2021 Vol. 42, No. 11

Dynamics and Control
Motion Prediction of Free-Floating Space Non-Cooperative Targets
WANG Qishuai, ZHOU Bangzhao, LIU Xiaofeng, CAI Guoping
2021, 42(11): 1103-1112. doi: 10.21656/1000-0887.420017
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Abstract:
Motion prediction of space non-cooperative target is an important issue for spacecraft on-orbit service. With obtained high-precision motion prediction results, the chaser can plan its motion trajectory to approach the target and then capture it. A motion prediction method was proposed for free-floating space non-cooperative targets. The core idea of this method is to identify kinematic parameters of the target’s mass center and attitude dynamic parameters, and then with dynamic equations for the target to realize the motion prediction. In the identification of the attitude dynamic parameters, inertia parameters of the target were preliminarily identified firstly, then an adaptive unscented Kalman filter (UKF) was used to roughly identify the attitude dynamic parameters, and finally the identification precision was further improved through optimization. In the identification of the kinematic parameters, the parameters were roughly identified firstly with the optimal attitude dynamic parameters obtained above and the kinematic equations for the target’s mass center, and then the identification precision was further improved again through optimization. In the end, the effectiveness of the proposed motion prediction method was verified by numerical simulations. Simulation results indicate that, the proposed method can achieve long-time high-precision motion prediction of the non-cooperative target whether the target is in uniaxial rotation or tumbling motion.
Numerical Study on Dynamic Responses and Failure Behaviours of Aramid Fabrics Subject to Blast Loads
FENG Zhenyu, JIANG Chao, GAO Binyuan, XIE Jiang, PEI Hui
2021, 42(11): 1113-1125. doi: 10.21656/1000-0887.420025
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Abstract:
In order to study the anti-blast performance of flexible fabrics, the dynamic response and failure behavior of aramid fabric under blast impact were analyzed with the numerical simulation method. Mechanical tests of aramid fabric H1000D-AP220 were carried out, and the constitutive model for woven fabric and the explosive numerical analysis model were established. The dynamic responses and failure modes of the fabrics under different loads were obtained by the analysis of fabrics with different thicknesses and different stacking angles. The results show that, there are 2 typical failure modes of fabrics under the explosive impact: the failure of the central hole and the tensile tear at the boundary, with obvious folds in the width direction of the fabric. The front and back layers absorb more energy than the middle ones. Better anti-explosion ability can be achieved through adjustment of the fabric stacking angle.
Transient Primary Resonance Phase-Frequency Characteristics of Stay Cables With Different Tensions
DENG Zhengke, SUN Ceshi, YANG Rudong
2021, 42(11): 1126-1135. doi: 10.21656/1000-0887.420033
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Abstract:
The transient phase-frequency characteristics of stay cables with different cable forces were studied in view of the cable sag and geometric nonlinearity. The method of multiple scales was used to solve the ordinary differential equations of motion for cables subjected to in-plane distributed excitations, and the approximate analytical expressions of in-plane and out-of-plane primary resonance responses were obtained respectively. Then, the transient phase difference and its amplitude between the response and the excitation were obtained through the Hilbert transform. The rule and reason for the transient phase difference between the response and the excitation under different cable forces were studied. The results show that, the phase difference between the out-of-plane response and the excitation is constant, while for the in-plane one it is related to the elastic parameters and the sag of the cable. A small change in cable tension may result in a significant change in the transient phase-frequency characteristics. The main reason is that there are a twice-frequency term and a drift term in the approximate solution of the in-plane response, the former makes the transient phase of response appear twice positive-negative alternations in a single cycle, and the latter determines the maximum value and the variation law of the transient phase difference between the in-plane response and excitation.
Solid Mechanics
Determination of Soil Mechanical Parameters From Posterior Distributions Under Different Prior Distributions
WEI Deyong, RUAN Yongfen, YAN Ming, GUO Yuhang, DING Haitao
2021, 42(11): 1136-1149. doi: 10.21656/1000-0887.410385
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Abstract:
The values of soil layer parameters in geotechnical engineering were determined according to field and laboratory test data with classical statistical methods, without use of the prior information. Unlike classical statistical methods, the Bayes method combines samples from the perspective of prior distribution to deduce the posterior distribution, providing a new analytical method for the evaluation of geotechnical parameters. The geotechnical engineering survey makes a random sampling of the overall strata. The density function of the sample distribution is determined when the sampling is completed. Therefore, the posterior distribution in the Bayes method depends on the prior distribution, and 2 different sets of prior distributions were derived: the prior distribution and the conjugate prior distribution were determined with the prior information. Through calculation of the parameters in the posterior distribution, with the sample generally conforming to the normal distribution of N(μ,σ2), unknown parameters μ and σ were analyzed, the interval lengths of the posterior distribution under different prior distributions were comprehensively compared, and the prior distribution selected for the optimal posterior distribution in the Bayes inference of the geotechnical parameter was given. The results show that, the posterior distribution in the conjugate case is always shorter than that in the absence of information, and the probability density function distribution is more centralized and the value determination is more convenient. Under the overall normal situation, the extreme value method obtained based on the joint posterior distribution of unknown parameters μ and σ to determine maximum probability mean μmax and variance σmax in the sample as the adopted values in the engineering design, provides a way for the value determination of geotechnical parameters, and has engineering significance.
Topology Optimization of Nonlinear Material Structures Based on Parameterized Level Set and Substructure Methods
LEI Yang, FENG Jianhu
2021, 42(11): 1150-1160. doi: 10.21656/1000-0887.420090
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Abstract:
In order to overcome the problems of complicated calculation process and lower computational efficiency of the traditional level set method (LSM), for nonlinear structure topology optimization, a parameterized level set method (PLSM) was introduced. Through interpolation of the initial level set function with the globally supported radial basis function (GSRBF), a nonlinear material structure topology optimization model was established with the interpolation coefficient as the design variable, the minimum strain energy of the structure as the objective function, and the material amount as the constraint condition. The equilibrium equation for the nonlinear material structure was established by finite element analysis, and solved with the iterative method. In addition, the substructure method (i.e. the domain decomposition method) was used to divide the design area into several sub-areas, and the solution to the full degree of freedom equilibrium equation was decomposed into a set of solutions of reduced equilibrium equations and solutions of multiple substructures’ internal displacements, which could reduce the computation cost. Examples show that, this method can ensure the numerical stability, improve the computational efficiency, and obtain the topology optimization configuration with clear boundaries and reasonable structures.
Lie Symmetries and Conserved Quantities of Lagrangian Systems With Time Delays
ZHENG Mingliang
2021, 42(11): 1161-1168. doi: 10.21656/1000-0887.410184
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Abstract:
The Lie symmetries and conserved quantities of non-conservative mechanical systems with time delays in configuration space were studied. Firstly, the piecewise Lagrangian equations for non-conservative systems with time delays were established according to the Hamiltonian principle of dynamics with time delay. Secondly, the determining equations of the Lie symmetry were obtained by means of the permissible Lie group theory for differential equations. Then, according to the relationship between symmetries and conserved quantities, the Lie theorem of non-conservative systems with time delays was obtained through construction of structural equations. Finally, 2 examples were given to illustrate the application of the method. The results show that, the time delay makes the Lagrangian equations of non-conservative systems piecewise, and the number of determining equations for Lie symmetry is twice of the number of degrees of freedom, which imposes higher restrictions on the generator functions. Meanwhile, the conserved quantity is also in a piecewise expression depending on the velocity term.
A Boundary Element Method for Steady-State Heat Transfer Problems Based on a Novel Type of Interpolation Elements
HOU Junjian, GUO Zhuangzhi, ZHONG Yudong, HE Wenbin, ZHOU Fang, XIE Guizhong
2021, 42(11): 1169-1176. doi: 10.21656/1000-0887.410394
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Abstract:
To improve the computational accuracy of the boundary element method (BEM) for solving the steady-state heat problems, a new method was studied with a new element interpolation method (called expansion element interpolation method). The novel expansion interpolation element was obtained through configuration of virtual nodes at the boundary of the traditional discontinuous element, to transform the original discontinuous element into a higher-order continuous element. The interpolation function constructed with the virtual node and the internal source node can accurately work in the continuous and discontinuous physical fields on the boundary, and the interpolation accuracy increases by 2 orders compared with that of the original discontinuous element. In addition, the boundary integral equation is only valid at the internal source nodes of the traditional discontinuous element and contains only the degrees of freedom of the source nodes, while the degrees of freedom of the virtual node can be eliminated through the relationship between the virtual node and the internal source node, so the size of the final linear system equations will not increase. This new interpolation element inherits the advantages of the traditional continuous and discontinuous elements and overcomes their disadvantages. The numerical results show that, the proposed method helps solve the steady-state heat transfer problem with high computational accuracy and convergence.
Identification of Crack Tip Positions Based on the Scaled Boundary Finite Element Method and the Grey Wolf Optimization Algorithm
YU Bo, SUN Wenjian
2021, 42(11): 1177-1189. doi: 10.21656/1000-0887.410381
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Abstract:
Based on the scaled boundary finite element method (SBFEM) and the grey wolf optimization algorithm (GWO), an identification method for crack tips was proposed. Firstly, the special advantages of the SBFEM were used to solve the fracture mechanics problem, the displacements of measurement points required in the inversion process were quickly and accurately calculated, and the correctness of the solution to the forward problem was verified in advance. Then, the objective function related to the crack tip position was established, and the identification of the crack tip position was converted to the optimization problem of solving the minimum value of the objective function. Finally, the GWO was used to optimize the objective function, that is, to search for the optimal position of the crack tip. The numerical example results show that, it is very effective to solve forward problems in the inversion process with the high precision and semi-analytical advantages of the SBFEM. The grey wolf optimization algorithm has good global convergence property, and can search for the crack tip position more quickly and accurately compared with the classical particle swarm optimization. The grey wolf optimization algorithm has good noise resistance.
Applied Mathematics
Stability of Neutral Volterra Stochastic Dynamical Systems With Multiple Delays
WANG Chunsheng
2021, 42(11): 1190-1202. doi: 10.21656/1000-0887.410323
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Abstract:
A class of nonlinear stochastic integro-differential dynamical systems were discussed, the necessary and sufficient conditions for the mean-square asymptotic stability of the zero solution to the system were given by means of the Banach fixed point method, and a mean-square asymptotic stability theorem for neutral Volterra stochastic integro-differential dynamical systems with multiple delays was established. Unlike the previous research methods, according to the characteristics of each time delay of the stochastic dynamical system with multiple time delays, the operators were constructed through introduction of the corresponding functions, and then the stability of the system was studied with the Banach fixed point method. The conclusion improves and develops the results of several related research papers to a certain extent. In addition, the results obtained supplement and extend those of the fixed point method in study of the stability of zero solutions to nonlinear neutral variable-delay Volterra stochastic integro-differential dynamical systems.
A Modified Euler-Maruyama Scheme for Multi-Term Fractional Nonlinear Stochastic Differential Equations With Weakly Singular Kernels
QIAN Siying, ZHANG Jingna, HUANG Jianfei
2021, 42(11): 1203-1212. doi: 10.21656/1000-0887.420067
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Abstract:
A modified Euler-Maruyama (EM) scheme was constructed for a class of multi-term fractional nonlinear stochastic differential equations with weak singularity kernels, and the strong convergence of this modified EM scheme was proved. Specifically, according to the sufficient condition for stochastic integral decomposition, the multi-term fractional stochastic differential equation was equivalently transformed into the stochastic Volterra integral equation, and then the corresponding modified EM scheme and its strong convergence were derived and proved, respectively. The order of strong convergence is αmm-1, where αi is the index of fractional derivative satisfying 0<α1<…<αm-1m<1. Finally, numerical experiments verify the correctness of the theoretical results.
Fault Estimation for Nonlinear Systems Based on Intermediate Estimators
WEI Yuheng, TONG Dongbing, CHEN Qiaoyu
2021, 42(11): 1213-1220. doi: 10.21656/1000-0887.410335
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Abstract:
Based on the intermediate estimator, the fault estimation problem was studied for the nonlinear systems with time delays and multiple faults. Intermediate variables and intermediate estimators were designed to realize fault estimation and avoid the limitation of observer matching conditions. According to the Lyapunov stability theory and the linear matrix inequality method, the error systems are asymptotically stable. At last, through the MATLAB simulation, the effectiveness of the proposed method was verified.