应用数学和力学

Abstract:
The adaptability and mobility of high-end equipment in extreme war environments guarantee national defense security and are of great strategic significance. To advance the upgrading of such equipment, a key step is to improve the lightweight level and functionality of the main load-bearing structures. The high-end equipment working under the extreme coupled multi-field environment puts forward high demands on lightweight and multifunctionality of the main load-bearing components. The separation of load-bearing structures and functional components (e.g., vibration and noise reduction, bullet and explosion resistance, impact energy absorption, heat dissipation, and wave absorption parts, etc.) in existing equipment, results in structure and weight redundancy, making it difficult to further improve the operational performances. Therefore, there is an urgent need to develop ultralight, compact, load-bearing, and multifunctional metastructures. Herein, the concept of ultralight, compact, and load-bearing metastructures was proposed for the first time and a clear definition was given. A series of design schemes for prototype metastructures were summarized in combination with practical engineering application requirements. Future development directions of metastructures are also envisioned.

A Review of Design Methods for Mechanical Metastructures

YAO Qian, YANG Zhao, WANG Xin, ZHAI Zhi, LI Zhen, GENG Xinyu, LI Bingyang, WANG Pengfei

2024, 45(8): 974-1000. doi: 10.21656/1000-0887.450106

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Abstract:
Mechanical metastructures have superior mechanical properties coming from the topology of specially designed representative elements, and have attracted wide attention due to their mathematical basis, supernormal features and broad applications. To optimize the design procedure, grasp the future trends and promote the interdisciplinary innovation, the fundamental design concepts and research advancements of mechanical metastructures were reviewed. First, the design methods for mechanical metastructures were classified based on the forward and inverse design concepts. Second, within the forward design category, the principles, applicable fields, and optimization directions of periodic superstructures, surface defect superstructures, and mathematical model-based superstructures were discussed. For the reverse design category, the progresses and existing problems in the application of optimization algorithms and learning algorithms in the field of mechanical metastructures were analyzed, with future challenges and open issues concluded.

Topology Review and Convective Heat Transfer Comparison of 3D Lattice Structures

DING Yi, WU Weitao, FENG Feng, LI Shulei, YAN Hongbin

2024, 45(8): 1001-1023. doi: 10.21656/1000-0887.450184

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Abstract:
The topologies of 3D lattice structures were reviewed and their overall heat transfer and heat dissipation performances compared, under the fixed mass flow rate, pressure drop and pumping power conditions, respectively. In total 12 lattice structures, with 6 different materials and in 2 orientations, were compared. The conjugate heat transfer in the lattice structures was solved with validated numerical models. Numerical results indicate that, the lattice topology, the lattice material and the operating conditions significantly affect the heat transfer and cooling performances. The optimal lattice differs under different comparison conditions. Under the fixed mass flow rate condition, the shifted X-lattice in orientation A and the octet lattice in orientation A exhibit the best heat transfer performance; the shifted X-lattice in orientation A also has the best cooling performance. Under the fixed pressure drop condition, the shifted X-lattices in both orientations A and B exhibit the best heat transfer performance; while the cubic lattice in orientation B and the shifted X-lattice in orientation B show the best cooling performance. Under the fixed pumping power condition, the shifted X-lattice in orientation A and the rectangular pyramid lattice in orientation B exhibit the best heat transfer performance; the shifted X-lattice in orientation B and the rectangular pyramid lattice in orientation B show the best cooling performance. The heat transfer and cooling performance database under a given lattice porosity and A characteristic length was presented as the benchmark for performance comparison of newly developed lattice structures. In addition, the database can benefit various engineering designs in selecting the appropriate lattice structures.

Study on Impact Resistance of Connection Joints for Honeycomb Sandwich Structures

ZHANG Zhiyang, ZHAO Zhenyu, REN Jianwei, GAO Huiyao

2024, 45(8): 1024-1036. doi: 10.21656/1000-0887.450131

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Abstract:
Sandwich structures are widely used in engineering fields, but their connection and assembly problems become more and more prominent, especially for combat equipment under strong dynamic loads. How to design connection joints to improve the reliability and maintainability of the structure is a hot research topic at present. Aimed at the connection and assembly problem of honeycomb sandwich protection structures in typical combat environment, a quick assembly joint locked by square tubes was designed, and the dynamic responses of the connection structure under different impulses were obtained by foam projectile impact tests. Then the finite element method was used to simulate the impact test, and the simulation results agree well with the experimental results. On this basis, the effects of geometric parameters such as wall thicknesses and connection unit widths on the peak deflections of the structure under the foam projectile impacts were further discussed with the finite element model. The results indicate that, the thinner wall thickness(t_t/t_f≤0.375) of the square tube makes the connection structure prone to collapse, leading to a significant increase in peak deflections. However, a smaller width (2a/W≤0.267) of the connection unit causes the panel tensile strength to decrease, thereby weakening the impact resistance of the connection structure. In addition, as the connection unit width increases, the peak deflection of the connection structure will first decrease and then increase. This is due to the competition mechanism between the effective cross-sectional area of the connection unit and the mechanical interlocking contact area. The proposed quick assembly connection joint can effectively resist dynamic impact loads, has good impact energy absorption abilities, and easy maintenance and replacement. It is hopeful to be applied to the connection of various types of main combat equipment protection structures, and provides reference for the impact resistance design of sandwich connection structures.

Load-Bearing and Multi-Point Ballistic Performances of Hybrid Sandwich Meta-Structures

ZHENG Bingqian, QIANG Lusheng, SONG Xiaotong, NI Changye, ZHANG Rui

2024, 45(8): 1037-1046. doi: 10.21656/1000-0887.450101

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Abstract:
Lightweight, load-bearing, and penetration-resistant integrated meta-structures have significant potential in military equipment and defense facilities, as they can effectively reduce weight and improve space utilization compared to traditional load-bearing structures and armors. Based on hybrid sandwich meta-structures, the load-deflection curves of the meta-structure and the traditional corrugated sandwich under 3-point bending loads were compared. The protective performance and energy absorption mechanism of the meta-structure under multiple ballistic impacts were experimentally studied. The research results indicate that, the hybrid sandwich meta-structure mainly experiences brittle fracture of ceramic, plastic fracture of face-sheets, and debonding of the adhesive layer under bending loads. Its load-bearing capacity is higher than those of traditional corrugated sandwiches. Furthermore, the study also reveals that the impact location and the lattice core type influence the multi-impact resistance of the meta-structure, with the honeycomb core demonstrating superior multi-impact resistance compared to the corrugated core. The corrugated sandwich lacks longitudinal constraints on the ceramic, while the honeycomb core provides stronger constraints on the ceramic, limiting the area of ceramic damage. As a result, the penetration-resistant performance remains relatively consistent as the number of impacts increases.

Investigation on Mechanical Properties and Temperature Control Efficiency of Novel Load-Bearing and Heat-Storing Metastructure Walls in Hot Summer-Cold Winter Regions

YAO Xiangyu, MA Jianbin, WANG Feiya, YANG Xiaohu

2024, 45(8): 1047-1057. doi: 10.21656/1000-0887.450172

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Abstract:
A phase change material (PCM) heat-storing wall can effectively mitigate the impact of outdoor temperature fluctuations on internal wall surface temperatures, enhance the stability of the indoor thermal environment, and reduce building energy consumption. The selection of the PCM melting point is crucial due to the differing weather conditions in the winter and the summer. To optimize the performances of heat-storing walls for both seasons in hot summer-cold winter regions, a numerical model for a novel load-bearing and heat-storing metastructure wall incorporating multi-melting point PCMs was developed. This model was used to evaluate the mechanical properties and simulate the heat transfer characteristics of the wall under air convection heat transfer conditions on representative winter and summer days. The results demonstrate that, the mechanical properties of the phase change thermal storing wall meet the engineering application requirements, and its heat transfer characteristics surpass those of ordinary walls. Specifically, the wall with a PCM melting point of 20 ℃ exhibits superior thermal performance in the winter, with a peak phase transformation rate of 0.30 ℃ and a maximum inner wall temperature fluctuation of 5.8 ℃. In the summer, the wall with a PCM melting point of 30 ℃ shows a higher phase transformation utilization rate of 0.48, while the wall with a melting point of 24 ℃ experiences the lowest temperature fluctuation. Therefore, with both the utilization ratio and the attenuation ratio considered, the optimal melting point for a phase change wall would be 24 ℃.

Acoustic Performance Rapid Prediction and Structural Optimization for Resonant Sound-Absorbing Metamaterials Based on Artificial Neural Networks

GAO Zhaorui, LI Zheng, JIANG Yongfeng, SHEN Cheng, MENG Han

2024, 45(8): 1058-1069. doi: 10.21656/1000-0887.450170

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Abstract:
A sound performance prediction method based on the artificial neural network (ANN) was proposed to meet the requirements of rapid prediction and optimization design of resonant sound-absorbing metamaterials. Firstly, a theoretical model was established for multilayer perforated resonant sound-absorbing metamaterials (MPRSMs) composed of microperforated panels and Helmholtz resonators, which was then verified through simulation and experiments; subsequently, a dataset was generated with the theoretical model, and in turn an ANN model was constructed by means of the back propagation (BP) neural network to build the mapping relationship between structural parameters and acoustic performances; afterwards, the trained ANN model was combined with the genetic algorithm to optimize the acoustic performance of the MPRSMs. The results show that, the trained ANN model can accurately predict the sound absorption performance of the MPRSMs, and the prediction efficiency improves by more than 50% compared to the theoretical model; the combination of the ANN model and the optimization algorithm can not only improve the optimization efficiency, but bring good low-frequency broadband sound absorption performance of the optimized structure. The ANN provides convenience for large-scale structural performance prediction calculations and has broad application prospects in structural design and optimization of metamaterials.

Study on Sound Insulation Characteristics of Thin Plate Acoustic Metamaterials With Flexoelectric Effects

YANG Shasha, PENG Cong, MENG Han, SHEN Cheng

2024, 45(8): 1070-1081. doi: 10.21656/1000-0887.450115

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Abstract:
When the structure size is reduced to the micro-and nano-scale, a new mechanoelectric coupling effect, the flexoelectric effect, cannot be ignored. The governing equations and boundary conditions for the sound insulation problem of thin plate acoustic metamaterial structure with the flexoelectric effects were derived by means of the variational principle. The sound insulation curves of thin plate mass blocks were predicted based on the Kirchhoff theory. The effects of flexural effects, geometric sizes and mass densities on the sound insulation performances of the structure were systematically discussed. The results show that, for the micro-and nano-scale structure sizes, the flexoelectric effect significantly increases the sound insulation valley values and peak frequencies of the sound insulation curves, so it is necessary to consider the flexoelectric effects. This work provides a theoretical basis for the research of noise control in MEMS.

Research on Mechanical Properties of Negative Stiffness Torsion Metastructures

WANG Qinze, HAN Bin, ZHENG Peiyuan, LIU Zhipeng, ZHANG Qi

2024, 45(8): 1082-1095. doi: 10.21656/1000-0887.450082

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Abstract:
The negative stiffness metastructures provide a novel design strategy for reusable protective devices with the non-damage buckling energy dissipation mechanisms. However, the weak cushioning capacity and the measly overloading protection restrict the practical applications. To enhance the energy dissipation and maximum allowable deformation, a negative stiffness torsion metastructure was developed with substructures including buckling hinged beams and inclined beams. Through introduction of compression-torsion coupling effects, the stress concentration caused by overload can be alleviated. Based on a series model for the negative stiffness torsion element, a strategy to control the mechanical properties was proposed through design of the matching relations of stiffnesses. Snap-through behaviors and hysteresis phenomena can be obtained on the non-overlapping loading and unloading curves, to greatly improve the energy dissipation capacity. The optimization of geometric parameters and stiffness relations increases the maximum equivalent compressive strain of the negative stiffness torsion metastructure by 71%. Additionally, compared to the traditional buckling beam metastructures with the same number of layers, the negative stiffness torsion metastructure can double in the energy dissipation capacity.

Electromagnetic Wave Dual-Polarized Absorption and Flexural Performance Design of Composite Laminates Based on Carbon Fibers

JI Zhengjiang, CHENG Linhao, ZHENG Xitao, YAN Leilei

2024, 45(8): 1096-1105. doi: 10.21656/1000-0887.450102

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Abstract:
To address the challenge of balancing load-bearing and electromagnetic (EM) wave absorption properties in aircraft composite skin, the outstanding mechanical and electrical characteristics of carbon fiber (CF) prepregs were utilized to construct a carbon fiber dual-polarized absorbing laminated structure (CFDALS). The bidirectional CF arrays were introduced into the glass fiber (GF) laminated structure, to endow the laminated structure with dual-polarized EM wave absorption performances. Additionally, the excellent load-bearing capacity of the CF reflector was used to enhance the mechanical properties. Simulation results indicate that, the CFDALS achieves an average absorptivity over 90% within the 8~18 GHz frequency band at incident angles of 0°~45°, and within the 5~18 GHz band at incident angles of 0°~60° for TE and TM polarized EM waves, respectively. The 3-point bending simulation results show that, the CFDALS exhibits higher specific flexural strengths and stiffnesses along 2 directions of the CF arrays while achieving dual-polarized EM wave absorption. Incorporation of bidirectionally arranged CF prepregs into GF prepregs enhances the dual-polarized EM wave absorption performance and the bidirectional flexural performance of the CFDALS simultaneously. The work provides a novel solution for the EM wave absorbing and load-bearing integrated design for aircraft composite skin applications.

Design and Analysis of High Strength and Toughness Bio-Inspired Helicoidal Composite Metastructures

WANG Xin, LI Zhen, JI Haibo, YANG Hongjun, LI Bingyang, WANG Pengfei

2024, 45(8): 1106-1116. doi: 10.21656/1000-0887.450103

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Abstract:
With the increasing frequency of human space activities, the orbital space environment is deteriorating. It is of great practical significance to enhance the strength and toughness of spacecraft structures. High strength & toughness bio-inspired helicoidal composite metastructures with mid-plane symmetry characteristics were designed and a corresponding hot-pressing preparation process was developed. The carbon fibre reinforced polymer metastructures with cross-ply, quasi-isotropic and 5°, 10° and 20° helicoidal lay-ups were characterized by quasi-static indentation performance tests, and the damage modes and the failure mechanisms were analyzed. The load-displacement curves, peak forces, failure displacements, stiffnesses and energy absorptions, were used as the mechanical property measures, with the thicknesses of the structures including 37 and 73 layers. The results show that, compared with the traditional lay-up method, the symmetric helicoidal lay-up can effectively reduce the interlayer stress and significantly improve the quasi-static indentation performances of the metastructures. Especially with a helicoidal angle of 10°, the metastructures have excellent performance enhancement in terms of peak loads and energy absorptions. The research results not only provide a theoretical support for the design and fabrication of high-performance composite metastructures in the aerospace field, but also lay a practical foundation for their practical application.