力学学报

REVIEW OF HYDRODYNAMICS AND FLOW FIELD CHARACTERISTICS OF PUMP-JET PROPULSORS

Li Han, Huang Qiaogao, Pan Guang, Dong Xinguo

A pump-jet propulsor is a multi-component integrated hydrodynamic propulsion device consisting of a guide tube, a rotating cascade (referred to as rotor) in the guide tube, and a stationary cascade (referred to as stator) in the guide tube. Pump-jet propulsor has the features of high critical sailing speed, heavy load, high propulsion efficiency, and low radiated noise. Pump-jet propulsor was first invented abroad in the middle of the last century, and mainly used for torpedo propulsion in the initial stage, and then extended to submarine propulsion. Nowadays, pump-jet propulsor is widely equipped in foreign submarines and high-speed torpedoes. There are great differences in pump-jet propulsor research and practical application at home and abroad. In recent years, pump-jet propulsor propulsion technology has become a research hotspot in the field of underwater equipment due to the technical blockade from abroad, the development needs of submarine equipment, and the extension of pump-jet propulsor application. The components of the pump-jet propulsor have complex flow interactions with each other, and the pump-jet propulsor is highly coupled with the hull. The application and popularization of pump-jet propulsors need a thorough understanding of hydrodynamic and flow field characteristics. This paper introduces the basic composition and characteristics of pump-jet propulsor and summarizes the research advance according to research interest and purpose. From the perspective of hydrodynamic characteristics, the propulsion features, prediction approaches, and hydrodynamic variation laws are summarized. From the perspective of flow field characteristics, the published investigations are categorized and summarized as tip clearance flow field, rotor-stator interference flow field, and wake flow field. This paper analyzes and summarizes the challenges in the research on hydrodynamic and flow field characteristics of pump-jet propulsor and the practical application of pump-jet propulsor. Finally, the prospect of further investigations on pump-jet propulsor is proposed.

2022, 54(4): 829-843. doi: 10.6052/0459-1879-21-529

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SPECIAL ISSUE PREFACE: RESEARCH ON KEY MECHANICAL PROBLEMS IN MARINE ENERGY DEVELOPMENT EQUIPMENT

Yan Jun

2022, 54(4): 844-845. doi: 10.6052/0459-1879-22-156

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PROSPECT AND PROGRESSION OF KEY MECHANICAL PROBLEMS IN MARINE CABLES

Yan Jun, Hu Haitao, Su Qi, Yin Yuanchao, Wu Shanghua, Lu Hailong, Lu Qingzhen

Marine energy is a key area that countries around the world are competing to develop today. Marine cable connecting various facilities of marine energy production system is one of the key equipment for energy transmission and production control and is known as the “lifeline” in marine energy development. Designing marine cables that can resist extreme marine environments, meet the requirements of bending flexibility in installation and service, and achieve structural performance with “rigid and flexible”, is the core challenge to be addressed in the field of marine energy development. This paper discusses the structural characteristics of multi-component and multi-layer spiral winding of marine cables, and comprehensively summarizes the research progress of key mechanical issues in the field of marine cable design, analysis and testing. Firstly, for the theoretical analysis method of marine cable, the general theories of tension, torsion and bending stiffness, and the research advances of the tension-torsion coupling mechanism and nonlinear bending behavior are described. Secondly, the application of numerical simulation methods in marine cable engineering is introduced, especially the research results of purpose-built simulation software for numerical analysis of marine cables. Thirdly, the multi-field coupling analysis, optimum structural design and fatigue life calculation method of marine cables are discussed. Finally, the test technology and test equipment for marine cables are introduced in detail. Through a detailed summary of research methods and hotspots of marine cables, this paper reveals the main research methods and key technical difficulties in this field, and looks forward to the main technical requirements and research directions of marine cables for future development. The above summary provides basic theory and technical reference for the high reliability engineering application of marine cables in China's offshore oil and gas energy development.

2022, 54(4): 846-861. doi: 10.6052/0459-1879-22-113

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NONLINEAR DYNAMIC RESPONSE OF A FLOATING ICE SHEET TO A MOVING LOAD

Meng Yanghan, Wang Zhan

Vibrations of a floating ice cover on top of a two-dimensional ideal fluid of arbitrary depth are studied when the effects of nonlinearity, inertia, and damping are all considered. We reduce the fully nonlinear problem to a cubic-truncation system involving variables on the free surface by expanding the relevant pseudo-differential operators and retaining nonlinear terms up to the third order. To validate the accuracy of the reduced model, we focus on the free wavepacket solitary wave solutions. In the absence of damping, the normal form analysis is performed to derive the cubic nonlinear Schrödinger equation, which predicts the existence of free wavepacket solitary waves in the primitive equations and the accuracy of the cubic-truncation model. The main advantage of the cubic-truncation approximation over the quadratic-truncation model is that the resultant NLS equation has correct coefficient of the nonlinear term, which allows a better approximation of dynamic responses of the ice cover near the phase speed minimum. Solitary waves are then numerically computed, and it is shown that the cubic-truncation approximation agrees well with the full Euler equations for bifurcation curves and wave profiles, indicating that the reduced model is more accurate than the quadratic truncation model. The nonlinear dynamic response of a floating ice sheet to a fully localized constant-moving load is investigated based on the cubic-truncation model. The time-dependent solutions are compared with the data from the field measurements, and good agreement is achieved between the numerical results and experimental records.

2022, 54(4): 862-871. doi: 10.6052/0459-1879-22-040

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NUMERICAL STUDY OF DYNAMIC CHARACTERISTICS FOR OFFSHORE WIND TURBINE UNDER COMPLEX ATMOSPHERIC INFLOW

Xu Shun, Zhao Weiwen, Wan Decheng

With the great development of wind energy technology, the blades of wind turbine have gradually developed to large-scale, which makes the real and complex atmospheric inflow have more and more significant impacts on the operating performance of wind turbines. The numerical simulation of bottom-fixed offshore wind turbine under neutral complex atmospheric inflow is performed to study the dynamic responses of wind turbine under that complex inflow. A precursor simulation method based on large eddy simulations is used to generate the complex atmospheric inflow, and the actuator line model is combined to model the wind turbine blades. The numerical results are compared with the uniform inflow condition, and the results are focusing on the analysis of aerodynamic performance and the dynamic characteristics of rotor and blade root. The numerical results show that the large-scale low-velocity airflow in the neutral and complex atmospheric inflow is responsible for the lower output of wind turbine aerodynamic power in a long period time. In addition, the high turbulence intensity characteristics of the neutral and complex atmospheric inflow lead to the significant increase of varying amplitude and standard deviation of wind turbine aerodynamic power. The standard deviation of rotor thrust increased to 53 times of the uniform inflow condition, and the maximum value, root mean square and standard deviation of yaw moment increased to 10, 4.4 and 4.3 times of uniform inflow condition, because of the disturbance of the neutral and complex atmospheric inflow. The standard deviation values of flapwise shear force and bending moment reach up to 2 and 4.6 times of uniform inflow condition, respectively, caused by the collective effects between the inhomogeneity of the velocity vertical distribution and the large-scale low-velocity plume structures near the hub height.

2022, 54(4): 872-880. doi: 10.6052/0459-1879-21-693

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RESEARCH ON DYNAMIC CHARACTERISTICS OF LARGE-SCALE MONOPILE OFFSHORE WIND TURBINE UNDER TYPHOON EVENT

Qin Mengfei, Shi Wei, Chai Wei, Fu Xing, Li Xin

Large scale wind turbine is an important direction of offshore wind technology in China. The southeast coast is a vital base for the development of offshore wind. However, the impact of typhoon events, which frequently occurs in this area, can not be neglected. The turbulent properties of typhoon are different from the normal strong wind. Meanwhile, the high wind speed during the typhoon events can lead to large typhoon waves. The aim of present work is to study the dynamic characteristics of the large scale monopile offshore wind turbine (OWT) during different typhoon stages, considering the unique wind and wave fields caused by typhoon. The DTU 10 MW monopile-type OWT were investigated using an integrated software, Simulation Workbench for Marine Application (SIMA) and the numerical model is established. The results show that pitch control can effectively reduce the wind loads on the blade during the typhoon event, and the wind loads on the turbine supported by monopile foundation mainly comes from the tower. At the different stages of the typhoon, the large-scale monopile offshore wind turbine exhibits different dynamic characteristics. The tower movement during the entire typhoon process is controlled by the first-order nature frequency which was excited by waves. The dynamic load of the structure above the tower base is dominated by inertial loads. The response energy growth rate at the first-order frequency of the tower movement is decreasing as the wind speed is increasing. And the response energy transfer to low frequency and wave frequency. The dynamic load under the base is obviously affected by wave load and wind load, shear response is controlled by wave frequency while bending moment response is controlled by first order eigen frequency and it is also greatly affected by the wave frequency and low frequency induced by wind at the mudline below tower base.

2022, 54(4): 881-891. doi: 10.6052/0459-1879-21-606

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THE NUMERICAL INVESTIGATION OF THE RESPONSE OF RISERS INDUCED BY INTERNAL SOLITARY WAVES BASED ON POTENTIAL FLOW THEORY

Hu Yingjie, Zou Li, Sun Zhe, Jin Guoqing, Ma Xinyu

Internal solitary waves are large waves that occur below the ocean surface and are widely present in all sea areas of the world. The huge wave profile undulations and energy pose a serious threat to marine structures like marine risers. Analysis of the flow field characteristics in the propagation and evolution process of internal solitary waves and the dynamic response law of the risers under the action of internal solitary waves are of great significance to the design of the marine risers. Multi-domain boundary element method is adopted to establish a numerical model to analyse and calculate the flow field of internal solitary wave based on the nonlinear potential flow theory in stratified fluids in this paper, and the flow field characteristics of internal solitary wave in real time can be obtained. The Morison equation is used to calculate the load distribution including inertia force and drag force induced by the internal solitary wave on the marine risers according to the flow field information calculated using the numerical simulations. The nonlinear potential flow calculation model of the internal solitary wave flow field is coupled with the dynamic finite element model to solve the dynamic response characteristics of the marine riser under the action of the nonlinear internal solitary wave. The influences of the internal solitary wave parameters, the top tension and the internal fluid densities on the dynamics of the riser are calculated and discussed. It is found that the displacement in flow direction of the ocean riser increases significantly as the amplitude of the internal solitary wave increases. The top tension has a significant impact on the response of the marine risers by changing the value of the geometric stiffness matrix. However, the density of the internal fluid has little effect on the displacement of the pipeline at flow direction for the weakly restrained risers.

2022, 54(4): 892-900. doi: 10.6052/0459-1879-21-677

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STUDY ON VORTEX-INDUCED VIBRATION SUPPRESSION OF MARINE RISER BASED ON ENERGY TRANSFER

Ma Yexuan, Song Zhiyou, Xu Wanhai

Vortex-induced vibration is an important factor which may cause serious fatigue damage of marine risers. The suppression of vortex-induced vibrations can ensure structural safety and prolong service life of marine risers. Most of the suppression methods of vortex-induced vibrations are based on disturbing the flow fields. In some complex environmental conditions, only disturbing the flow fields behind marine risers may have limited effect on the suppression of vortex-induced vibration. Therefore, the vortex-induced vibration suppression of marine risers was studied from the perspective of structure. Based on the theory of energy transfer, the law of energy transfer during vortex-induced vibrations of marine riser was described. The vibration energy propagates from the energy input region to the energy dissipation region in the form of traveling wave and is mainly consumed in the energy dissipation region. By locally increasing the damping in the energy dissipation region, the consumption of vibration energy in the propagation process can be increased to achieve the suppression of vortex-induced vibrations. In order to solve the vortex-induced vibration response of the marine riser, a theoretical model was established based on the wake oscillator model, and the reliability of the theoretical model was verified by the experimental results. The energy input region and energy dissipation region of the vortex-induced vibrations were determined by the energy coefficients calculated from the theoretical method. The suppression effect of the vortex-induced vibrations was studied by comparing the response of the marine riser before and after increasing the damping. If the damping in the energy input region is increased, the suppression effect of vortex-induced vibrations is not obvious. The vibration displacements in the upper and bottom locations of the marine riser significantly decrease when the energy attenuation coefficient reaches the critical value by increasing the damping in the energy dissipation region. When the energy attenuation coefficient exceeds the critical value, the suppression effect of vortex-induced vibrations is not improved by increasing damping in the energy dissipation region.

2022, 54(4): 901-911. doi: 10.6052/0459-1879-21-664

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RANDOM VIBRATION ANALYSIS OF A SEA-CROSSING BRIDGE AND POWER CABLE COMPOSITE STRUCTURE UNDER TRAFFIC LOADS

Zhang Zhenpeng, Zhao Jiankang, Li Wenjie, Zhao Peng, Huang Kaiwen

Laying power cables along the bridge is a new way of laying submarine cables across the sea. This paper focuses on the vibration of power cables laid on sea-crossing bridges induced by automobile and vehicle traffic loads. The overall combined structural analysis model of the bridge and cable is established, and the automobile and vehicle loads are simplified into random moving concentrated load sequence. The pseudo-excitation method (PEM) is developed to calculate the standard deviation and evolutionary power spectrum density of displacement and stress responses of the cable under random moving loads. The influence of automobile and vehicle speed on the standard deviation of cable dynamic response is studied. The PEM transforms the problem of random moving loads into dynamic response analysis under simple harmonic moving loads with specific frequencies, and it can calculate the standard deviation of dynamic response of the cable which is very consistent with Monte Carlo (MC) method, but the number of time-domain response analysis required is far less than that of MC method. The numerical results show that the standard deviation of displacement and stress of the cable increases with the increase of automobile and vehicle running speed. Under automobile and vehicle traffic loads, the standard deviation and power spectrum of displacement of aluminum sheath are larger than that of the cable core, which may make the fatigue failure of the cable occur in the aluminum sheath layer first. This work has a certain reference significance for the actual project of cable laying along the sea-crossing bridges.

2022, 54(4): 912-920. doi: 10.6052/0459-1879-21-626

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RESEARCH ON DYNAMIC RESPONSE ANALYSIS AND CABLE FORCE IDENTIFICATION METHOD OF SUBMERGED ANCHOR CABLES

Han Fei, Duan Zunyi

The development and utilization of marine resources and space are two major themes of human development of the ocean in the 21st century. As an important force-supporting and anchoring component of marine equipment and deep-sea structures, the damage and destruction of anchor cable will directly affect the safety and durability of the whole structure, so it is necessary to monitor and evaluate the service state of anchor cable in real time. Cable force is an important physical quantity reflecting the static and dynamic characteristics of anchor cable. It is of great significance to master the real-time change of cable force for the health monitoring and state assessment of anchor cable. The existing researches usually use modified cable force formula or intelligent optimization algorithm to identify cable force on the basis of tension string or simply supported beam model, but fail to fully consider the geometric nonlinearity caused by sag. In order to give a more explicit physical meaning and more accurate identification formula of anchor cable force in theory, aiming at the geometric nonlinearity and damping nonlinearity of underwater anchor cable, firstly, the perturbation solution of free vibration frequency and response of anchor cable is derived by using equivalent linearization technique, and the analytical expression of frequency considering sag of anchor cable is given. On this basis, the cable force identification scheme based on vibration method is given. Numerical examples show that the recognition results of this method are consistent with the real values, thus verifying the accuracy of this method. The relevant theories and conclusions can provide theoretical basis for dynamic analysis and health monitoring of such engineering structures.

2022, 54(4): 921-928. doi: 10.6052/0459-1879-21-583

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NONLINEAR STIFFNESS TOPOLOGY OPTIMIZATION FOR THE BEND STIFFENER OF FLEXIBLE RISER

Fan Zhirui, Yang Zhixun, Xu Qi, Su Qi, Niu Bin, Zhao Guozhong

The bend stiffener, as the key over-bending protection accessory, is of significant importance to improve the safety of the flexible riser used in deep water. At present, the size optimization method is mainly used in the structural design of the bend stiffener. However, compared with the topology optimization, the design freedom provided by this method is limited, and it lacks capacities in sufficiently improving the mechanical performance and finding the novel configurations of the bend stiffener. In the present study, under Dirichlet boundary conditions, a topology optimization method considering the material and geometric nonlinearity is developed to maximize the structural stiffness of the bend stiffener. The Helmholtz-PDE filter and Heaviside projection are introduced to eliminate the numerical issues caused by the checkerboard pattern and the gray element phenomenon, respectively. The symmetry operator is employed to enhance the load bearing capability under the reciprocating ocean wave load and improve the manufacturability of the bend stiffener. Making use of the adjoint method, a sensitivity analysis is performed to enable a gradient-based algorithm for solving the optimization problems. Simultaneously, a parallel computational framework based on PETSc library is also utilized to improve the efficiency of the structural analysis and optimization. In the numerical examples, with the constant material volume fraction, 2D and 3D optimizations for the bend stiffener are performed to improve the stiffness of the bend stiffener, respectively. Based on that, the load carrying capacity of the two optimization results under different load directions are compared. The numerical examples show that, compared to the 2D optimized result, the 3D optimization can significantly improve the stiffness of the bend stiffener in most loading directions. The present 3D nonlinear topology optimization method provides the new theorical model and implementation technology for the high-performance bend stiffener with the severe water environment in the deep ocean.

2022, 54(4): 929-938. doi: 10.6052/0459-1879-21-589

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STRUCTURAL DESIGN AND LOAD REDUCTION PERFORMANCE ANALYSIS OF GRADIENT DENSITY HEAD CAP OF VEHICLE

Shi Yao, Liu Zhenpeng, Pan Guang, Gao Xingfu

Aiming at the problem that the structure damage and trajectory out of control may be caused by the huge impact load when the vehicle enters the water at a high speed of more than 100 m/s, and the load reduction capacity of the existing buffer measures is limited, a gradient density buffer head cap for the vehicle entering the water at a high speed is designed in this paper to ensure that the vehicle can enter the water safely at a high speed, and the detailed design process is given. At the same time, based on the ALE (arbitrary Lagrangian-Eulerian) algorithm, a numerical calculation model of high-speed water entry of the vehicle with a buffer head cap is established, and the results of numerical calculation are in good agreement with the experimental data. Then, on this basis, the numerical research on the characteristics of high-speed water entry and load reduction of the vehicle with gradient density buffer head cap is carried out, and the influence laws of important parameters such as different layer thickness, positive and negative density gradient arrangement and interlayer density difference of the double-layer buffer on the energy absorption and load reduction effect of the buffer head cap are explored, and the large-scale model high-speed water entry impact test is carried out, The test data are filtered according to the natural frequency of the second-order bending mode in the dry modal analysis of the vehicle model. The results show that in the range studied in this paper, the layered buffer shows a stronger impact energy absorption effect than the non layered buffer, and the impact energy absorbed by the buffer increases with the increase of the number of layers; The buffer with negative density gradient is better than that with positive density gradient; The greater the density difference between layers, the greater the loss of impact energy, and the better the load reduction effect of buffer head cap.

2022, 54(4): 939-953. doi: 10.6052/0459-1879-21-620

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LARGE EDDY SIMULATION OF HYPERSONIC COMBUSTION BASED ON DYNAMIC ZONE CONCEPT

Yao Wei, Liu Hang, Zhang Zheng, Xiao Yabin, Yue Lianjie

Based on the concept of dynamic zone partition, improved delayed detached eddy simulation (IDDES) modeling of high-Ma full-scale scramjets with more than 100 million cells was conducted for the integrated internal and external flow fields. A complete dynamic zonal combustion modeling framework was established, including dynamic zone flamelet model (DZFM), zonal dynamic adaptive chemistry (Z-DAC), and zonal in situ adaptive tabulation (Z-ISAT). The fidelity of the zonal modeling framework is preliminarily verified by the 115-million-cell modeling of a benchmark hypersonic combustor named REST, which was designed to operate at Mach 12. Through the idea of local flow-chemistry decoupling within each zone, DZFM not only accurately represents the local turbulence-chemistry interaction but also effectively improves the computational efficiency of turbulent combustion in the whole field. Z-DAC and Z-ISAT can further improve the resolving efficiency of chemical reactions in each zone by dynamically reducing the chemical mechanism and tabulating the thermochemical states. Then based on 125 and 140 million cells, respectively, the characteristics of hydrogen-fueled strut and pylon hypersonic combustors were comparatively analyzed for Mach 10. Both the pylon and strut structures induce obvious boundary layer separation and fore-body recirculation zone, resulting in long pre-combustion regions in front of the injection point in both combustors. Numerical analysis based on the Borghi diagram shows that the diffusion-dominated flame mode widely exists in the current hydrogen-fueled hypersonic combustor, and the bottleneck of efficiency improvement lies in efficient mixing. The pylon combustor has higher jet penetration depth and better near-field mixing, and thus the combustion efficiency of 80% is above the criterion of achieving net thrust. The specific impulse of 1234 s in the pylon combustor is also much higher than the 437 s in the strut combustor. Z-DAC reduces the computational cost of reaction systems in nearly half of the computational domain, especially in the fuel-free regions. Compared with the traditional finite-rate PaSR model, the DZFM model achieves an acceleration ratio of up to 11.

2022, 54(4): 954-974. doi: 10.6052/0459-1879-21-363

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NUMERICAL STUDY ON THE GENERATION POSITION OF SCREECH TONE IN AXISYMMETRIC SUPERSONIC JET BASED ON MODAL DECOMPOSITION

Li Hu, Luo Yong, Han Shuaibin, Wang Yimin, Wu Conghai, Liu Xuliang

For the imperfectly expanded supersonic jet, the quasi-periodic shock-cell structures in jet core interacts with the coherent structures in shear layer to generate shock-associated noise. Screech tone is the shock-associated noise component with discrete frequency and high intensity, and it propagates primarily toward upstream direction. Its generation is driven by a nonlinear acoustic feedback loop. The exact nature of screech-generation mechanism, including source positions, has remained an open question. Accurately locating the sound source position of screech tone is a key point to quantitatively understand the screech feedback loop mechanism and to develop exact screech prediction model. In this paper, numerical simulations of underexpanded supersonic cold jet issuing from a circular sonic nozzle are carried out through solving axisymmetric compressible Navier-Stokes equations directly, using fifth order finite difference weighted essentially non-oscillatory scheme and third order total variation diminishing Runge-Kutta scheme. The fully expanded jet Mach numbers are 1.10 and 1.15. The present numerical result is compared and in good agreement with the experimental result in the literature. The axisymmetric A₁ mode and A₂ mode screech tones are captured. The time sequential pressure field and velocity field of the jet are analysed through the Fourier mode decomposition, the proper orthogonal decomposition and the dynamic mode decomposition. The spatial evolution of screech-associated coherent flow structures are studied and the sound source positions of axisymmetric A₁ mode and A₂ mode screech tones are accurately located. The results show that each screech-associated coherent flow structure has its own saturation state region, where the screech waves generate and radiate outward. It is also found that the effective source positions of axisymmetric A₁ mode and A₂ mode screech tones are the trailing edges of the fourth and the third shock-cells respectively for the jet Mach numbers considered.

2022, 54(4): 975-990. doi: 10.6052/0459-1879-21-609

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THE AERODYNAMIC PERFORMANCE OF NON-UNIFORM FLEXIBLE DRAGONFLY'S FOREWING IN FLAPPING FLIGHT

Liu Xiaochen, He Xinyi, He Guoyi, Wang Qi, Sun Shumei

In order to explore the effect of flexibility on the aerodynamic performance of dragonfly forewing when flapping forward, this paper is established the forewing model according to the actual parameters of dragonfly, and put forward two flexible distribution modes along the chordwise, which are uniform flexibility distribution and variable flexibility distribution. Firstly, the overlapping grid and bidirectional fluid structure coupling technology are used to realize the fluid structure coupling of the dragonfly forewing in the flapping process by STAR-CCM+. Secondly, then the non-uniform flexible distribution of the forewing is realized by changing the young's modulus function in the solid region of the dragonfly forewing. According to the calculated results, it can be concluded that under the condition of uniform flexible distribution, only when the young's modulus is small, the change trend of the lift coefficient and drag coefficient curves of the flexible wing lags behind the half period of the rigid wing and further added more drag to the flight. However, with the gradual increase of Young's modulus, the drag of the dragonfly forewing decreases, the thrust increases, and the momentum increment, acceleration and time average thrust coefficient given by the thrust to the dragonfly forward flight first increase and then decrease. Under the condition of reasonable non-uniform flexible distribution, the flexible wing significantly improves the peak thrust coefficient and time average thrust coefficient. When flying forward, the dragonfly forewing is given a large momentum increment and acceleration. Compared with the rigid wing and the dragonfly forewing with two flexible distribution modes, the dragonfly forewing can obtain better aerodynamic performance when the flexibility is non-uniform flexible distribution.

2022, 54(4): 991-1003. doi: 10.6052/0459-1879-21-622

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NUMERICAL STUDY ON GAS-LIQUID INTERFACE WAVES IN PARTIALLY FILLED TANKS UNDER MICROGRAVITY CONDITION

Wei Lie, Du Wangfang, Zhao Jianfu, Li Kai

The characteristics of liquid-gas interface movement, as well as the distribution and motion of the liquid and gas phases, under the interference of residual gravity or acceleration in partially filled tanks in microgravity are the key fundamental for advanced space fluid management technology. According to the general configuration and size of space propellant tanks, three scale-down models are designed based on the similarity criterion of the Bond number. The gas-liquid two-phase flow and the wave propagation along the interface caused by changes in gravity in the prototype tank and scale-down models are numerically simulated. The numerical simulations verify the flow similarity among the prototype tank and the scale-down models. It is found that on the premise of satisfying the similarity criterion of the Bond number, the systems also approximately satisfy the similarity criterion of the Weber number, or equivalently, approximately satisfy the similarity criterion of the Froude number. In addition, the results also show that there exist slight deviations among the prototype tank and the scale-down models, which may be mainly caused by the difference of viscous dissipation. Based on the similarity criterion of the Weber number, with the increase of scale, the size of tank decreases, the driving forcing by the surface tension after the change of gravity strengthens, the flow velocity increases, and thus the viscous dissipation increases at the same Weber number. The numerical results in this paper confirm the above conclusions. The relevant findings can be helpful for the design of ground simulation tests of the liquid management technology of space propellant tanks.

2022, 54(4): 1004-1011. doi: 10.6052/0459-1879-21-645

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NUMERICAL INVESTIGATION ON THE WATER-ENTRY CAVITY FEATURE AND FLOW STRUCTURE OF A SPINNING SPHERE BASED ON LARGE-EDDY SIMULATION

Yan Chenyi, Chen Ying

The water-entry process of spinning sphere has great significance to the research of the up-to-date load reduction method of water-entry based on pre-launched object. In the present work, large-eddy simulation method is used together with the homogeneous multiphase flow model and VOF algorithm of interface capturing, to simulate the water-entry free motion of a fast-spinning sphere with hydrophobic coating at low Froude number, thus to investigate the water-entry cavity evolution, the flow structure and the hydrodynamic features. The free motion of the sphere is achieved through the dynamic mesh and sliding mesh techniques. The reliability and accuracy of the numerical simulation results are validated by comparison with previously published experimental results with good agreement on the transient cavity shape and the motion of the sphere. The spinning motion induces a lift force on the sphere and the trajectory of the sphere has significant curvature along its descent. A persistent wedge of fluid is emerged across the center of the cavity due to the fluid along the surface dragged by the sphere. The velocity and spin rate were normalized with the impact velocity and spin rate to analyze the numerical results. It shows that the spin rate has significant influence on the cavity evolution and hydrodynamic characteristics. Both of those cavity shapes have asymmetrical splash curtain and collapse asymmetrically. As spin rate increases, the horizontal velocity and the maximum lift force increase, while the maximum lift force is also limited by the impact velocity. The spin rate increase also leads to a stronger wedge of fluid forming. As a result, the pinch-off pressure maximum decreases and less vortex structures are observed. And also, the spin rate increase leads to lower side pressure during the initial impact phase. However, the vertical dynamic characteristics of spheres, like vertical velocity, acceleration and immersion depth of pinch-off, are less affected by the spin rate. Moreover, the sphere spin rate is less affected by the impact spin rate increase before cavity pinch-off.

2022, 54(4): 1012-1025. doi: 10.6052/0459-1879-21-634

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CRACKING SIMULATION OF QUASI-BRITTLE MATERIALS BY COMBINING SBFEM WITH NONLOCAL MACRO-MICRO DAMAGE MODEL

Du Chengbin, Huang Wencang, Jiang Shouyan

Concrete is a typical quasi-brittle material which is widely used in civil engineering and hydraulic engineering. Under the influence of various internal and external factors, cracking is the most commonly encountered failure mode of concrete structure. It is of great importance to accurately simulate the cracking process of structures for the safety evaluation of concrete structures. A new crack initiation and propagation simulation method for quasi-brittle materials is proposed by combing scaled boundary finite element method and nonlocal macro-micro damage model. The scaling centre of the scaled boundary finite element subdomain is taken as the material point. The microscopic damage is defined in terms of the stretch rate of bonds of material points, and then the macro-scale topologic damage is evaluated as the weighted averaging of micro-scale damage over bonds in the influence domain. Through the energetic degradation function, which connects the energy-based damage and the macro-scale topologic damage, the nonlocal macro-micro damage model is inserted into the framework of scaled boundary finite element method. The quadtree mesh discrete technique is used to achieve fast and high-quality multilevel mesh by taking full advantage of the hanging nodes allowed in the scaled boundary finite element mesh. Two typical examples including a mode I and a mixed-mode cracking simulation show that the proposed method can be used to simulate crack initiation and propagation of quasi-brittle materials and capture the correct crack propagation path and load-deformation curve. Compared with other existing methods, using the nonlocal macro-micro damage model in this paper can obtain more accurate local cracking damage zone, and the results are more reasonable with higher calculation accuracy and efficiency. The numerical examples also indicate that there is no mesh sensitivity problem when the mesh size of the damage process region is less than 1/5 of the radius of the influence domain.

2022, 54(4): 1026-1039. doi: 10.6052/0459-1879-21-608

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FULL-FIELD DYNAMIC MEASUREMENT METHOD FOR FATIGUE CRACKS BASED ON DECORRELATION DIC

Cheng Bin, Li Derui

The decorrelation effect of digital image correlation (DIC) can cause DIC calculation failure, and it is always been regarded as a defect of DIC, the problem seriously hinder the promotion and application of DIC in the field of fracture mechanics. Meanwhile, structures (such as steel structures) are prone to fatigue cracking under repeated loads. Fatigue crack measurement is very important for carrying out model test research and engineering problem analysis. However, the existing methods are not suitable for full-field dynamic fatigue crack measurement with high-precision. This research proposed a novel full-field dynamic fatigue crack measurement approach and its visualization by using the principle of DIC. The approach first constructs point-cloud data structure with topological relations and calculates the crack displacement fields for the captured digital images of cracks. The zero-mean normalized cross-correlation (ZNCC) criterion is employed to eliminate the vanishing points within cracked regions, and the discrete birth and death boundaries of cracks are extracted and interpolated by a presented "three-living point" algorithm. The least square method is finally utilized to convert the discrete crack boundaries into continuous crack boundaries, and as a result the dynamic varying process of crack length and width are automatically calculated. Numerical simulation and fatigue tests are carried out to verify the accuracy of fatigue crack measurement algorithm. Results show that the digital reconstruction errors of fatigue crack boundaries are within 0.5 pixel. The calculated errors of crack length and width are respectively 0.46 pixel and 0.08 pixel. Furthermore, refined measurement for the dynamic propagation process of cracks are successfully achieved in fatigue tests of welded steel joints. This research proves that, due to the advantages in accuracy, efficiency, and cost, the presented full-field dynamic fatigue crack measurement approach and its visualization using DIC technology is highly effective, and thus is applicable to laboratory measurement and engineering field testing.

2022, 54(4): 1040-1050. doi: 10.6052/0459-1879-21-650

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EFFECT OF SURFACE PROCESSING PLASTIC LAYER ON SELF-ORGANIZED SINGLE ROTATION INITIATION OF SHEAR BANDS IN METAL CYLINDRICAL SHELL

Liu Longfei, Liu Lianhuang, Hu Li, Yang Zhicheng

In the process of high-speed collapse of metal cylindrical shell loaded by external explosion, the shear band formed by plastic shear instability has high self-organization characteristics, and even forms a single direction spiral pattern - shear bands are dominant in clockwise or counterclockwise direction. When the cylindrical shell collapses, the maximum shear stress is located on the inner surface of the cylindrical shell. The nucleation and propagation behaviors of the shear band are significantly affected by the mesoscopic state of the material on the inner surface. In this paper, AISI 1020 steel cylindrical shells with plastic layers of different thickness on the inner surface are obtained by selecting materials and controlling the cylindrical shell processing technology. The effect of surface processing plastic layer on the initiation of self-organized single rotation phenomenon of adiabatic shear band of metal cylindrical shell and its physical mechanism are studied by using thick-walled cylinder experiment. The experimental results show that the processed plastic layer on the inner surface of the metal cylindrical shell significantly changes the initial conditions of the shear band. Shear bands are nucleated and distributed in the clockwise and counterclockwise direction. The proportion of clockwise or counterclockwise shear bands in the total shear bands is dependent on the thickness and grain stretching direction of the plastic layer in samples. The results indicate that the thicker plastic layer with a single grain stretching direction is easier to form a single direction spiral structure of shear bands, either clockwise or counterclockwise. In addition, samples with a thick layer have a higher nucleation rate, a smaller spacing and a higher propagation velocity of shear bands, in comparison with those of a thin layer at the same effective strain. The results can provide a valuable reference for understanding the dominant orientation of adiabatic shear bands in the process of high-speed collapse of metal cylindrical shell.

2022, 54(4): 1051-1062. doi: 10.6052/0459-1879-21-482

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NUMERICAL SIMULATION ON RESPONSE OF SHEET METAL SUBJECTED TO LASER SHOCK WITH FINITE DIFFERENCE METHOD

Wang Yinkai, Zhang Xingquan, Zuo Lisheng, Zhang Peng, Zhang Yan, Fang Jinxiu

With the action of laser pulse, the deformation velocity of sheet metal is fast, and the propagation of stress wave induced by laser shock wave in material is complex. It is difficult to effectively measure the dynamic responses of sheet metal with traditional measuring tools during the forming process. To solve this problem, theoretical analyses and experiments are used in this paper, a two-dimensional axial symmetric numerical model of sheet metal subjected to laser shock is constructed, the Lagrangian equation of motion is established to obtain its explicit solution with finite difference method, the displacement responses and the propagation of stress wave in the forming process of sheet metal with laser shock are studied, and the effects of different technological parameters on dynamic response characteristics of sheet metal are discussed. The results show that the velocity of sheet metal increases in an oscillatory manner in the initial stage of forming process, an obvious phenomenon of bounce can be observed during the rapid tensile deformation, and the stress wave formed at the edge of laser spot propagates inwards and outwards respectively along the redial. In addition, the dynamic response characteristics of sheet metal very rely on the spatial distribution of pressure pulse and the boundary conditions have considerable effects on final forming results of sheet metal. The results of laser shock experiment are consistent well with the numerical results and the theoretical prediction value. The method and the conclusions in this paper can be utilized to provide a reference for the parameters optimization in the process of laser shock forming.

2022, 54(4): 1063-1074. doi: 10.6052/0459-1879-21-548

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DEM SIMULATION ON PLASTICITY BEHAVIOR OF SOIL-ROCK MIXTURES WITH DIFFERENT FINE CONTENTS

Wang Tao, Zhu Jungao, Liu Sihong

Soil-rock mixtures are heterogeneous materials composed of coarse rocks with high strength and fine filling soils. The plasticity behavior of soil-rock mixtures is closely dependent on fine content. When the fine content is low, the soil-rock mixture is a rock-dominated structure and the plasticity behavior of soil-rock mixture is primarily controlled by the coarse grains. While the fine content is high, the soil-rock mixture is a soil-dominated structure and the plasticity behavior of soil-rock mixture is primarily controlled by the fine grains. However, the effect of fine content on the plasticity behavior of soil-rock mixtures and its mechanism remain unclear. This manuscript investigates the instability and non-associated behavior of rock-dominated soil-rock mixtures with different fine contents based on second order theory. In addition, the mesoscopic mechanism on how fine content affects plasticity behavior of soil-rock mixtures is revealed. It is found that fine grains help to stabilize the granular assembly by limiting macroscopic plastic deformations. Macroscopic plastic deformations decrease with the increase of fine content of soil-rock mixtures compared at the same stress ratio. The fine content is found to greatly affect the flow direction of soil-rock mixtures (i.e. normal direction of plastic potential surface). With the increase of fine content, the angle between normal direction of yield surface and plastic potential surface decreases. It means that the non-associated behavior becomes less pronounced with the increase of fine content. It is also found that the bifurcation domain of soil-rock mixtures becomes narrower when fine content increases. In spite of the fact that some fine grains act as skeleton grains together with coarse grains, fine grains are found not to influence the internal mechanical state of soil-rock mixtures. As a result, fine content does not change the normal direction of yield surface. Those conclusions drawn from this manuscript is of great significance to build elasto-plastic constitutive models for rock-dominated soil-rock mixtures considering the effect of fine content.

2022, 54(4): 1075-1084. doi: 10.6052/0459-1879-21-618

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A STUDY OF DYNAMICAL MECHANISMS OF THE FAST-SLOW OSCILLATIONS OF HARMONIC GEAR SYSTEM

Han Xiujing, Huang Qixu, Ding Muchuan, Bi Qinsheng

A harmonic gear reducer is an advanced driving device, and it has been widely used because of many advantages. A harmonic gear reducer involves the coupling of different oscillation scales. This usually induces complex fast-slow oscillations, which have great impact on the proper operation of the system. In this paper, a harmonic gear system with the nonlinear factor of torsional stiffness is considered. The purpose of this paper is to study fast-slow dynamics of the system and to reveal a novel dynamical mechanism of the fast-slow oscillations. To begin with, the fast-slow dynamical model of the harmonic gear reducer with the nonlinear factor of torsional stiffness is built. Then, the transition of the system from normal oscillations to the fast-slow oscillations is obtained by varying the torsional stiffness. Subsequently, we give a brief description of the basic theory related to fast-slow systems. Based on this, dynamical characteristics of the fast subsystem are investigated by the fast-slow analysis and the generation mechanisms of fast-slow oscillations are revealed. Our results show that, when the system parameter is varied, the equilibrium curve of the fast subsystem does not lose its stability or bifurcate. However, near some point, a sharp quantitative change can be observed in the equilibrium point curve, characterized by the fact that the equilibrium point is able to undertake a fast transition between positive and negative coordinate values in a local small area of the equilibrium point curve. Based on this, we reveal a novel dynamical mechanism underlying the appearance of fast-slow oscillations, and compare the mechanism with other related dynamical mechanisms of fast-slow oscillations. Our results enrich the routes of dynamical systems to the fast-slow oscillations, and besides our study provides important reference to the research on the dynamical mechanisms and control of fast-slow oscillations in the actual systems of harmonic gear drive.

2022, 54(4): 1085-1091. doi: 10.6052/0459-1879-21-621

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SUBHARMONIC RESONANCE OF QUASI-ZERO-STIFFNESS VIBRATION ISOLATION SYSTEM WITH DRY FRICTION DAMPER

Niu Jiangchuan, Zhang Wanjie, Shen Yongjun, Wang Jun

The 1/3 subharmonic resonance of the quasi-zero-stiffness nonlinear vibration isolation system with dry friction damper is studied by using the incremental averaging method, which is subjected to external simple harmonic excitation. Firstly, the approximate analytical solution of the primary resonance of the quasi-zero-stiffness vibration isolation system with dry friction damper is obtained by using the averaging method. Then, based on the approximate analytical solution of the primary resonance of the system, the subharmonic resonance response of the system is regarded as an increment, and the approximate analytical solution of the subharmonic resonance of the quasi-zero-stiffness vibration isolation system is obtained by using the averaging method. The stability conditions of the steady-state solutions of the primary resonance and subharmonic resonance of the quasi-zero-stiffness vibration isolation system are obtained by using the Lyapunov method, and the existence condition of the 1/3 subharmonic resonance of the quasi-zero-stiffness vibration isolation system is deduced. According to the approximate analytical solution, the primary resonance and subharmonic resonance force transmissibility of the quasi-zero-stiffness vibration isolation system with dry friction damper are obtained respectively. Compared with the numerical solution, the accuracy of the approximate analytical solutions of the primary resonance and subharmonic resonance of the quasi-zero-stiffness vibration isolation system is verified. By using the approximate analytical solution of the system, the effects of quasi-zero stiffness parameters and dry friction force on the amplitude-frequency response and force transfer characteristics for the primary resonance and subharmonic resonance of the system are analyzed in detail. The results show that the subharmonic resonance of the quasi-zero-stiffness vibration isolation system in the primary resonance region can be eliminated by selecting appropriate dry friction force parameter. The addition of dry friction damper can not only improve the amplitude suppression effect of the quasi-zero-stiffness vibration isolation system in the low frequency region, but also reduce the initial vibration isolation frequency. However, it will increase the force transmissibility of the system in the vibration isolation frequency band with vibration isolation effect.

2022, 54(4): 1092-1101. doi: 10.6052/0459-1879-21-680

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DESIGN AND ENERGY CAPTURE CHARACTERISTICS OF MAGNETICALLY COUPLED BISTABLE WIDE BAND PIEZOELECTRIC ENERGY HARVESTER

Zhang Wei, Liu Shuang, Mao Jia-Jia, Lai Siu-Kai, Cao Dongxing

In order to improve the efficiency and practicality of energy harvester simultaneously, the compatibility of the vibration characteristics of the energy harvester and the environment is of utmost importance. The complex dynamic behaviors of nonlinear system lay important foundation for designing efficient energy harvesters. However, once the structures are designed and fabricated, their work frequencies are decided and invariable, and cannot be adjusted to adapt the vibration in environment. A movable hinge support and nonlinear magnetic force are introduced in this paper to design a wide band piezoelectric energy harvester with bistable states. The vibration properties of the designed energy harvester can match with the wide vibration frequencies in environment by widening its working band. In order to make sure the low frequency and wide band energy capture ability, we analyze the influences of structural length ratio, distance between magnets, load impedance, frequency and amplitude of external excitation on the linear stiffness, nonlinear stiffness and dynamic behaviors characteristics of the designed energy harvester system in detailed. Experiments are tested to validate our design and results. Firstly, the designed magnetically coupled bistable wide band piezoelectric energy harvester is simplified as a Euler-Bernoulli beam. Then, the nonlinear dynamic equations of the system are deduced by the Lagrange equation, which can be solved via harmonic balance method. The optical length ratio according to different frequency of external excitation are forecasted theoretically and validated via experimental tests. Numerical and experimental results show that the introduced nonlinear magnetic force makes the system exhibit negative stiffness, which enables the system to switch between monostable and bistable states and finally realize energy capturing in low frequency. What’s more, it can change the length ratio of the designed system by adjusting the location of the movable hinge support, which can make the system capture energy with a wide band from 0 to 16 Hz.

2022, 54(4): 1102-1112. doi: 10.6052/0459-1879-21-676

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ADJOINT SENSITIVITY METHODS FOR TRANSIENT RESPONSES OF VISCOUSLY DAMPED SYSTEMS AND THEIR CONSISTENCY ISSUES

Zhang Lei, Zhang Yan, Ding Zhe

Design sensitivity analysis (DSA) of transient response is indispensable in a time domain gradient-based optimization algorithm. DSA usually only requires the differentiation with respect to certain design variables. But for the problem of transient response sensitivities, it also contains the process of time discretization. Therefore, the order of discretization and differentiation may also affect the results of the DSA. In this paper, two new DSA methods, namely the differentiate-then-discretize adjoint variable method (AVM) and the discretize-then-differentiate AVM method, are derived based on a modified precise integration method (MPIM) to compute the transient response sensitivities for viscously damped systems. The damping force of the viscously damped systems is assumed to be proportional to the instantaneous velocity. The equations of motion of the viscously damped systems are transformed into a state-space formulation and the transient responses are calculated by the MPIM. The differentiate-then-discretize AVM method firstly differentiates the augmented function constructed by the adjoint vectors and then discretizes the function at each time point based on the MPIM. On the contrary, the discretize-then-differentiate AVM method discretizes the augmented function built by the residual equation at each separated time point first and then differentiates the discrete augmented function to obtain the transient response sensitivities. Two numerical methods are presented to show the correctness and effectiveness of the proposed method. The performances of the proposed methods are also compared them with the conventional Newmark-based method. The results show that, when calculating the sensitivities of the transient responses for viscously damped systems, the time integration method, the time step size and the order of discretization and differentiation all have influences on the consistency error. By considering the accuracy, efficiency and consistency issue, the proposed MPIM-based differentiate-then-discretize AVM is more suitable than other compared methods for applying in gradient-based time domain optimizations for viscously damped systems.

2022, 54(4): 1113-1124. doi: 10.6052/0459-1879-21-562

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STUDY ON DYNAMICS OF PLANETARY TRANSMISSION GEAR CONSIDERING WEAR AND DYNAMICS COUPLING

Ning Zhiyuan, Bai Zhengfeng, Jiang Xin, Wang Siyu

The planetary gear wear leads to the nonlinear increase of gear tooth clearance, decrease of the transmission accuracy, and increase of the tooth surface impact force, which will cause the aggravation of the vibration of the gear transmission system. Therefore, it is necessary to analyze the tooth surface wear and dynamic characteristics of planetary gears. In this paper, the nonlinear dynamic coupling calculation model of gear nonlinear wear and gear backlash is established and the gear wear characteristics of the planetary transmission is investigated. Firstly, the nonlinear dynamic model of gear meshing is established. And then, the nonlinear meshing force of gear motion is obtained. Secondly, the wear distribution law of gear tooth surface is presented by combining the nonlinear meshing force with the wear model of gear tooth surface. Further, the tooth surface is reconstructed according to the tooth clearance after wear, and the dynamics model of the gear is updated. Finally, the trend of dynamic meshing force and wear characteristics of planetary gear transmission can be obtained. The gear tooth vibration responses of the gear transmission system are presented. The numerical calculation results show that the increases of the planetary gear wear mainly affect the gear force in the alternating single-double tooth meshing. Moreover, the sun-planetary meshing tooth is more sensitive to wear, and the meshing condition of the tooth surface deteriorates greatly, which is the main reason causing the deterioration of planetary gear transmission. The presented work provides a theoretical basis for the working performance evaluation and reliability prediction of planetary gear transmission system.

2022, 54(4): 1125-1135. doi: 10.6052/0459-1879-21-554

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MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION OF PHONONIC CRYSTALS CONSIDERING MANUFACTURING CONSTRAINT

Cao Leilei, Wu Jianhua, Fan Hao, Zhang Chuanzeng, Sun Linlin

Topology optimization of phononic crystals can achieve the structures with the targeted band-gap characteristics, which provides potential applications in the vibration reduction and sound insulation. However, the topology optimization results of phononic crystals often have isolated material elements, which are rather difficult to be manufactured. In this paper, a manufacturing-constrained topology optimization model considering both the band-gap performance and the manufacturability for the multi-objective topology optimization of two-dimensional (2D) multi-phase phononic crystals is proposed. The objective functions for maximizing the band-gap width in a specified frequency range and minimizing the structural weight are established. The manufacturing constraint is additionally introduced based on the connectivity analysis of the micro-structures of the constituent materials. The optimization problem is solved by the finite element method (FEM) and the non-dominated sorting genetic algorithm II (NSGA-II). The rationality and effectiveness of the proposed model and strategy are demonstrated by representative numerical examples. The results show that the isolated material elements can be avoided effectively by introducing an additional manufacturing constraint. Moreover, the optimized results can ensure both the band-gap performance and the manufacturability requirement. Compared with the results of the single-objective optimization (SOOP), the multi-objective optimization (MOOP) shows great advantages, since it can obtain non-dominated solution sets and achieve a balance between different optimization objectives.

2022, 54(4): 1136-1144. doi: 10.6052/0459-1879-21-605

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PREDICTION MODEL OF COMPRESSIVE STRENGTH OF ULTRA LOW TEMPERATURE FROZEN SOIL BASED ON WOA-BP NEURAL NETWORK

Wang Enliang, Tian Yu, Liu Xingchao, Ren Zhifeng, Hu Shengbo, Yu Jun, Liu Chengqian, Li Yu’ang

In order to obtain the prediction model of compressive strength of ultra-low temperature frozen soil and explore the changes of physical and mechanical properties of frozen soil under ultra-low temperature, the uniaxial compressive strength test of −180 °C ~ −10 °C was carried out on the low liquid limit clay soil samples with water content of 19%, 22%, 25% and 28%, and the unfrozen water content of −80 °C ~ −10 °C soil samples was measured. Using the above data, a prediction model based on WOA-BP neural network and BP neural network was established to explore the relationship between moisture content, temperature, unfrozen water content and compressive strength of ultra-low temperature frozen soil. The prediction results show that there is a complex nonlinear relationship between moisture content, temperature, unfrozen water content and the compressive strength of ultra-low temperature frozen soil, especially in the range of −180 °C ~ −80 °C, the existing linear fitting formula can not accurately predict the compressive strength of frozen soil in this range. The overall prediction effect of the prediction model based on WOA-BP neural network is good. The average absolute error is 1.167 MPa and the average relative error is 7.62%. The average absolute error of BP neural network prediction model is 8.462 MPa and the average relative error is 47.99%. The prediction error of BP neural network prediction model based on whale optimization algorithm is significantly less than that of BP neural network prediction model and linear fitting value, and is closer to the measured value. The prediction model has high accuracy and can effectively solve the complex nonlinear relationship between the compressive strength of ultra-low temperature frozen soil and its influencing factors. It can provide a reference for the application of artificial freezing technology in stratum emergency engineering.

2022, 54(4): 1145-1153. doi: 10.6052/0459-1879-21-502

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