2022 Vol. 43, No. 12

Solid Mechanics
Lamination Design Optimization for Continuous Fiber Reinforced Composites of Variable Thicknesses
DU Chen, PENG Xiongqi
2022, 43(12): 1313-1323. doi: 10.21656/1000-0887.420410
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Due to the high specific strength and stiffness, the use of continuous fiber reinforced composites instead of traditional metal materials to achieve structural lightweight has been widely considered by designers. However, the structural complexity brings great challenges to the design and optimization of composite lamination. Aimed at the problem of multiple constraints in the design of aviation composite laminates, the ply information of the structure was accurately expressed with gradually constructed design variables. Based on the classical genetic algorithm framework and the characteristics of all design variables, the genetic operators in the lamination optimization algorithm were defined, and the repair strategy was introduced to ensure that each generation of solutions could satisfy the design constraints and be distributed in the feasible region. Finally, the elite reservation strategy was used to improve the local optimization ability of the algorithm, which can reduce the computation cost of the lamination design of complex composite structures. Through the resolution of the classical benchmark problem and the comparison with the existing optimization results, the global and local optimization ability of the proposed lamination optimization algorithm was verified. The work provides theoretical supports for the optimization of composite lamination design in engineering practice.

Structural Crack Identification Based on the Variational Mode Decomposition
YANG Qihang, LI Lin’an, LI Liqing, MI Shaoxuan
2022, 43(12): 1324-1335. doi: 10.21656/1000-0887.420338
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In order to enrich the bridge damage detection method and further improve the accuracy of bridge damage identification, a detection method for simply supported beams with cracks under dynamic loads was proposed not based on the complete finite element model. Under the premise of not blocking traffic, the method only needs to analyze and deal with the acceleration responses of the simply supported beam span, which reduces the mounting, dismounting and maintenance of sensors in practical engineering. At the same time, based on the model, an analytical formula of the acceleration at the midspan of the simply supported cracked beam was derived. Based on the theoretical derivation, the instantaneous energy and the mean energy difference were constructed through the variational mode decomposition and the Hilbert transform, and these 2 crack identification indexes were used to effectively identify small cracks with a crack depth ratio of only 5%. Then the influences of different wheel loads, environmental noises and damage degrees on detection results were studied. The results show that: ① the instantaneous frequency has a better recognition effect for crack positions; ② the mean energy difference is sensitive to crack depth ratio δ and the wheel load magnitude; ③ this method has strong noise robustness.

Effects of Time Delay on Bifurcation and Synchronization of Flux-Coupled and Chemically Coupled Neurons
ZHANG Jie, LI Xinying, YANG Zongkai, DA Hu
2022, 43(12): 1336-1346. doi: 10.21656/1000-0887.420381
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Based on the chemical synaptic coupled neuron model, the differences and types of synchronization under inhibitory and excitatory conditions were discussed. According to the effect of the magnetic flow coupling on neuron discharge, the discharge states, bifurcation types and synchronization of the Morris-Lecar (ML) neuron models with time delay, magnetic flux coupling and chemical coupling, were analyzed. The results show that, the ML neuronal systems with magnetic flow coupling and chemical coupling can produce rich inverse periodic bifurcation or incremental periodic bifurcation behaviors under different parameters. The introduction of time delay, although can increase the periodicity of the system, will also break the system synchronization. Conversely, an appropriate coupling strength can enhance synchronization.

Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip
LI Xu, SU Rui, ZHANG Huan, WENG Qianru, JIANG Xiaoyu
2022, 43(12): 1347-1358. doi: 10.21656/1000-0887.420333
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The solution of an infinite plane containing a macro crack and a cluster of micro cracks under uniaxial tensile load was presented based on Muskhelishvili’s complex function method and the stepwise recursive method. The stress field and stress intensity factor K were obtained. Combined with the damage mechanics, damage parameter D of the macro-crack tip and the micro-crack tip under uniaxial tension was redefined, and the influence of different damage zone forms on the damage of the crack tip was analyzed. The results show that, both the chain-distribution and the reverse-chain-distribution micro cracks have an amplifying effect on the macro crack growth, and the damage parameter increases with the decrease of the inclination angle of the micro crack and the reduction of the distance between the macro crack and the micro cracks. For a relatively small inclination angle of the micro crack, the damage parameters of the macro crack and the micro crack heightens, and the damage parameter of the macro crack increases with the micro-crack length. For evenly distributed micro cracks in the continuous damage zone, the micro cracks have an amplifying effect on the macro-crack growth, and the damage parameter of the macro crack increases with the micro-crack number.

Fluid Mechanics
Wave Surface Identification Based on Stereo Vision and Wave Theory: an Initial Attempt
LI Shan, LI Ye
2022, 43(12): 1359-1369. doi: 10.21656/1000-0887.430026
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The wave height is the most basic element of wave information, and accurate measurement of wave heights plays a crucial role in both understanding wave theory and verifying numerical models. An improved optical measurement system was proposed based on the principle of binocular stereo vision, which breaks through the limitations of traditional measurement devices such as wave gauges and other single-point measurements, and improves the commonly used optical measurement method relying solely on images by involving the water wave theory into the data post-processing procedure. Through the identification and reconstruction of the unidirectional regular wave surface in a towing tank and the comparison of the results with the wave gauges and theoretical incoming wave parameters for validation, the research shows that, the measuring system has an error of about 1% in the measurement of a wide-area wave surface. Finally, a preliminary attempt was made on the irregular wave surface identification.

Study on Multiphase Pressure Wave Velocity Characteristics of Automatic Kill Annulus in Chuanyu Fractured Formation
KONG Xiangwei, LIU Zuocai, JIN Yanxin
2022, 43(12): 1370-1379. doi: 10.21656/1000-0887.430006
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In view of the virtual mass force, the annulus pressure, the gas-liquid resistance, the gas slippage, the annulus void fraction and other factors, the mathematical model for annular multiphase pressure wave velocities of automatic kill in fractured formation, was proposed based on the small perturbation theory. With the Pengzhou PZ-5-3D well (vertical depth 5 827 m) as an example, the model was solved programmatically with the semi-explicit difference method. The results show that, the gas from the fractured formation is characterized by the slug flow. With the increase of the void fraction, the pressure wave velocity first decreases and then increases. For a void fraction between 0% and 16%, the pressure wave velocity is mainly of liquid slug, and decreases sharply. For a void fraction between 16% and 40%, the pressure wave velocity tends to be flat and constant. For a void fraction between 42% and 100%, the pressure wave velocity shows an increasing trend, and is mainly of bubble slug. With the decrease of the annulus well depth, the void fraction decreases and the pressure wave velocity falls. The pressure wave velocity increases with the back pressure of the kill circulating exhaust wellhead. For an annular void fraction between 0% and 13%, the gas slippage velocity has little influence on the pressure wave velocity. For an annular void fraction between 13% and 85%, the pressure wave velocity decreases with the gas slippage velocity. The time interval of the throttle valve follows the response time of the bottom hole pressure, and increases with the response time.

High Accuracy Numerical Simulation of Non-Isothermal Viscoelastic Polymer Fluid Past a Cylinder
ZHUANG Xin, LIU Fujun, SUN Yanping, WANG Huiling
2022, 43(12): 1380-1391. doi: 10.21656/1000-0887.430127
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The collocated grid finite volume CLEAR (coupled and linked equations algorithm revised) method was applied to solve the governing equations for viscous and XPP (eXtended Pom-Pom) viscoelastic fluids. The high accuracy AVLsmart schemes for the convection terms of momentum and constitutive equations were constructed based on the deferred correction method. Firstly, the incompressible viscous fluids past a cylinder at different Reynolds numbers were simulated to verify the validity of the developed numerical method. Then, the isothermal and non-isothermal XPP viscoelastic fluids past a cylinder were studied numerically, with the distribution patterns of velocity vectors, stress components, stretches and temperatures obtained. Especially, the effects of We on horizontal velocities, normal stresses and stretches were analyzed. The results provide a theoretical foundation for accurate prediction of fiber reinforced viscoelastic polymer dynamic filling process in complex cavities.

Applied Mathematics
The Inverse Source Problem for a Class of Stochastic Convection-Diffusion Equations
ZHAO Lizhi, FENG Xiaoli
2022, 43(12): 1392-1401. doi: 10.21656/1000-0887.420399
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The inverse source problem for a class of stochastic convection-diffusion equations driven by the fractional Brownian motion with the Hurst index, was considered. The direct problem is to study the solution to the stochastic convection-diffusion equation. The inverse problem is to determine the statistical properties of the source from the expectation and covariance of the final-time data. The direct problem is well-posed. The uniqueness and instability of the inverse source problem was proved. Some numerical simulation examples verify the theoretical analysis.

Adaptive Constrained Control of Unknown Strict Feedback Nonlinear Systems With Dead Zone Input
GONG Chikun, RU Qingyang, YUAN Lipeng
2022, 43(12): 1402-1411. doi: 10.21656/1000-0887.430081
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To tackle the problem of unknown strict feedback nonlinear control systems with dead zone input and pre-assigned tracking control, a novel adaptive tracking control strategy was proposed based on the immune function, the active disturbance rejection control and the pre-assigned funnel constraint. The immune function and the extended state observer were utilized to estimate the unknown information of the control system. Through combination with the Lyapunov function, the funnel control was introduced to design the controller, and guarantee the tracking error within the pre-assigned funnel boundary. The adaptive control law was designed based on the rapid changing rate of the hyperbolic tangent function, and the command wave filter was introduced to avoid repeated differentiation problem in the backstepping method. The stability analysis demonstrates the boundedness of all the closed-loop signals. A simulation example shows the effectiveness of the proposed control strategy.

Non-Probabilistic Structural Reliability Analysis Integrating the PSO and the Kriging Model
QIAO Xinzhou, CHEN Yongjing, LIU Peng, FANG Xiurong
2022, 43(12): 1412-1421. doi: 10.21656/1000-0887.420308
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In view of the problems with implicit performance functions and limited experimental data in the reliability analysis of complex structures, a non-probabilistic reliability method combining the particle swarm optimization (PSO) with the Kriging model was presented. A multidimensional ellipsoid was first used to characterize the uncertain parameters of structures. The Kriging model was then constructed for the implicit performance function, wherein its optimal related parameters was determined through the PSO. Based on the proposed model the reliability analysis was explicitly conducted. The results of 3 numerical examples show that, the proposed method is of effectiveness and feasibility, and has higher accuracy and efficiency than those based on the traditional Kriging model.

Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators
SHEN Shilei, SONG Chuanjing
2022, 43(12): 1422-1433. doi: 10.21656/1000-0887.430091
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Noether’s symmetry and conserved quantity of singular systems under generalized operators were studied. Firstly, the Lagrangian equation of singular systems under generalized operators was established, and the primary constraints on the system were derived. Then the Lagrangian multiplier was introduced to establish the constrained Hamilton equation and the compatibility condition under generalized operators. Secondly, based on the invariance of the Hamilton action under the infinitesimal transformation, Noether’s theorem for constrained Hamiltonian systems under generalized operators was established, and the symmetry and corresponding conserved quantity of the system were given. Under certain conditions, Noether’s conservation of constrained Hamiltonian systems under generalized operators can be reduced to Noether’s conservation of integer-order constrained Hamiltonian systems. Finally, an example illustrates the application of the results.