力学学报

MECHANICAL DESIGN, IMPACT ENERGY ABSORPTION AND APPLICATIONS OF AUXETIC STRUCTURES IN AUTOMOBILE LIGHTWEIGHT ENGINEERING

Wu Wenwang, Xiao Dengbao, Meng Jiaxu, Liu Kai, Niu Yinghao, Xue Rui, Zhang Peng, Ding Wenjie, Ye Xuan, Ling Xue, Bi Ying, Xia Yong

Lightweight and multi-function structures with negative Poisson's ratio have excellent auxetic mechanical properties, and have been demonstrated promising industrial application potentials as energy absorption structures and multifunctional devices in automobile industry due to their enhanced indentation resistance, shear modulus, fracture toughness, impact energy absorption, shock absorption, noise reduction performances and so on. This paper mainly summarizes the mechanical properties of structures with negative Poisson's ratio effect, and their typical structural design and applications in automotive engineering. The contents could be classified into six parts: (1) The concepts and mechanical characteristics of different materials and structures with negative Poisson's ratio are introduced firstly, and the rapid developments in recent decades are also discussed; (2) main design method of materials and structures with negative Poisson's ratio are performed, corresponding manufacturing technologies of foams with negative Poisson's ratio effect are summarized, the design developments of composite materials with negative Poisson's ratio and the frontier artificial intelligence design method for advanced structure with negative Poisson's ratio are also presented; (3) mechanical designs of typical cellular structures with negative Poisson's ratio are introduced in detail including: chiral structure, rigid node rotation structure, double-arrow structure with negative Poisson's ratio, re-entrant honeycomb structure, structure with tensile-torsion effects and so on; (4) many experimental, theoretical and finite element simulation results about the energy absorption characteristics of materials and structures with negative Poisson's ratio are presented; (5) typical industrial applications of advanced materials and structures negative Poisson's ratio as high performance energy application structures in the field of lightweight vehicle design are demonstrated, mainly including: automobile energy absorption box, B-pillar, engine hoods, seat belts, suspension structures, and non-pneumatic tires and so on; (6) industrial application prospects of advanced materials and structures with negative Poisson's ratio (NPR) in automotive engineering, and the technical challenges and promising industrial application potentials are also pointed out.

2021, 53(3): 611-638. doi: 10.6052/0459-1879-20-333

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Ji Shunying

2021, 53(3): 639-640. doi: 10.6052/0459-1879-21-096

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REVIEW ON THE INTERACTION BETWEEN SEA ICE AND WAVES/CURRENTS

Ni Baoyu, Zeng Lingdong, Xiong Hang, Wu Qiyuan

With global warming and the increasing frequency of Arctic activities, the interaction between sea ice and waves/currents has become an attractive research issue at home and abroad. The existence of sea ice changes the propagation characteristics and dispersion relationships of waves, and also changes the boundary conditions of ocean currents, inducing vortex shedding at the lower surface of the sea ice. The sea ices generate and extinct, fracture, overlap and accumulate under the effects of waves and currents. There are several difficulties in studying the interaction between sea ice and waves/currents. The first is the construction of sea ice model appropriately, which needs to consider the differences of the types and properties of sea ice in different cold regions. The distributions of sea ice also should be taken into account in the sea ice model. The second is the coupling problem between sea ice and water. The boundary of sea ice affects the exchange of momentum and energy between sea ice and water. The boundary conditions of sea ice should be dealt with appropriately in terms of ice sheet and ice floes. There are many fracture modes of sea ice, but the sea ice may have complex fracture modes with coexistence of many different fracture modes under the action of sea ice and water coupling. The third is the construction of wave-current joint field. At present, there is no efficient method to construct the wave-current joint field, which leads to lack of relevant research on interaction for sea ice and wave-current joint field to understand the physic problem. Therefore, this paper reviews and discusses the research status and technical difficulties of interactions between sea ice and wave, current and wave-current fields. The problems that can be further studied in the future are predicted and the preliminary ideas are put forward for reference.

2021, 53(3): 641-654. doi: 10.6052/0459-1879-20-394

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PROGRESS AND TREND IN THE STUDY OF RIVER ICE HYDRAULICS

Guo Xinlei, Wang Tao, Fu Hui, Pan Jiajia, Lu Jinzhi, Guo Yongxin, Li Jiazhen

This study reviews the latest research progress on the basic theory of river ice hydraulics, river ice modeling and ice flooding forecasting, key ice parameters recording equipment and technology in China and other countries. The river ice hydraulics is constructed of water heat budget analysis, ice runs interactions and transport, anchor ice and border ice formation and release, ice jamming in freezing period, ice dam in breakup period, and ice jamming before infrastructure, the flow-ice-sediment coupled mechanics. Through detailed analysis on recent research progresses and existing questions of ice hydraulics and engineering applications, this study proposes several promising research topics in the future. It is still challenging in understanding the ice dynamics in terms of the anchor ice growth and release, ice stoppage and initial ice cover formation driven by thermal-dynamic-geometrical properties, flow structures under ice-covered compound channels, and flow-ice-sediment coupling mechanics in riverbank retreats. In terms of ice information forecast under changeable situations, it is helpful to focus on influence of long-term climate change and short-term extreme events on northern river ice flooding. The development of hydrology and hydraulics coupled forecasting model is promising in combining different spatial and temporal scales for supporting ice flooding prevention. For ice flooding monitoring system and disaster prevention equipment, it is suggested to record seepage flow in ice jam, internal ice resistance and friction, physical structure evolution in ice jam to collect field observation database. In terms of glacial lake outburst floods, laboratory experiments are needed in exploring opening mechanics under freezing environment and promoting interdisciplinary research, especially in processes of outburst flow erosion, moraine soil undercut and side slope collapses.

2021, 53(3): 655-671. doi: 10.6052/0459-1879-20-407

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ADVANCES IN RESEARCH WORK REGARDING IMPACTS OF BRIDGE PIERS ON ICE ACCUMULATION AND LOCAL SCOUR PROCESSES

Wang Jun, Hou Zhixing, Sui Jueyi, Cheng Tiejie

River ice is an important factor affecting alluvial channels in winter. The appearance of bridge piers in channel changes the flow condition, and therefore affects the accumulation or ice jam process around bridge pier. On the other side, under ice-covered conditions, due to the extra boundary imposed by ice cover, the location of the maximum flow velocity is closer to the riverbed. Consequently, the riverbed scour around bridge pier under ice cover should be greater than in the absence of ice cover. By means of mechanical analysis of the stability of ice jams around bridge piers, a formula has been proposed to assess the stability of ice jams under the influence of bridge piers. The calculated results using the proposed formula were in good agreement with those measured in laboratory. Experiments have been conducted to study the impacts of bridge piers on the initiation of an ice cover. A formula for determining the critical concentration of ice floes on water surface for initiating an ice cover around bridge piers was developed. The proposed equation has been validated by data collected in laboratory and natural rivers. The relevant research works with respect to the local scour process around bridge piers/bridge abutments under both open flow and ice-covered (ice-jammed) flow conditions have been carried out in laboratory. Considering different bed material, pier size and ice-cover roughness, empirical formulas have been developed to calculate the maximum scour depth in the vicinity of bridge piers under ice-covered condition. Laboratory experiments have been conducted to study the local scour process around bridge piers under the ice-jammed flow condition. Results show that, under an ice-jammed flow condition, the local scour depth around bridge piers is much more than that under a sheet-ice-covered flow condition. Also, the bed deformation interacts with ice accumulation; namely, the thicker the ice jam, the more the scour depth, and vice versa. Under an ice-jammed condition, both the maximum depth and length of scour holes around a bridge pier increase with the flow velocity. Also, the height of a deposition dune downstream of a scour hole is affected by flow velocity This paper also summarizes further research work that needs to be carried out in the future.

2021, 53(3): 672-681. doi: 10.6052/0459-1879-20-392

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ANALYSIS OF ICE-INDUCTED STRUCTURE VIBRATION OF OFFSHORE WIND TURBINES BASED ON DEM-FEM COUPLED METHOD

Yang Dongbao, Gao Junsong, Liu Jianping, Song Chu, Ji Shunying

The ice load is one of the most important factors that cannot be ignored for offshore wind turbines (OWTs) in cold regions. The ice-induced vibrations (IIVs) can bring serious fatigue and damage to the OWTs structure. In this paper, a coupling method of the discrete element method (DEM) and the finite element method (FEM) is adopted to establish the IIVs model of monopile-type OWTs. The breakage and failure process of level ice are simulated with the spherical DEM with bonding-breaking effect, and the finite element model of monopile-type OWTs is constructed by the beam element and triangular plate shell element. The DEM-FEM coupled method is adopted to simulate the interaction progress between monopile-type OWTs and level ice under different ice velocity and ice thickness conditions. The accuracy of ice load calculated by the DEM-FEM coupled method is verified by comparing with the empirical formula of IEC (International Electrotechnical Commission) and ISO (the International Organization for Standardization). By comparing the displacements and the acceleration of the top of the wind turbine tower and the top of the foundation, the dynamic response characteristic of the OWTs is qualitatively analyzed. The reason for the difference of dynamic characteristics in different parts of OWTs is structural model characteristic of OWTs：the lower part is a large stiffness pile foundation and the upper part is a high flexibility tower, which makes its dynamic characteristic show the characteristics of the main and subordinate structure. The characteristics of “Main-Subordinate structure” make the tower (subordinate) and pile foundation (main) show different response behaviors under complex ice load, and the vibration period and acceleration power spectrum density (PSD) of different parts of OWTs are different. This study can provide a useful reference for the OWTs anti-ice design and the fatigue analysis of OWTs in cold regions.

2021, 53(3): 682-692. doi: 10.6052/0459-1879-20-386

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STUDY ON FREQUENCY LOCK-IN RESONANCE IN ICE-INDUCED VIBRATION

Huang Guojun

Frequency lock-in resonance in ice-induced vibration (IIV) threatens severely the safety of the structures and worsens the working environment for operators. Its underlying mechanism is unclear yet. This paper presents a theoretical study on the mechanism of the frequency lock-in resonance for compliant structures. The study is based on an intermittent ice-crushing type of IIV model developed previously by the author and co-worker (Huang and Liu, 2009). The frequency lock-in resonance is predicted over an ice velocity span. Then the parametric analysis is performed on IIV and frequency lock-in resonance for some influential factors, including structural damping and stiffness, ice stiffness, ice-crushing zone length, ductile-brittle transitional ice-velocity and randomness in the ice-crushing strength and ice-crushing zone length. From these theoretical studies, the mechanism of the frequency lock-in resonance is investigated. It is shown that although both the predominant ice and structural response frequencies are locked to the structural natural frequency when frequency lock-in resonance takes place, the time history profiles of ice force and structural response and their frequency spectra are different corresponding to the different ice velocity. Not only the conventional mono-frequency resonance with the uniform amplitude but also the multi-frequency beat resonance with the periodically changing amplitudes are predicated. For the frequency lock-in resonance, structural and ice properties affect the length and location of the ice velocity span as well as the response amplitude, and the randomness and strain rate effect in ice-crushing are the two competing factors. It is unveiled that the strain rate effect of the ice-crushing strength is responsible for the frequency lock-in resonance, by frequency modulation and by promoting the uneven kinetic energy transfer between ice and structures, a positive feedback mechanism. The present novel mechanism is a coupled vibration that is essentially different from the conventional one, i.e., the negative damping in self vibration predicted from the continuous ice-crushing type of IIV models. The present result is instructive to the further systematic experimental study on the frequency loc-in resonance and to devising some effective techniques for the mitigation of intensive IIV.

2021, 53(3): 693-702. doi: 10.6052/0459-1879-21-087

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CLASSIFICATION MODEL OF ICE TRANSPORT AND ACCUMULATION IN FRONT OF CHANNEL FLAT SLUICE BASED ON PCA-SVM

Liang Naisheng, Tuo Youcai, Deng Yun, Jia Yunxiao

Floating ice is easy to formed an ice jam in front of flat sluice of channel water delivery during the ice-affected seasons, which will affect the efficiency and safe operation of the channel in severe cases. Here, an experimental for free outflow of flat sluice in the open channel were studied based on indoor physical model test. In order to judge the condition of ice float in front of gates of the water conveyance channel. A discriminant model of ice accumulation and entrainment in front of gate based on Principal Components Analysis-Support Vector Machine(PCA-SVM) algorithm is proposed. The correlation analysis method is used to determine the information correlation between input features, and then the PCA method is used to reduce the dimension of the feature vectors. The aim is to improve the computational performance of the model. The first principal component with a contribution rate of 86% and the second principal component with a contribution rate of 7% were extracted as input features. The optimal parameters of Polynomial kernel function (POL), Gaussian Radial basis kernel function (RBF) and Sigmoid kernel function (SIG) were determined by grid search method. The optimal kernel function was determined as RBF by confusion matrix, and the optimal kernel function parameters C were 137 and $\gamma $ were 0.37. The PCA-SVM model was used for supervised learning of the experimental data. It is found that the $Fr_{1}$ and $Fr_{2}$ are the main influencing factors of ice entrainment or jam in front of gates, and the $H/e$ and $H_{1}/H$ are the secondary influencing factors. Furthermore, the established model was applied to the identify the floating ice state in front of the inverted siphon. The aim is to verify the classification performance of the developed model. The results are of the great value for the dispatching management and safe operation of water delivery channels during ice period.

2021, 53(3): 703-713. doi: 10.6052/0459-1879-20-391

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EXPERIMENTAL STUDY OF THE ICE BREAKING RESISTANCE ON AN AIR CUSHION PLATFORM

Huang Yan, Sun Ce, Tian Yufeng

The ice breaking processes of an air cushion platform were investigated and the corresponding resistances were also measured through model tests performed in ice tank. An actual ice-breaking air cushion platform that is in-service was modelled during the tests, and a reasonable similarity law was established. By obeying the similarity law, each part of the actual platform was simulated, including the structural frame, air ducting, air cell and the cushion system and thus, structural shape and cushion mechanism of model platform was kept in similar with the prototype platform. During the tests, the model platform was towed by the main carriage passing through the model ice sheet with different hover-heights and navigation speeds. The ice breaking process was investigated under each test condition. By analyzing on the test phenomena and measured results, the ice breaking process was deeply discussed and, the ice breaking mechanism was revealed for the air cushion platform. It could be found that the non-full-cushioning condition is more beneficial to the ice breaking operations for the model platform through model tests. The key ice breaking mechanism of an air cushion platform was that a stable air space is formed under the ice sheet. Thereby the ice sheet was pressed down by the model platform and risen upward by the air space, and then the bending failure of the ice sheet occurred. The ice breaking wind pressure of an air cushion platform varying with the structural attitudes was tested during the model tests. Afterwards, the ice breaking wind pressure was analyzed in time and frequency domain respectively, and the regularities of ice breaking wind pressure varying with the navigation speed were discussed. The regularities of ice breaking resistance varying with the hover-height and navigation speed were finally established as the necessary basic data for guiding the structural design and operating control of such type of platform in practice.

2021, 53(3): 714-727. doi: 10.6052/0459-1879-20-418

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MECHANISM AND SIMPLE ANALYSIS METHOD OF ICE INDUCED FREQUENCY LOCK-IN VIBRATION OF OFFSHORE STRUCTURES

Qu Yan, Huang Ziwei, Zou Ke, Yin Haoyang, Zhang Dayong

Ice induced frequency lock-in vibration of offshore structures has been recognized as a serious load condition in ice regions. The traditional mechanism cannot fully explain all the physical phenomena in the frequency lock-in vibration, nor can a reasonable analysis method be obtained. Based on the analysis of full scale measurement data, this paper proposes a new mechanism of frequency lock-in vibration caused by the coupling of sea ice ductile damage-collapse failure and structural vibration. It is believed that the ductile damage-collapse failure of sea ice occurs during the frequency lock-in vibration of vertical structures, which is coupled with the phase of structural motion, resulting in frequency lock-in vibration. Saw-teeth-shape ice load is caused by the action between sea ice and the structure. The action process can be divided into loading and unloading stages, the loading stage takes about 3 times the time of the unloading stage. In the loading stage, the structure moves against ice from equilibrium position to its maximum negative amplitude and then moves back together with ice at the same direction to its maximum positive amplitude. Cracks are formed in the contact part of the sea ice and the structure, but not collapse. The sea ice undergoes ductile damage at this stage. In the unloading stage, the structure moves in the opposite direction to the sea ice, swinging back from the maximum amplitude to its equilibrium position. The sudden increase of strain rate leads to the accelerated propagation and instable fracture of cracks. The sea ice with ductile damage collapses at this stage. Based on the new mechanism explanation, this paper presents a simple analysis method of ice induced frequency lock-in vibration of offshore structures. It is considered that the sea ice break length is the key parameter of frequency lock-in vibration. In the ideal situation, the sea ice break length is about 2.2 times of the vibration amplitude at the waterline of the structure. When the ice velocity is close to the ratio of sea ice break length to the natural vibration period of the structure, frequency lock-in vibration will occur. This method has guiding significance for evaluating the occurrence probability of frequency lock-in vibration and fatigue damage of offshore structures.

2021, 53(3): 728-739. doi: 10.6052/0459-1879-20-382

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PRELIMINARY INVESTIGATION ON UNSTRUCTURED MESH GENERATION TECHNIQUE BASED ON ADVANCING FRONT METHOD AND MACHINE LEARNING METHODS

Wang Nianhua, Lu Peng, Chang Xinghua, Zhang Laiping

Mesh generation and adaptation are bottleneck problems restricting future development of computational fluid dynamics (CFD). Automatic and intelligent mesh generation is still worth continuous investigation. With the rapid progress in high-performance computing power and big data technology, artificial intelligence, represented by machine learning, has been successfully applied to multiple fields including fluid dynamics, which has revolutionarily boosted the development of these fields. This paper reviews briefly the application of machine learning in the unstructured mesh generation in CFD and analyzes the key issues in the mesh generation based on machine learning. Meanwhile, the sample data format is designed and the automatic extraction of unstructured mesh sample data sets is realized. By integrating the advancing front (AFT) method with the artificial neural network, a novel two-dimensional triangular grid generation method is developed based on machine learning. Finally, several isotropic unstructured grids and hybrid grids (2D cylinder, 2D NACA0012 airfoil, and 30p30n three-element airfoil) are generated and mesh quality and elapsed time are counted, it indicates that mesh quality is generally equivalent to commercial software and the efficiency is 30% higher than the traditional AFT method.

2021, 53(3): 740-751. doi: 10.6052/0459-1879-20-402

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BASE FLOW STABILITY OF RETURN CAPSULE DURING REENTRY PROCESS WITH HIGH REYNOLDS NUMBER

Zhu Dehua, Shen Qing, Yang Wubing

There are some problems of return capsule during reentry process, such as high heat flux of shoulder, prediction of base drag and unsteady vibration. Solve these problems, the key is accurate identification of separation and transition physical phenomenon. In this paper, separation and transition phenomenon of return capsule during reentry process under high Reynolds number condition are investigated by means of large eddy simulation (LES), base flow patterns and stability characteristics of return capsule are obtained. Physical mechanisms of base flow instability are analyzed from the aspects of shoulder shear instability, base flow structure instability and wake region instability. The results show that base flow stability of return capsule all includes shoulder shear instability mode and base flow structure instability mode, there is interaction between the two instability modes, there is are oscillation characteristics of Karman vortex street in the far wake turbulent region. These understandings support mechanism of the effect of external disturbances on the base region and stability control of return capsule in the theory.

2021, 53(3): 752-760. doi: 10.6052/0459-1879-20-318

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EXPERIMENTAL INVESTIGATION ON THE EVOLUTION MECHANISM OF UNIFORM MOMENTUM ZONES IN TURBULENT BOUNDARY LAYER

Wang Chaowei, Wang Kangjun, Li Biaohui, Jiang Nan

Uniform momentum zone is one type of local regions where the instantaneous momentum of fluid approaches, and its generation and distribution are closely related to the coherent structure. The study of uniform momentum zone contributes to further understanding of the coherent structure in turbulent boundary layers, but there is still a lack of experimental support and mechanism analysis for the evolution process of uniform momentum zone. The moving TRPIV system was designed and used to measure the velocity fields of the turbulent boundary layer on a smooth surface as it moved downstream. The data is denoised by filtering, and the fluctuating velocity signal is obtained by combining the interpolation results of the direct numerical simulation data. After the influence of non-turbulence removed by an improved method,this thesis detects the uniform momentum zone in turbulent boundary layer, and obtain the time series of its quantity. In combination with the change of the streamwise velocity probability density distribution, the stepwise variation in the number of uniform momentum regions from one steady state to another over large time scales is obtained. The fluctuating velocity of different scales was decomposed, and the conditional average of large-scale and small-scale fluctuation signals were carried out. The results show that the large-scale fluctuations play a major role in the quantity change of the uniform momentum zone, the action mode is that the probability density function distribution of streamwise velocity is changed by different burst events of fluid in different velocities. By analyzing the changes of different fluctuation regions in the streamwise large-scale fluctuation space, it is found that a uniform momentum zone often contains multiple large-scale fluctuation regions. The expansion, contraction, splitting and merging of different large-scale fluctuation regions affect the concentration degree of streamwise velocity, leading to significant changes of the number of uniform momentum zones.

2021, 53(3): 761-772. doi: 10.6052/0459-1879-20-223

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A FINITE VOLUME METHOD WITH WALSH BASIS FUNCTIONS TO CAPTURE DISCONTINUITY INSIDE GRID

Ren Jiong, Wang Gang

The traditional finite volume or finite element method assumes that the flow variables are continuous in the control volume, and the position of discontinuity is restricted to the interface of the control volume, therefore it is impossible to capture discontinuity inside a control volume. In this paper, the hypothesis that the flow variables are continuous in the control volume is abandoned. The Walsh basis functions constituted by square waves are applied to represent the conservative variables in a control volume with discontinuous forms rather than the traditional continuous forms. According to the positions of discontinuities contained in the Walsh approximation forms of conservative variables which are introduced by the Walsh functions, the control volume can be divided into series of virtual sub-cells. Integrating and solving the conservative equations represented by Walsh basis function coefficients on each sub-cell, the discontinuity can be captured inside a control volume. This solving method is named as “Finite volume method with Walsh basis functions”. Compared with the traditional finite volume method, this method can reduce the numerical errors by a certain proportion and improve the resolution of capturing discontinuities. While for sub-cell scale, this method has only first-order calculation accuracy. In order to further improve the resolution of the smooth solutions, the linear / nonlinear approximations can be reconstructed by using the sub-cell average values of conservative variables in each control volume to realize second order / higher order calculation accuracy. Finally, in numerical tests, the finite volume method based on Walsh basis functions is used to solve several typical unsteady problems of inviscid Burgers equation and Euler equations with respect to one-dimensional and two-dimensional cases. By comparing the obtained numerical results of the new method and the traditional finite volume method, the accuracy, efficiency, robustness and the ability of capturing discontinuity of the proposed method are verified.

2021, 53(3): 773-788. doi: 10.6052/0459-1879-20-253

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TUNABLE CONTROL AND FUNCTIONAL SWITCH OF TRANSMITTED ACOUSTIC WAVES BY AN ARCH-SHAPED METASURFACE

Chen Ali, Wang Xinmeng, Wang Yuesheng

A tunable transmitted three-tunnel helix unit cell is designed based on the working principle of the “screw-nut”. The length of the acoustic tunnel is changed by the screw-in depth of the screw, and then the phase of the transmitted waves can be tuned accordingly. The variations of the phase shift and transmittance of the unit cell with the screw-in depth and frequency are calculated by the finite element method. The generalized Snell's law of an flat surface is extended to an arc-shaped surface in this paper. The arch-shaped and toroidal metasurfaces are designed to regulate the wavefront of the transmitted acoustic wave. According to the presupposed acoustic function and the working frequency, the phase gradient of the metasurface and the screw-in depth of every unit can be determined by the generalized Snell's law of the arc-shaped surface and the variation of the phase shift of the unit cell with the screw-in depth. And the screw-in depth will be modified according to the variation of the transmittance of the unit cell in order to obtain the high transmission. The functional switch between the directional refraction, beam splitting and beam focusing for the arch-shaped metasurface is realized in a broadband frequency region. And the functional switch between the three-way splitting of wave beam, spiral wave generation and virtual movement of the source position is also realized for the toroidal metasurface. The full-field numerical simulations are performed by using the finite element method. And the experimental measurements are also carried out for both arch-shaped and toroidal metasurfaces. The experimental results have a good agreement with the numerical ones, which shows that the metasurfaces we designed are effective for the wavefront modulation of the transmitted acoustic waves. The study in this paper is relevant to the development of tunable irregular non-planar conformal acoustic devices.

2021, 53(3): 789-801. doi: 10.6052/0459-1879-20-456

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PHASE FIELD SIMULATION ON THE SUPER-ELASTICITY AND SHAPE MEMORY EFFECT OF GRADIENT NANOCRYSTALLINE NiTi SHAPE MEMORY ALLOY

Xu Bo, Kang Guozheng

A two-dimensional phase field model was established to simulate and predict the super-elasticity, one-way and stress-assisted two-way shape memory effects of gradient nanocrystalline NiTi shape memory alloy system. The simulated results show that in the super-elastic process of gradient nanocrystalline NiTi alloy, the characteristics of martensite transformation and its reverse in the traditional coarse-grained NiTi alloy, i.e., nucleation-expansion and reduction-disappearance of local martensite band, are retained in the relatively coarse-grained region, but with the decrease of grain size, a homogeneous transformation mode, i.e., without the formation of local martensite band, is observed in the fine-grained region; moreover, in the super-elastic and shape memory processes, both the martensite transformation and reorientation originate from the relatively coarse-grained region and then propagate progressively to the fine-grained one, while the reverse transformation is opposite. The gradual propagations of martensite transformation and reorientation make the stress-strain and strain-temperature curves of gradient nanocrystalline NiTi alloy show a remarkable “hardening”, which can be attributed to the grain size-dependence of martensite transformation and re-orientation in nanocrystalline NiTi alloy, i.e., with decreasing the grain size, the transformation or re-orientation barrier increases gradually, and the nucleation and expansion of martensite transformation or re-orientation becomes more and more difficult. It is concluded that the gradient nanocrystalline structure has wider transformation stress, reorientation stress and transformation temperature windows than the traditional uniform-grained NiTi alloys, which means that the controllability of the inelastic deformation of such alloy is significantly improved.

2021, 53(3): 802-812. doi: 10.6052/0459-1879-20-397

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EFFECT OF SURFACE ROUGHNESS ON THE FORMATION OF SHEAR BAND IN Ti-6Al-4V ALLOY CYLINDRICAL SHELL

Yang Tao, Liu Longfei, Yang Zhicheng, Hu Li, Lu Liwei, Shi Xiankun

Shear band is one of the special deformations and damage forms of materials under high strain rate loading. The research on the sensitive factors and mechanism of shear band formation in metal materials has always been one of the key issues in scientific research and engineering design. In the process of high-speed collapse of cylindrical shell, the shear band nucleates preferentially in the inner surface, and its nucleation and propagation behavior are significantly affected by the mesoscopic state of the inner surface. In the presented study, the detonation loading of Ti-6AL-4V alloy cylindrical shell was carried out by thick walled cylinder collapse experiment. Combined with surface treatment technology, microstructure characterization technology and shear banding analysis model, the effect of inner surface roughness on the law of mesodynamics of shear band formation in Ti-6AL-4V alloy cylindrical shell was studied through the shear band pattern in samples. The experimental results show that the inner surface roughness has a significant effect on the formation of adiabatic shear bands in Ti-6AL-4V alloy cylindrical shells under high strain rate. The number, length and nucleation rate of adiabatic shear bands in the specimen increase with the increase of the inner surface roughness under the same deformation condition. The results indicate that, the larger surface roughness leads to a stronger shielding effect for the shear bands. Furthermore, the propagating velocity and length of partial adiabatic shear bands in the specimen increase with the increase of the inner surface roughness. The experimental results of shear band spacing are in good agreement with the prediction of W-O model and M model, but the spacing values are influenced by the inner surface roughness of the specimen. With the increase of the inner surface roughness, the experimental results are gradually smaller than the prediction of models.

2021, 53(3): 813-822. doi: 10.6052/0459-1879-20-433

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A TEMPLATED METHOD FOR PARTITIONING OF SOLID ELEMENTS IN DISCONTINUOUS PROBLEMS

Wang Lixiang, Wen Longfei, Xiao Guizhong, Tian Rong

The extended finite element method (XFEM) has been one of the privileged tools for crack analysis due to its significant advantages: (1) Independence of crack geometry on the simulation mesh; (2) no necessity of remeshing when a crack grows; and (3) high accuracy. However, the method is hindered in engineering practices by the partitioning difficulty of discontinuous elements, i.e. the geometric interaction between discontinuous interfaces and solid elements. Though current partitioning algorithms are geometrically exact, they are cumbersome to implement, computationally expensive, and insufficiently robust. To overcome these issues, a templated partitioning algorithm is proposed based on element level sets for subdivision and numerical integration of discontinuous elements. Firstly, a templated partitioning library for standard discontinuous elements is established by enumerating all the patterns of element level set values. Secondly, the pattern of a non-standard element to be partitioned is looked up and the sub-coordinates are interpolated based on the element level set values. Lastly, the non-standard element is efficiently partitioned into sub-triangles based on the standard element template. The algorithm is incorporated into the conventional XFEM and the improved XFEM for analysis of discontinuous problems, i.e. the problems with holes, inclusions, cracks and so forth. Numerical examples indicate that the proposed algorithm achieves favorable accuracy. Without cumbersome geometrical operations, the templated partitioning algorithm is also efficient and robust, thereby enabling itself to support the extended finite element methods in practical engineering problems.

2021, 53(3): 823-836. doi: 10.6052/0459-1879-20-360

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FUNCTIONAL PERSPECTIVE OF UNCERTAINTY QUANTIFICATION FOR STOCHASTIC PARAMETRIC SYSTEMS AND GLOBAL SENSITIVITY ANALYSIS

Wan Zhiqiang, Chen Jianbing, Michael Beer

Uncertainty exists broadly in real engineering design and analysis. For instance, some mechanical parameters of structures in civil engineering may be of randomness and usually cannot be ignored. Therefore, the process of uncertainty quantification, e.g., the sensitivity analysis on parameters of stochastic systems is, of paramount significance to reasonable engineering design and decision-making. In the present paper, the perspective of functional space analysis on uncertainty quantification and propagation in stochastic systems is firstly stated. On this basis, the global sensitivity index (GSI) is introduced based on the functional Fréchet derivative, of which some basically mathematical and physical properties are studied. Besides, the correspondingly defined importance measure and direction sensitivity of the GSI are also discussed, in terms of their geometric and physical meanings. Moreover, based on the definition of $\varepsilon$-equivalent distribution, the parametric form of the proposed GSI is elaborated in detail. By incorporating the probability density evolution method (PDEM) and the change of probability measure (COM), the numerical algorithm of the GSI and the procedure of sensitivity analysis are illustrated. Four numerical examples, including the analytical function of the linear combination of normal random variables, stability analysis of the rock bolting system of tunnel, the analysis of steady-state confined seepage below the dam, and the stochastic structural analysis of the reinforced concrete frame, are analyzed to demonstrate the effectiveness and significance of the GSI.

2021, 53(3): 837-854. doi: 10.6052/0459-1879-20-336

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BURSTING OSCILLATIONS AND ITS MECHANISM IN A NONSMOOTH SYSTEM WITH THREE TIME SCALES

Mao Weihong, Zhang Zhengdi, Zhang Suzhen

Dynamic models established from practical engineering application are non-smooth systems owing to non-smooth factors, such as impact, dry friction and switching, etc. Up to now, most studies are in terms of the non-smooth dynamic systems with a single scale or two scales. While more complex dynamic phenomena may be observed in the non-smooth dynamic systems with more scales. The main purpose of this work is to explore multiscale effect in a non-smooth electric system and the related bifurcation mechanism. Upon the traditional Chua's circuit, by introducing a periodically excited oscillator with an order gap from the natural frequency of the system and taking suitable parameter values, a coupled 4-dimensional piecewise linear dynamic system with three time-scales and two boundaries is established to study the bursting oscillations as well as the corresponding bifurcation mechanism under three time-scales. Merging the variables corresponding to the fast scale and the variables related to the intermediate scale into the fast variables, while regarding the variable corresponding to the slow scale as the slow variable, the coupled problem with three time-scales is transformed into that with two time-scales. According to the relevant Hopf bifurcation curve under two independent parameters and the stability analyses of the slow submanifold of the fast subsystem, two different bursting oscillations of the coupled dynamic system are given in the case of two different parameter values. On the basis of the fast-slow analysis method, the transformed phase portrait and the non-smooth dynamics of the slow submanifold occurring on the non-smooth boundaries, the bifurcation mechanism of the mutual transformation of different bursting oscillations is analyzed in details, in which some helpful numerical simulations are given to illustrate the validity of our study simultaneously. At the same time, a new evolution of bursting oscillations is found, i.e., the bursting oscillation induced by destructive grazing bifurcation.

2021, 53(3): 855-864. doi: 10.6052/0459-1879-20-331

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DYNAMICAL ANALYSIS OF A PERIODIC POTENTIAL DRIVEN BY ADDITIVE AND MULTIPLICATIVE TRICHOTOMOUS NOISES

Jin Yanfei, Wang Heqiang

The periodic potentials have been widely applied in the fields of engineering, physics, chemistry and neurobiology, whose stochastic dynamics has become the focus of nonlinear science. Trichotomous noise is a kind of three-level Markovian noise and can converge to dichotomous noise or Gaussian white noise under some limits. The trichotomous noise is a better representation of real noise than the widely used Gaussian white noise to display the diversity of environmental excitation. This paper studies the evolutions of probability density function (PDF) and stochastic resonance (SR) in a periodic potential driven by additive and multiplicative trichotomous noise. The average stationary joint PDF and transient joint PDF are obtained by numerical simulation. It is found that the shape of the stationary PDF has the multi-modal structure as the amplitude of the periodic force increases, which indicates the noise-induced hopping among the potential wells. Furthermore, the stochastic energy method is used to explore the SR phenomenon. The obtained results show that the average input energy curve attains a maximum at an optimal noise intensity and amplitude of periodic force. That is, the SR happens. Moreover, the SR happens at an optimal transition rate of noise and the proper amplitude of periodic force under the excitation of only multiplicative or additive noise. Especially, for the case of additive noise, transition rate of additive noise can induce the suppression of SR for a small amplitude of periodic force. While the SR appears at a proper transition rate of additive noise for a large amplitude of periodic force.

2021, 53(3): 865-873. doi: 10.6052/0459-1879-20-199

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LOCKING PROBLEM AND LOCKING ALLEVIATION OF ANCF/CRBF PLANAR BEAM ELEMENTS

Zhang Dayu, Luo Jianjun, Wang Hui, Ma Xiaofei

In this paper, the Poisson locking on the consistent rotation-based formulation (CRBF) of the planar beam element based on the absolute nodal coordinate formulation (ANCF) kinematic description is discussed. First of all, in order to fully understand the locking problem of ANCF/CRBF element, two new ANCF/CRBF planar beams are developed by constraining all of the position-vector gradients of ANCF planar fully-parameterized beam with an orthogonal matrix. Using this orthogonal matrix, a nonlinear velocity transformation matrix is evaluated to write the time derivatives of the ANCF gradients at the nodes in terms of the time derivatives of the rotation parameter. Two new ANCF/CRBF beams have a rigid cross-section and no shear effect. One of the new ANCF/CRBF beams has two position vectors, one rotation angle and one axial extensibility parameter as the nodal coordinates, while the other does not have a longitudinal extensibility parameter. Then, the difference in the Poisson locking problem among the two new ANCF/CRBF beams and traditional ANCF/CRBF beam is discussed. It can be concluded that since the constraints imposed on the position-gradient vectors, ANCF/CRBF beam has an insufficient Poisson effect on the nodes and a sufficient Possion effect in the interior of the element. This inconsistent Poisson effect will lead to a more severe locking problem than ANCF fully-parameterized elements. Furthermore, the locking problem increases with the number of constraints on the nodal gradients, that is ANCF/CRBF new beams have a more serious locking effect compared to traditional ANCF/CRBF beam. Finally, in order to achieve a better convergence of the new elements, two locking alleviation methods, Elastic Center Line (ECL) and Strain Split Method (SSM), are used. The locking problem on the performance of ANCF/CRBF beams is tested using several examples that include static and dynamic examples, in order to identify the scope of applicability of such elements. The numerical results obtained from ANCF/CRBF beams are compared with the ANCF beam, and with the conventional beam implemented in a commercial finite element software LS-DYNA.

2021, 53(3): 874-889. doi: 10.6052/0459-1879-20-296

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INFLUENCE OF THE CAPSULE ON THE SUPERSONIC RIGID DISK-GAP-BAND PARACHUTE SYSTEM

Gong Sheng, Wu Chuijie

The influence of aerodynamic deceleration performances and flow features of the rigid disk-gap-band parachute system at Mach 2.0 with/without the capsule was studied. For the numerical simulation of unsteady compressible fluid, it adopted the three-layer block-structured adaptive mesh refinement, and a hybrid TCD (tuned center difference) and WENO (weighted essentially non-oscillatory) algorithm and the large-eddy simulation method with the stretched-vortex sub-grid model were used to process the shock waves and large scale turbulence vortex in supersonic flow. The results show that, the flow structure of the parachute system is stable and the disturbance is small without the capsule; when the capsule exists, the periodic interaction between the turbulent wake behind the capsule and the reverse fluid from the inside of the canopy and the parachute shock wave, makes the position of the shock wave move forward and the angle of it become smaller. The flow flied inside the canopy is difficult to reach a stable state, which intensifies the aerodynamic drag oscillation of the parachute system. The aerodynamic drag coefficient of the parachute system is reduced, and the wake structure of the parachute system is more complicated.

2021, 53(3): 890-901. doi: 10.6052/0459-1879-20-339

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STUDY ON EVOLUTIONARY ALGORITHMS FOR INITIAL ORBIT DETERMINATION OF NEAR-EARTH ASTEROIDS WITH TOO-SHORT-ARC

Li Xinran, Zhao Haibin

Surveying projects of near-earth asteroids continue to emerge, and obtain massive observation data. However, this pattern makes the obtained arc too short, and the traditional methods have great difficulty in orbit determination and identification with ill-posed problem in itself when the arc is short. Then how to effectively use these short arc is of great significance for discovering, monitoring and evaluating the threat of asteroids. Under the evolutionary algorithms, a calculation framework for too-short-arc is constructed with three-variable $(a,e,M)$ optimization, which keeps the dimensionality low while makes the optimization results no longer rely on observational measurements. The differential evolution algorithm with fewer parameters and simple operation is used to conduct experiments using orbital simulation data of asteroids with different eccentricity, then the optimal solutions and their aggregation regions are analyzed. The large eccentricity orbits will have an impact on the sensitivity of the algorithm search due to its complexity, it is need to reduce the search space to improve the search ability. The results show that the algorithm performs well in small eccentricity problem, and can obtain valid results to provide information for subsequent work. And for large eccentricity problem, while the traditional method fails, the distribution of the algorithm still contains the real solution. For the phenomenon that the optimal solution is not obvious in the global distribution, it can be analyzed by combining the distribution density and fitness value. Further research on the issue of large eccentricity is needed in the future, the influence of different observation positions and observation time on the algorithm should be considered, and calculate by classification.

2021, 53(3): 902-911. doi: 10.6052/0459-1879-20-084

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IMPULSIVE TRAJECTORY OPTIMIZATION OF KINETIC IMPACTOR MISSIONS FOR ASTEROID DEFLECTION BASED ON AN APPROXIMATION DEFLECTION MODEL

Wang Yirui, Li Mingtao, Zhou Binghong

Asteroid impacts pose a major threat to all life on Earth. The kinetic impactor remains a promising strategy for asteroid deflection. One objective function of a kinetic impactor mission is to maximize the deflection distance (the change of the closest-approach distance before and after the asteroid is deflected). If the deflection distance is accurately calculated by a numerical integration, the efficiency of the optimization problem will be reduced. The dynamical model and the deflection distance calculation method can be simplified in the preliminary design of a kinetic impactor mission. This paper first simplifies the high-precision N-body dynamic model to the two-body dynamic model. Two classic deflection distance analytical models are introduced, at the same time, an approximate model of deflection distance based on closest-approach epoch estimation. Considering the launch performance and simplifying the chemical propulsion to the impulsive maneuver, the direct transfer trajectory optimization model and the planetary gravity assist trajectory optimization model are established. The Genetic Algorithm is used to solve the optimization problem. Taking deflecting Apophis as an example, compared with the analytical model, it is verified that the approximate model proposed in this paper can simultaneously improve the optimality and reduce the complexity of the solution. The simulation results show that the optimal deflection effect of the three-impulse direct transfer trajectory and the two-impulse direct transfer trajectory is almost the same, and the improvement of the planetary gravity assist transfer trajectory on the deflection distance is not obvious compared with the direct transfer trajectory. During the preliminary design stage of a kinetic impactor mission, the deflection distance can be quickly evaluated based on the two-body model. Although there is a certain error in the deflection distance, it does not affect the deflection window. The main gravitational perturbation terms (Venus, Earth, Jupiter) can be introduced to further modify the two-body dynamic model, so that the deflection distance error between modified two-body and the high-precision dynamic model is below 1%.

2021, 53(3): 912-928. doi: 10.6052/0459-1879-20-210

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2021 Vol. 53, No. 3

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