, were obtained through numerical integration. The shear band thickness factor is particularly useful in determination of the micro-strength parameter of the constitutive model.
High-order continuum models are needed for properly capturing the post-failure mechanical responses of soils involving shear bands. Through analysis on the evolution of shear band in granular soils based on a previously proposed micropolar hypoplastic model, a governing equation for the shear band in the critical state was obtained, which is a special nonlinear ordinary differential equation satisfied by the Cosserat angular velocity. A concise derivation of the governing equation was conducted. The properties of the governing equation, the range of the chief parameter and the approach to the solution were mainly discussed. An energy balance equation was formulated as a complementary condition for the determinant of the problem through analysis on the mechanical properties of the shear band. Then, the complete solutions, including the shear-band thickness factor, the stress distribution, the strain rate components, and the shear velocity, were obtained through numerical integration. The shear band thickness factor is particularly useful in determination of the micro-strength parameter of the constitutive model.
2024, 45(3): 295-302.
doi: 10.21656/1000-0887.440289
Abstract:
According to the cohesive crack model, there is a cohesive region near the crack tip of a cracked elastomer, and the expressions of fracture parameters in the cohesive region make the core research content. Under the assumption of a cohesive zone existing at the tip of a linear crack in an elastic plate, the zone was replaced by a fictitious linear crack, and a definite nonlinear functional relationship between the fictitious crack opening displacement and the cohesion was given. An elastic plate with a mode-Ⅰ edge crack was taken as an example, and the analytical solution satisfying the fictitious crack condition was derived. On this basis, the calculating methods for energy release rate Ga of physical crack tip propagation and energy release rate Gb of cohesive crack tip propagation, were proposed. The relationships between Gb, the J integral and fracture energy GF were discussed. The results show that, critical energy release rate Gbc equals fracture energy GF, which can be used as a fracture parameter for crack instability propagation of materials with cohesive regions. The proposed method is applicable to all elastic bodies with mode-Ⅰ, Ⅱ and Ⅲ cohesive cracks.
According to the cohesive crack model, there is a cohesive region near the crack tip of a cracked elastomer, and the expressions of fracture parameters in the cohesive region make the core research content. Under the assumption of a cohesive zone existing at the tip of a linear crack in an elastic plate, the zone was replaced by a fictitious linear crack, and a definite nonlinear functional relationship between the fictitious crack opening displacement and the cohesion was given. An elastic plate with a mode-Ⅰ edge crack was taken as an example, and the analytical solution satisfying the fictitious crack condition was derived. On this basis, the calculating methods for energy release rate Ga of physical crack tip propagation and energy release rate Gb of cohesive crack tip propagation, were proposed. The relationships between Gb, the J integral and fracture energy GF were discussed. The results show that, critical energy release rate Gbc equals fracture energy GF, which can be used as a fracture parameter for crack instability propagation of materials with cohesive regions. The proposed method is applicable to all elastic bodies with mode-Ⅰ, Ⅱ and Ⅲ cohesive cracks.
2024, 45(3): 303-317.
doi: 10.21656/1000-0887.440302
Abstract:
Considering the thermal conductivity of the medium inside the crack, the plane thermoelastic problem of the 1D hexagonal quasicrystal with a central open crack in an aperiodic plane, was studied. With the Fourier integral transformation technology, the closed form solutions of thermal stresses, thermal stress intensity factors and strain energy density factors were obtained. Numerical examples were used to analyze the effects of the thermal conductivity, the external load, and the phonon field-phason field coupling coefficient on the thermal stress intensity factor and the strain energy density factor at the crack tip. The results indicate that, the heat flux density gradually increases but the thermal stress intensity factor gradually decreases with the thermal conductivity. The phonon field-phason field coupling coefficient has a significant impact on the crack propagation. When the phonon field load is relatively small or the heat flux density is relatively high, the crack is not easy to propagate. The heat flux density exhibits a concentration effect at the crack tip. The work provides a theoretical basis for the application of thermodynamic properties of quasicrystals, and the optimization of design and preparation of quasicrystal components.
Considering the thermal conductivity of the medium inside the crack, the plane thermoelastic problem of the 1D hexagonal quasicrystal with a central open crack in an aperiodic plane, was studied. With the Fourier integral transformation technology, the closed form solutions of thermal stresses, thermal stress intensity factors and strain energy density factors were obtained. Numerical examples were used to analyze the effects of the thermal conductivity, the external load, and the phonon field-phason field coupling coefficient on the thermal stress intensity factor and the strain energy density factor at the crack tip. The results indicate that, the heat flux density gradually increases but the thermal stress intensity factor gradually decreases with the thermal conductivity. The phonon field-phason field coupling coefficient has a significant impact on the crack propagation. When the phonon field load is relatively small or the heat flux density is relatively high, the crack is not easy to propagate. The heat flux density exhibits a concentration effect at the crack tip. The work provides a theoretical basis for the application of thermodynamic properties of quasicrystals, and the optimization of design and preparation of quasicrystal components.
2024, 45(3): 318-336.
doi: 10.21656/1000-0887.440294
Abstract:
Following Professor P-Y CHOU’s idea, i.e., to study numerical simulation of turbulence, it is necessary to analyse and solve the fluctuating velocity field, based on the first principles, the spatiotemporal low-dimensional optimal dynamical systems of multi-scale simulation method (LMS method) is established systematically in this work, and in its application to the numerical simulation of re-shock Richtmyer-Meshkov problem, the turbulent middle-scale flow field and an approximate solution of turbulence which is different from the DNS approximate solution of turbulence, are obtained for the first time; the numerical results show that LMS method can be used with fewer grids to obtain more accurate approximate solutions of turbulence. Several problems encountered in the research are solved first, which paved the road to construct LMS method. These problems are: based on the physical characteristics of turbulence, a new concept of large, middle and small scale decomposition of turbulence is proposed; calculation method of spatial correlation of box filtering is find; a long-standing logical error in the theory of turbulence modelling is pointed out and the concept of multi-scale turbulence models is suggested; essence and key of closure problem of turbulence are discussed and numerical method for overcoming the closure problem of turbulence is given. With the box filtering/the space grid average and in the sense of a large-scale grid, the essence of the LMS method is a new turbulence numerical simulation method that integrates the RANS, LES, DES and DNS. It is necessary to indicate that the LMS method can also serve as an auxiliary tool for turbulence model research to examine whether the turbulence model corresponding to each term in the SGS-scale/fluctuations equation is correct or not.
Following Professor P-Y CHOU’s idea, i.e., to study numerical simulation of turbulence, it is necessary to analyse and solve the fluctuating velocity field, based on the first principles, the spatiotemporal low-dimensional optimal dynamical systems of multi-scale simulation method (LMS method) is established systematically in this work, and in its application to the numerical simulation of re-shock Richtmyer-Meshkov problem, the turbulent middle-scale flow field and an approximate solution of turbulence which is different from the DNS approximate solution of turbulence, are obtained for the first time; the numerical results show that LMS method can be used with fewer grids to obtain more accurate approximate solutions of turbulence. Several problems encountered in the research are solved first, which paved the road to construct LMS method. These problems are: based on the physical characteristics of turbulence, a new concept of large, middle and small scale decomposition of turbulence is proposed; calculation method of spatial correlation of box filtering is find; a long-standing logical error in the theory of turbulence modelling is pointed out and the concept of multi-scale turbulence models is suggested; essence and key of closure problem of turbulence are discussed and numerical method for overcoming the closure problem of turbulence is given. With the box filtering/the space grid average and in the sense of a large-scale grid, the essence of the LMS method is a new turbulence numerical simulation method that integrates the RANS, LES, DES and DNS. It is necessary to indicate that the LMS method can also serve as an auxiliary tool for turbulence model research to examine whether the turbulence model corresponding to each term in the SGS-scale/fluctuations equation is correct or not.
2024, 45(3): 337-347.
doi: 10.21656/1000-0887.440183
Abstract:
To investigate the non-Newtonian dynamic behavior of water droplets hitting deicing fluid films under rainy weather conditions, the phase interface control equation was coupled with the component transport equation to construct a dynamic behavior model for multi-phase, multi-component and multi-system coupling actions of droplets hitting non-Newtonian liquid films. The non-steady-state evolution characteristics of water droplets hitting deicing fluid films were numerically studied, and the model was validated and modified based on experimental results. Furthermore, the influence mechanisms of shear-thinning characteristics of the deicing fluid and slope gradients on the impact process were further analyzed. The results indicate that, an asymmetric liquid crown will form after a droplet impacts the inclined liquid film. The viscosity disparity resulting from the non-Newtonian characteristics of the deicing liquid further contributes to the asymmetrical motion following the impact. During the formation of the liquid crown, the deicing liquid is taken away from the film, and the dilution effect of water reduces the film viscosity. Increasing the slope restricts the upstream range of water droplets, facilitating the growth of the downstream liquid crown and accelerating the deicing of the film. Consequently, the viscosity of the downstream liquid film significantly decreases.
To investigate the non-Newtonian dynamic behavior of water droplets hitting deicing fluid films under rainy weather conditions, the phase interface control equation was coupled with the component transport equation to construct a dynamic behavior model for multi-phase, multi-component and multi-system coupling actions of droplets hitting non-Newtonian liquid films. The non-steady-state evolution characteristics of water droplets hitting deicing fluid films were numerically studied, and the model was validated and modified based on experimental results. Furthermore, the influence mechanisms of shear-thinning characteristics of the deicing fluid and slope gradients on the impact process were further analyzed. The results indicate that, an asymmetric liquid crown will form after a droplet impacts the inclined liquid film. The viscosity disparity resulting from the non-Newtonian characteristics of the deicing liquid further contributes to the asymmetrical motion following the impact. During the formation of the liquid crown, the deicing liquid is taken away from the film, and the dilution effect of water reduces the film viscosity. Increasing the slope restricts the upstream range of water droplets, facilitating the growth of the downstream liquid crown and accelerating the deicing of the film. Consequently, the viscosity of the downstream liquid film significantly decreases.
2024, 45(3): 348-364.
doi: 10.21656/1000-0887.440212
Abstract:
The mesoscopic phase change lattice Boltzmann method was used to study the effect of the medium porosity on pool boiling heat transfer at the pore scale. The motion processes of bubbles were mainly considered for different porosities, and the force balance was analyzed in typical states of bubbles in porous media, to explore the mechanism of the influence of medium porosity on boiling heat transfer. The results show that, compared with the flat surface without a porous medium, porous materials can effectively reduce the wall superheat of initial nucleation, enhance the disturbance of fluid, and significantly improve the critical heat flux (CHF). In the simulation case, the CHF value grows the greatest with porosity ε=73.2%, which is about 3.6 times that of the flat plate case. In the cases of other porosity values, the presence of porous media can increase the CHF value for at least 2.3 times that of the flat plate case. The numerical simulation further demonstrates that, as the porosity gradually decreases from 97.7%, the CHF value will gradually increases, and the boiling heat transfer curve will shift to the upper left. This is because a decrease in the porosity can increase the effective heat transfer area, reduce the wall superheat of bubble nucleation, and strengthen boiling heat transfer. When the porosity decreases to ε=73.2%, the heat flux density will suddenly drop and the boiling heat transfer performance will significantly decrease with the reduction of the porosity. The analysis of force balance of the bubbles during the boiling process indicates that, for a low porosity, too small pore diameters would significantly increase the escape resistance of bubbles, reduce their rising speed, and lengthen the time of bubbles leaving the porous medium; at the same time, bubbles will gather on the surface of the heater under the combined actions of the evaporation momentum, the contact pressure, and the friction, thus deteriorating the boiling heat transfer performance.
The mesoscopic phase change lattice Boltzmann method was used to study the effect of the medium porosity on pool boiling heat transfer at the pore scale. The motion processes of bubbles were mainly considered for different porosities, and the force balance was analyzed in typical states of bubbles in porous media, to explore the mechanism of the influence of medium porosity on boiling heat transfer. The results show that, compared with the flat surface without a porous medium, porous materials can effectively reduce the wall superheat of initial nucleation, enhance the disturbance of fluid, and significantly improve the critical heat flux (CHF). In the simulation case, the CHF value grows the greatest with porosity ε=73.2%, which is about 3.6 times that of the flat plate case. In the cases of other porosity values, the presence of porous media can increase the CHF value for at least 2.3 times that of the flat plate case. The numerical simulation further demonstrates that, as the porosity gradually decreases from 97.7%, the CHF value will gradually increases, and the boiling heat transfer curve will shift to the upper left. This is because a decrease in the porosity can increase the effective heat transfer area, reduce the wall superheat of bubble nucleation, and strengthen boiling heat transfer. When the porosity decreases to ε=73.2%, the heat flux density will suddenly drop and the boiling heat transfer performance will significantly decrease with the reduction of the porosity. The analysis of force balance of the bubbles during the boiling process indicates that, for a low porosity, too small pore diameters would significantly increase the escape resistance of bubbles, reduce their rising speed, and lengthen the time of bubbles leaving the porous medium; at the same time, bubbles will gather on the surface of the heater under the combined actions of the evaporation momentum, the contact pressure, and the friction, thus deteriorating the boiling heat transfer performance.
2024, 45(3): 365-378.
doi: 10.21656/1000-0887.440271
Abstract:
To improve the braking performance and roll stability limits of liquid tank vehicles, a numerical bi-directional fluid-structure coupling model was established to study the anti-slosh effects of elastic membranes on liquid sloshing in partially filled tank vehicles. Laboratory experiments were conducted to verify the validity of the numerical model. The validated model was further used to study the effects of various configurations of elastic membranes on sloshing responses, such as liquid load transfer, sloshing forces, pitch moments, and tank wall pressures. Two different tank configurations, namely tanks without membrane and tanks with various combinations of elastic membranes, were considered in the study for comparison. The results show that, the addition of membranes can significantly limit the movement of the liquid, resulting in dramatically reduced pitch moments caused by sloshing, which will improve the braking performance and roll stability limits of the tank vehicles.
To improve the braking performance and roll stability limits of liquid tank vehicles, a numerical bi-directional fluid-structure coupling model was established to study the anti-slosh effects of elastic membranes on liquid sloshing in partially filled tank vehicles. Laboratory experiments were conducted to verify the validity of the numerical model. The validated model was further used to study the effects of various configurations of elastic membranes on sloshing responses, such as liquid load transfer, sloshing forces, pitch moments, and tank wall pressures. Two different tank configurations, namely tanks without membrane and tanks with various combinations of elastic membranes, were considered in the study for comparison. The results show that, the addition of membranes can significantly limit the movement of the liquid, resulting in dramatically reduced pitch moments caused by sloshing, which will improve the braking performance and roll stability limits of the tank vehicles.
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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
