应用数学和力学

2023 Vol. 44, No. 8

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Fluid Mechanics
Solid Mechanics
Applied Mathematics

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Eulerian Finite-Element Numerical Simulation Investigation on the Dynamic Characteristics of Out-of-Phase Bubbles in Underwater Explosions

TANG Hao, LIU Yunlong, FENG Jituan, JU Xinyang, ZHANG Aman

2023, 44(8): 895-908. doi: 10.21656/1000-0887.440047

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Abstract:
An underwater explosion out-of-phase bubbles dynamics model was developed based on the Eulerian finite-element method, with the calculation results compared to the unified bubble theory and the out-of-phase explosion experiment to validate the calculation model. Compared with the case of a single bubble in the free field, it is found that the work done by the shock wave of the out-of-phase explosion on the bubble is the cause for the increase of the total energy of the bubble. The closer the absolute value of the phase difference is to π, the smaller the distance parameter is, and the less the total energy loss of the bubble is. The later bubble can cause the first bubble to collapse in advance. The jet direction of the bubble is influenced by the phase difference. When the phase difference is zero, jets are directed toward each other, but for other phase differences, the backward jets occur.

Analytical Solutions of Steady Flow Toward a Partially Penetrating Well in a Rectangular Leaky-Confined Aquifer

SUN Qianlin, TAN Weijia, XU Beiyi, WANG Xudong

2023, 44(8): 909-920. doi: 10.21656/1000-0887.430398

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Abstract:
For the complicated problem of groundwater flow to a partially penetrating well in a rectangular confined aquifer, a mathematical model describing the groundwater flow to a partially penetrating well pumped at a constant rate in a rectangular leaky-confined aquifer, was established. The analytical solutions of the 3D steady flow in the Cartesian coordinate system under different boundary conditions, were derived through the finite Fourier transform and the inverse transform. After the verification of the analytical solution of drawdown, the number of calculation items satisfying the calculation accuracy requirement was given, based on the analysis of the calculation accuracy of the analytical solution and the characteristics of the groundwater flow to a partially penetrating well. Moreover, the effects of orthotropy, well integrity and well location on the drawdown and seepage fields, were discussed. The engineering examples demonstrate the applicability of the proposed analytical method.

Simulation Study on Dam Break Flow Based on the B-Spline Material Point Method

XU Yunqing, ZHOU Xiaomin, ZHAO Shiyi, XU Shengfei, SUN Zheng

2023, 44(8): 921-930. doi: 10.21656/1000-0887.430363

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Abstract:
The dam break flow poses a common free surface flow problem in hydraulic engineering, and its accurate simulation is of great engineering significance. The B-spline material point method (BSMPM), as an improved algorithm of the material point method (MPM), has optimized accuracy and convergence in material point calculations and unique algorithmic advantages in free surface flow problems. Based on the BSMPM, a weakly compressible BSMPM (WC-BSMPM) was developed through introduction of an artificial equation of state. The simulation of the dam break flow problem was carried out, with the effects of the order of the B-spline interpolation basis function on the simulation results analyzed. The results show that, the simulated fluid wavefront position, the wavefront velocity and the elevation variation at a given position are basically consistent with the existing experimental results. As the order of the basis function increases, the computation time will lengthen for about 1.5 times. However, the computation times of the BSMPM of different orders will uniformly increase approximately linearly with the background grid size. The validity of the WC-BSMPM simulation of the dam break flow problem was verified. The research provides a new idea and method for the simulation of dam break flow problems.

Solid Mechanics

An Unconstrained Structural Dynamic Load Reconstruction Method Based on the Sparse Bayesian Learning Algorithm

CHEN Xianzhi, ZHOU Xinyuan, ZENG Yaoxiang, ZHANG Yahui

2023, 44(8): 931-943. doi: 10.21656/1000-0887.430336

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Abstract:
For rapid and exact reconstruction of dynamic loads on unconstrained structures with unknown initial conditions, a dynamic load reconstruction method was proposed based on the sparse Bayesian learning algorithm. With the idea of the function fitting technique, the control equations were built. The noise was assumed to obey the Gaussian distribution, and the fast algorithm was used in the sparse Bayesian learning model. An improved piecewise fitting method was formulated to rationally express the initial conditions in the piecewise fitting, the end state response of the previous segment was used as the possible initial condition, and the low-order vibration modes were applied as the supplement to the initial displacements and initial velocities. The numerical simulations of simplified launch vehicle models prove the accuracy and efficiency of the proposed method, under the effects of different noise levels and different expressions of initial conditions.

Experimental Study on Dynamic Responses of Fuel Tanks Under Fragment Impacts

JIA Haobo, REN Kerong, QING Hua, ZHANG Jingfei, XU Wentao, TANG Guangwu

2023, 44(8): 944-952. doi: 10.21656/1000-0887.440002

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Abstract:
The dynamic responses of fuel tanks under fragment impacts were investigated. The ballistic impact tests on fuel tanks were carried out, the test processes were recorded with a high-speed camera, the dynamic morphologies of the fuel tank back wall were obtained with the 3D digital image correlation technique, and the damage forms and dynamic responses of the tanks under different fragment impact velocities were analyzed. The results show that, the damage to the tank front wall is in the form of circular holes and that to the back wall is in the form of "petal-shaped" breaches with radial cracks at fragment impact velocities of 955~1 667 m/s. The dynamic response speed and strain level of the tank back wall dramatically increases with the fragment impact velocity. The dynamic response of the tank back wall mainly includes 2 parts: the plastic deformation of the wall center and the overall deformation of the wall. With the increase of the deformation extent of the tank back wall, plastic hinge lines will occur along the wall diagonals and edges.

Lightweight Design of Arc Rib Stiffened Plates Based on the Smeared Stiffener Method

LIU Chenyu, LUO Xuanhe, LIU Kangxiang, MENG Zeng, XIAO Shan

2023, 44(8): 953-964. doi: 10.21656/1000-0887.430342

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Abstract:
Stiffened plates are common bearing components in aerospace structure design, which can bring great economic benefits and reduce the structure weight based on the insurance of the plate performance. Therefore, the lightweight design of stiffened plate structures is a research focus in the aerospace field. Based on the concept of synchronous failure, a new type of arc rib stiffened plate was proposed to sufficiently make use of the axial bearing capacity of ribs. Then, the critical buckling load of the arc rib stiffened plate was accurately predicted based on the smeared stiffener method. The lightweight design of arc rib stiffened plates was carried out by means of the particle swarm optimization algorithm. The results show that, the arc rib stiffened plate has excellent bearing capacity, significant lightweight design effects, and promising optimization results.

Parametric Solution Domain Structures for Bifurcation and Non-Meshing Dynamic Characteristics of Straight Bevel Gear Systems

TIAN Yaping, YANG Jianghui, WANG Ruibang

2023, 44(8): 965-976. doi: 10.21656/1000-0887.430330

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Abstract:
Aimed at the coupling transition relationship between the periodic motion, the tooth surface impact, the non-meshing state and the dynamic load of straight bevel gear systems with backlash, the 2-parameter plane with respect to the time-varying meshing stiffness and the frequency ratio was built based on the cell mapping principle. Besides, the improved CPNF (continuous-Poincaré-Newton-Floquet) method was applied to solve the solution domain structure of the periodicity, impact, non-meshing and dynamic load characteristics of the system cells. The simulation results show that, there are plentiful bifurcation modes with 3 kinds of tooth surface impacts coexisting in the 2-parameter solution domain structure, including the saddle node bifurcation, the Hopf bifurcation, the period-doubling bifurcation, the catastrophe bifurcation and the period-3 bifurcation. The tooth surface impact and chaos will intensify due to increase of the time-varying meshing stiffness coefficient. The tooth surface non-meshing, the tooth back meshing and the dynamic load coefficient will exhibit mutations under the influences of the tooth impact and the periodic motion. Meanwhile, in the same domain, the tooth surface non-meshing and the tooth back meshing will weaken with the frequency ratio but heighten with the stiffness coefficient.

Applied Mathematics

An Electrocardiogram Signal Classification Algorithm Based on Improved Deep Residual Shrinkage Networks

GONG Yuxiao, GAO Shuping

2023, 44(8): 977-988. doi: 10.21656/1000-0887.440074

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Abstract:
The electrocardiogram (ECG) signal classification is a significant research topic in the healthcare field. Most existing methods could not effectively reduce the missed diagnosis rate of classification with small-size samples and tackle the complexity of preprocessing operations. An electrocardiogram signal classification algorithm based on the improved deep residual shrinkage networks was proposed, namely the DRSL algorithm. Firstly, the small-size classification samples were augmented with the synthetic minority over-sampling technique to solve the classification imbalance problem. Secondly, the spatial features were extracted by mean of the improved deep residual shrinkage networks, where the residual module can avoid overfitting caused by deepening of network layers, and the squeeze-and-excitation operation with soft threshold subnetwork can extract important local features and remove noises automatically. Then, the time features were extracted with the long short-term memory networks. Finally, the classification results were output with the fully connected neural networks. The experimental results on the MIT-BIH arrhythmia database show that, the proposed algorithm is superior to IDRSN, DRSN, GAN+2DCNN, CNN+LSTM_ATTENTION, SE-CNN-LSTM in terms of classification performances.

A Self-Adaptive Alternating Direction Multiplier Method for Frictionless Elastic Contact Problems

YUAN Xin, ZHANG Shougui

2023, 44(8): 989-998. doi: 10.21656/1000-0887.440079

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Abstract:
A self-adaptive alternating direction multiplier method was designed for frictionless elastic contact problems. An augmented Lagrange function was introduced for the variational formulation of the problem with an auxiliary variable, to deduce a minimization problem and an equivalent saddle-point problem. Then the alternating direction multiplier method was used to solve the problem. To enhance the performance of the algorithm, a self-adaptive rule based on the iterative function on the boundary was proposed to automatically select the proper penalty parameter. The advantage of this algorithm is that, each iteration only needs to solve a linear variational problem and explicitly calculate the auxiliary variable and the Lagrange multiplier. The convergence of the algorithm was analyzed theoretically. The numerical results illustrate the feasibility and effectiveness of the proposed method.

Energy Conservation of the 4 D Incompressible Navier-Stokes Equations

WANG Bin, ZHOU Yanping, BIE Qunyi

2023, 44(8): 999-1006. doi: 10.21656/1000-0887.430370

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Abstract:
The energy conservation of 4D incompressible Navier-Stokes equations was studied. In the case of a singular set with a dimension number less than 4 for the Leray-Hopf weak solution (suitable weak solution), the $L^q\left([0, T] ; L^p\left(\mathbb{R}^4\right)\right)$ condition in the 4D space was obtained based on Wu's partial regularity results about the 4D incompressible Navier-Stokes equations, to ensure the energy conservation.

Lump Solutions, Interaction Solutions and Breather Solutions of Generalized (3+1)-Dimensional KdV Equations

YU Minghui, WANG Yunhu

2023, 44(8): 1007-1016. doi: 10.21656/1000-0887.430353

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Abstract:
Based on the bilinear form of the generalized (3+1)-dimensional KdV equation, the lump solution, the interaction solution and the breather solution of the equation were obtained. The obtained lump solutions were proved to be rationally localized in all directions of the space, then the "fusion" and "fission" phenomena were observed during the interaction between the lump soliton wave and the one-stripe soliton. Finally, the breather solution of the equation was obtained.