应用数学和力学

2024 Vol. 45, No. 1

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Invited Paper
Dynamics and Control
Solid Mechanics
Fluid Mechanics

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2024, 45(1)

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Invited Paper

Separation and Reconfiguration Dynamics of Stacked Satellites

SUN Jialiang, ZHANG Xiaoliang, JIN Dongping

2024, 45(1): 1-11. doi: 10.21656/1000-0887.440222

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Abstract:
The separation and reconfiguration of stacked satellites in orbit is an effective technique for constructing large space structures. The natural coordinates formulation is used to establish the dynamic equations for stacked satellite systems, which has the advantage of facilitating the handling of fixed constraints between satellites. Suitable strategies for autonomous assembly separation and assembly are devised. A spin separation method is employed to achieve collision-free separation of satellites, while PD control and the potential function is utilized for satellite assembly. Additionally, an optimization algorithm is employed to calculate the minimum distance between satellites, enabling precise determination of the potential function's magnitude. By implementing these methods in simulations, the complete process from separation of stacked satellites to segmented assembly is realized, which confirming the effectiveness of the proposed separation and assembly strategies.

Dynamics and Control

Dynamic Response and Energy Absorption Performances of Multi-Walled Tube Reinforced Aluminum Foam Structure

ZHOU Rui, ZHANG Zhijia, ZHANG Wang, ZHANG Qiancheng, WEI Xin, SUI Yaguang, WANG Jianqiang, JIN Feng

2024, 45(1): 12-24. doi: 10.21656/1000-0887.440186

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Abstract:
In order to improve the energy absorption performance of the aluminum foam, a multi-wall tube reinforced aluminum foam was proposed. The dynamic crushing characteristics of the aluminum foam, the multi-wall tube, and the multi-wall tube reinforced aluminum foam were studied by Hopkinson pressure rod tests & finite element analysis with software ABAQUS/Explicit. The deformation mode and energy absorption of the aluminum foam was compared with those of the multi-wall tube reinforced aluminum foam, with the strain rate effect on the coupling enhancement discussed. The results show that, the finite element analysis can simulate the test results well. The strain rate effect on the aluminum foam is not obvious, while that on the multi-walled tube and the multi-wall tube reinforced aluminum foam is considerably obvious, and the energy absorption improves with higher strain rates. Under the dynamic impact condition, the peak strength of the multi-walled tube reinforced aluminum foam has obvious coupling enhancement compared with that of the multi-walled tube or the aluminum foam, and the corresponding energy absorption of the former increases by 10.34% over the sum of those of the latter ones. The study on dynamic crushing characteristics of the multi-walled tube reinforced aluminum foam provides a reference for the application of energy-absorbing load-carrying components.

A Wave Finite Element Method for Free Vibration Analysis of Lattice Core Sandwich Cylindrical Shells

HAN Shaoyan, GAO Ruxin

2024, 45(1): 25-33. doi: 10.21656/1000-0887.440130

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Abstract:
A wave finite element method was developed for the free vibration analysis of lattice core sandwich cylindrical shells. Firstly, based on the propagation law of free waves, governing equations for a core element of the lattice core sandwich cylindrical shell was established. Compared with the full-scale finite element model, degrees of freedom of the governing equations for a core element are significantly reduced. Secondly, an explicit expression for the inverse of the constrained dynamic stiffness matrix was derived based on the Neumann series, which not only improves computation efficiency but also separates the natural frequency from the governing equations, thereby transforming the natural frequency solution of the lattice core sandwich cylindrical shell into a quadratic eigenvalue problem of a core element. Finally, according to the relationship between the structural vibration mode and the free wave, the expressions of the axial and circumferential wave propagation parameters of the cylindrical shell were given, and the natural frequencies and modes of the lattice core sandwich cylindrical shell were obtained. Numerical examples of the free vibration analysis on a lattice core sandwich cylindrical shell under different boundary conditions verify the validity and efficiency of the proposed method.

Study on Impact Resistance of Shape Memory Alloy Honeycomb Structures

LI Jinkuang, WAN Wenyu, LIU Chuang

2024, 45(1): 34-44. doi: 10.21656/1000-0887.440004

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Abstract:
The shape memory alloy (SMA) can deform pseudo-plastically under external load, based on which a reusable impact energy absorption structure was designed. According to the classical SMA constitutive model, the finite element model for thin-wall structures was established, and the dynamic characteristics such as deformation modes and energy absorption of different forms of honeycomb structures under different impacting velocities, were analyzed, and the optimal energy absorption performance of the SMA structures was obtained. In addition, through comparison of the energy absorption performance of the SMA honeycomb with that of the aluminum honeycomb, the energy absorption of the SMA honeycomb with different structure configurations was different from that of the aluminum honeycomb under different-velocity impacts, with the optimal structure changes. The work provides a reference for the selection and design of the SMA honeycomb structures.

Solid Mechanics

Application Study on the DDPG Method for Designing Variable Camber Airfoils/Wings Under Buffeting Constraints

ZHOU Sili, SUN Gang, WANG Cong

2024, 45(1): 45-60. doi: 10.21656/1000-0887.440204

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Abstract:
The application of the variable camber technology has promising results in improving the lift-to-drag performance during the cruise phase, particularly under multi-lift conditions. This improvement is crucial for enhancing the economic benefits of the entire flight. A smooth and continuous flow separation function was developed to constrain the buffeting performance. An optimization model for cruise performances under multi-lift conditions of wing cross sections was constructed through combination of this function with the variable camber technology and an artificial neural network surrogate model. The deep deterministic policy gradient (DDPG) method was used to optimize this model, resulting in a cruise average lift-to-drag ratio improvement of 6.8% under buffeting constraints. This improvement surpasses the results obtained by other optimization algorithms, such as the particle swarm optimization (PSO) and the improved gray wolf optimization (GWO). The results of the generation and analysis of 2 conical swept wings with the unoptimized and optimized airfoils, show the contribution of the 2D variable camber airfoil optimization to 3D wings.

The Perturbation Neural Network Surrogate Model Method for Size-Topology Synthetical Optimization of Wing Rib Trailing Edges With Flap Tracks

XIE Chuan, XU Chao, ZHOU Danfa, YAO Weixing

2024, 45(1): 61-71. doi: 10.21656/1000-0887.440033

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Abstract:
The design of wing rib trailing edges with flap tracks requires the determination of sizes of the rib edge strips, the webs and the topological shapes of the rib webs. Therefore, a perturbation neural network surrogate model method was proposed for the size-topology synthetical optimization. The basic idea is that, based on the sensitivity of topology optimization to parameters, the perturbation is introduced in the DOE samples to capture the topological mutation points by means of the filtering measure, and reduce the numerical noise, which greatly improves the prediction accuracy of the surrogate model. With the topology optimization process viewed as a black box, the surrogate model for the size variables and topology optimized structural responses was directly built up. Finally, optimization was carried out on the surrogate model to obtain the optimal combination of structural sizes and topological shapes. A typical calculation example of wing rib trailing edge optimization demonstrates the validity and superiority of the proposed method.

Topology Optimization of Heat Transfer Structures Under Gaussian Moving Heat Source Transient Effects

ZHOU Chongwei, ZHAO Qinghai, CHEN Jianliang, SHI Gaosong

2024, 45(1): 72-84. doi: 10.21656/1000-0887.440126

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Abstract:
For the structural heat transfer problem with heat sources moving with time, the Gaussian moving heat sources were considered for transient heat transfer topology optimization design. The design objectives are to minimize the total heat dissipation of the structure over the entire time history and to minimize the maximum temperature in particular regions, with the volume fraction as the constraint. Sensitivity information for the objectives and constraints was derived with the adjoint variable method, and design variables were updated with the moving asymptote method. The effects of different Gaussian heat source paths and speeds on the topology optimization results were studied. The numerical results indicate that, the transient topology structure exhibits pronounced time-varying characteristics compared to the steady-state results. Moreover, the optimal heat dissipation configuration depends on multiple factors, including the heating time, the path and the speed of the moving heat source.

Numerical Analysis on Thermal Performances of Metal Foam Composite Phase Change Materials Under Cavity Effects

PAN Hanting, XU Duo, XU Hongtao, LUO Zhuqing

2024, 45(1): 85-96. doi: 10.21656/1000-0887.440082

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Abstract:
A randomly distributed cavity model was constructed for 3D metal foam composite phase change materials (PCMs), and the multi-relaxation time lattice Boltzmann method was used to explore the cavity effects with different volume fractions, distribution locations, and thermal conductivity ratios of metal foam to PCM at the cavity scale. The results show that, with the increase of the cavity volume fraction, the heat transfer rate and latent heat storage capacity of composite PCMs would decrease. At a Fourier number of 0.7, compared to the case without cavity, the heat storage decreases respectively by 3.2%, 9.0%, and 13.0% for a cavity volume fraction of 2.4%, 7.6%, and 11.7%, respectively. The significant hindering effect on the melting process of composite PCMs occurs in the case of cavities with a volume fraction of 3% and concentrated near the high-temperature wall. The cavities act as an adiabatic layer, extending the complete melting time of composite PCMs by 6.1%. To weaken the cavity effect, the metal foam skeleton with a thermal conductivity ratio of more than 100 can be selected to improve its leading role in heat transfer.

Fluid Mechanics

The 2-Phase Lattice Boltzmann Simulation of Flow-Following Bubble Movement Through Microchannels in Orifice Plates

DING Hongyi, WANG Zhiyun, ZHAO Jingshuai, WANG Nan, LOU Qin

2024, 45(1): 97-109. doi: 10.21656/1000-0887.440099

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Abstract:
The 2-phase flow systems with bubbles exist in various industrial processes and involve complex phase interface changes, but the bubble movement through orifice plates accompanied by liquid flow in channels has not been fully studied. The phase field lattice Boltzmann model has advantages in simulating complex interface, and is suitable for studying the movement of bubble 2-phase flow through microchannels in orifice plates, and analyzing the effects of factors such as the We number, the relative bubble size and the orifice surface wettability on the dynamic characteristics of bubbles. The numerical results show that, with the increase of the We number, the surface tension of the bubble would decrease, which makes the bubble more likely to be torn and its peak velocity decrease when it passes through the orifice structure. There are 2 critical diameter ratios in the studied parameter range, which divide the bubble movement into 3 forms through the orifice, and the critical diameter ratio decreases with the We number. In addition, with the increase of the contact angle, the adsorption capacity of gas on the surface of the orifice plate would improve, and the contact area between the bubble and the orifice plate surface would increase, which would cause the bubble mass passing through the orifice plate to decrease and the bubble speed passing through the orifice plate to increase.

Stretching Flow and Magnetic Diffusion Analysis of Maxwell Magnetic Nanofluids in Non-Uniform Magnetic Fields

WU Xueke, LIU Chunyan, BAI Yu, ZHANG Yan

2024, 45(1): 110-119. doi: 10.21656/1000-0887.440164

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Abstract:
Magnetic nanoparticles can enhance the electrical and thermal conductivity of polymers, which are widely used in fields such as machinery, biomedicine, and energy storage. When a non-uniform magnetic field is imposed externally, the induced magnetic field cannot be ignored in the case of high Reynolds numbers. To explore the effects of magnetic nanoparticles on the unsteady flow and magnetic diffusion of viscoelastic fluid over the stretching sheet within the laminar boundary layer, the time distributed-order Maxwell constitutive equation was coupled with the momentum equation to establish partial differential equations for the velocity and magnetic diffusion of a 2D incompressible Maxwell magnetic nanofluid. Numerical analysis was performed with the finite difference method, and the velocity and the induced magnetic field distribution of the fluid within the boundary layer were analyzed by control of the magnetic nanoparticle type, the volume fraction and the magnetic parameter magnitude. The results show that, the velocity and induced magnetic field of the fluid are the largest in the case of Fe₂O₃ nanoparticles added to molten polymers, besides, the velocity and magnetic boundary layer thickness is the largest. With the increase of the Maxwell nanofluid relaxation time parameter, both the velocity and the magnetic diffusion will decrease. In addition, the velocity boundary layer thickness and the magnetic boundary layer thickness of the fluid decrease with the magnetic parameter. The larger the volume fraction of Fe₃O₄ nanoparticles is, the faster the fluid flow and the smaller the induced magnetic field will be. Therefore, the study of the addition of magnetic nanoparticles to polymers in non-uniform magnetic fields gives referential data for improving material properties.

Stable Radiation Baroclinic Potential Vortices Under Basic Flow Zonal Shear

LIU Nan, SONG Jian

2024, 45(1): 120-126. doi: 10.21656/1000-0887.440168

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Abstract:
In large-scale vertical shear, a new type of stably propagating baroclinic vortex was embedded, to radiate Rossby waves without attenuation. Numerical simulations were carried out based on the 2-layer model in the beta-effect plane, by means of the variation of the dispersion relation between the zonal quadratic shear flow and the stable radiation of the baroclinic fluid. The effect of the zonal quadratic shear flow on the baroclinic potential vortex instability of steady radiation, was derived. At the same time, the Rossby waves generated by the vortices cause the propagation of the meridional vortices and other coherent heat flows. For the westward flow of the subtropical ocean, with the latitude change, the approximate solution of the trigonometric function gives the numerical solution of the relevant Bessel function. The results show that, the quadratic shear flow reduces the PV gradient in the upper layer and continues to extend the life of the vortex.