应用数学和力学

2020 Vol. 41, No. 9

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Study on Instability of Clay Granular Slope Piles Based on Complex Network

LIU Xiaofei, YOU Shihui, XIE Chunkai1

2020, 41(9): 931-942. doi: 10.21656/1000-0887.400225

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Abstract:
The bonded-particle discrete element simulation of the instability and failure process of granular slope piles was conducted under lasting downward loading by metal plates, and the 2D total velocity vectors of soil particles and the slope sliding surface angles during the instability and failure were obtained. Macro-response processes such as the average velocity in the y-direction of the slope pile top were also considered. The normal force chain undirected network model for the granular slope pile under natural accumulation was constructed, and the position of the sliding surface was studied in comparison with experimental results. Finally, the complex network method was used to analyze the topological characteristics of the contact force chain network of the particles on the slope pile top, and the evolutionary rules of the average degree, the clustering coefficient and the average shortest path were obtained during the slope pile instability process, of which the correctness was verified with the strength reduction method. The research results show that, the average shortest path provides a more effective early warning of the instability and failure of slope piles. The complex network theory used to study the relationship between macro responses of the slope pile and its force chain mesoscopic structure, makes a new mathematical method for the study of slope instability.

Numerical Simulation and Test Validation for Concreted Filled Steel Tube Columns Under Blast Loading

ZHAO Junhai, SUN Shanshan, DANG Huixue, LI Xinzhong

2020, 41(9): 943-955. doi: 10.21656/1000-0887.400207

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Abstract:
Based on the LS-DYNA nonlinear finite element program and multi-material fluid-solid coupling method, the finite element model was developed to analyze dynamic responses and damage mechanisms of concreted filled steel tube (CFST) columns under blast loading, which were validated through comparison between simulated results and tested ones of the full-scale specimens. The effects of main parameters including the section form, the scale distance, the concrete strength, the steel strength and the section shape characteristics on the blast-resistant performance of the CFST columns were investigated with the finite element model. The results indicate that, the CFST columns have excellent anti-blast performances, and the proposed finite element model predicts the dynamic responses of the CFST columns under blast loading efficiently; the anti-blast performance of circular CFST columns is better than that of square ones; increasing the material strength and the length-width ratio of a rectangular CFST column can improve the blast-resistant performance, and decreasing the radius-thickness ratio of a circular CFST column also can promote that resistance.

Numerical Analysis on Debonding of Crystal-Binder Interface in TATB-Based Polymer-Bonded Explosive Caused by Heating and Cooling Processes

FAN Zhengjie, LIU Zhanfang

2020, 41(9): 956-973. doi: 10.21656/1000-0887.410062

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Abstract:
Polymer-bonded explosive (PBX) is a kind of heterogeneous material composed of energetic crystals and binder as a microstructure. The mechanical properties of crystals, binder layers and the crystal-binder interface under thermomechanical environment are the main factors on PBX damages. Based on the Voronoi theory and the Monte Carlo gradation thought, a 2D geometric model for PBX was established with 5 different crystal volume fractions. With the influence of temperature change on the thermodynamic properties of the crystals and binder, a bilinear cohesive contact relationship model was introduced to describe the mechanical properties of the crystal-binder interface, and the damage mechanism of PBX interface during the heating and cooling processes was analyzed numerically. The results show that, the interface tangential stress increases with the temperature, which leads to debonding of the interface. The debonding of the crystal-binder interface mainly depends on the interface normal stress at a decreased temperature. Compared with the heating process, the cooling process makes interface debonding easier to occur, in agreement with experimental observations. With the increase of the crystal volume fraction, the residual stiffness of interface after the cooling process goes higher, which means that the increase of the PBX crystal volume fraction is helpful to control interfacial debonding. With the same crystal volume fraction, the more uniform the crystal sizes are, the smaller the interfacial damage degree will be.

Identification of Dynamic Forces on Aircraft Engine Mounts With the Least Squares Method

HAN Feng, SHEN Chen, XU Junwei

2020, 41(9): 974-984. doi: 10.21656/1000-0887.410054

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Abstract:
For aircraft noise and vibration control, it is vitally important to identify dynamic forces on engine mounts caused by engine operation. Although such dynamic forces are needed to predict and control structural vibration and structure-borne noise in the cabin, they cannot be measured directly in the flight state. The least squares method was employed to identify the dynamic forces based on the frequency response function (FRF) between excitation points and response positions with the actual acceleration measurements in the flight state. A norm condition number criterion was used to evaluate the accuracy of the inverse calculation process, and relative errors of the predicted dynamic forces were calculated. The results show that, the identified forces meet engineering requirements.

Free Vibration of MultiSegment Beams With Arbitrary Boundary Conditions

BAO Siyuan, ZHOU Jing, LU Jianwei

2020, 41(9): 985-993. doi: 10.21656/1000-0887.410045

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Abstract:
The vibration characteristics of continuous multi-segment beams were studied. Other than classical boundary conditions (such as simple supports), the elastic constraints were considered to analyze the free vibration characteristics of multi-segment beams. Firstly, according to the spectro-geometric method, 4 auxiliary functions were added on the basis of the traditional Fourier series to construct the lateral displacement function for each segment of the beam. Secondly, new expressions of the Lagrangian functions for the beam structure were obtained by substitution of the supposed spectro-geometric form into the Lagrangian functions. The free vibration problem was transformed into the standard matrix eigenvalue form from the Hamiltonian principle, and the natural frequencies and modes of the beam under arbitrary boundary conditions were obtained. For 4 numerical examples, the natural frequencies and modes of the continuous multi-segment beams were calculated under different boundary conditions of variant spring stiffness values. Comparison of the results between existing literatures and this work shows correctness, standardization and efficiency of the proposed method.

Elastoplastic Analysis of Ellipsoidal Hole Expansion in Unsaturated Loess

DANG Xinghai, ZHOU Peng, CHAO Xin, GUO Qiming, WU Runlin

2020, 41(9): 994-1010. doi: 10.21656/1000-0887.400186

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Abstract:
In the unified strength criterion for unsaturated soils, the formulae of cohesion of unsaturated undisturbed loess and matrix suction were introduced. The method of changing hole pattern coefficient k was combined with boundary conditions, equilibrium equations and stress compatibility equations to derive stress and strain solutions under drainage and undrained conditions. Analytical solutions of the stress and strain fields, the plastic zone radii and the limit hole expansion pressure in the elastic and plastic regions around the ellipsoid hole in the plane, and the influences of the matrix suction, the strength criterion and the dilatancy on the analytical solutions were discussed with the MATLAB software. The results show that, the effective stresses of unsaturated loess under different drainage conditions will increase with hole pattern coefficient k and the matrix suction; when the parameters are constant, the effective strain under the drainage condition will increase with dilatation coefficient h and even more with the matrix suction; with the same condition, the effective stress and strain under the double shear stress strength criterion for b=1 will be larger than those under the MC strength criterion for b=0.

BAI Yuchuan, XIN Weiyan, XU Haijue

2020, 41(9): 1011-1025. doi: 10.21656/1000-0887.400364

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Abstract:
Sediment is carried by flow to the lake area during the formation process of the initial segment of a delta, which mainly depends on the initial momentum to maintain its own continuous movement. According to the characteristics of this process, the theoretical model for the plane jet boundary layer in the initial segment of the delta was established based on the shallow water equations for muddy water, and the flow field distribution of the initial segment of delta formation was obtained with the similarity solution method. Based on the general mathematical model of river bed evolution, the theoretical expression of the morphological characteristics of the initial segment was derived, and the erosion and deposition of the initial segment were quantitatively analyzed. Through the experimental verification, the theoretical solution can well describe the erosion and deposition trend and morphological characteristics in the early stage of delta formation.

Numerical Simulation of Free Surface Wave Elevations of Point Sources With the Same Source Intensity and Immersion Depth in Uniform Flow

DOU Yilin, LUO Zhiqiang

2020, 41(9): 1026-1035. doi: 10.21656/1000-0887.400219

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Abstract:
Based on the desingularization numerical method of dissipative Green’s function, the regular wave integral was extended to derive the multi-point source dissipative free surface wave. The variation regularity of free surface wave elevations, profiles and contour lines was simulated numerically with multi-point sources under different arrangements. The proposed numerical method was verified to be correct and effective. The numerical results show that, with double point sources arranged longitudinally, the wave crests and troughs of the 2 sources will superpose mutually when the added point source is located near the wave crest of the single point source; the wave crests and troughs of the 2 sources will interfere mutually when the added point source is located near the wave trough of the single point source, and the wave amplitude will decrease rapidly and oscillate slowly up and down the horizontal line of the free surface. With multi-point sources arranged longitudinally, the wave elevation will undergo the similar periodic changes when the point sources are located at different positions. With multi-point sources arranged transversely, the wave surface changes obviously, and the free surface wave diffuses backward in the form of transverse wave.

Continuous Dependence on Boundary Parameters of the Original Equations for LargeScale Wet Atmosphere

GUO Lianhong, LI Yuanfei

2020, 41(9): 1036-1047. doi: 10.21656/1000-0887.410028

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Abstract:
Large-scale dynamic equations for atmosphere are controlled by the original equations derived from the Navier-Stokes equations, and coupled with the thermodynamics and salinity diffusion transport equations. In the past few decades, the atmosphere, ocean, and atmosphere-ocean coupling original equations were extensively studied from the perspective of mathematics. The previous literatures mainly focused on the mathematical logic or well-posedness of the original equations. The stability of the original equations was addressed. Given the inevitable errors in the model establishment and simplification, the effects of coefficients’ small changes on solutions’ great changes were studied for the original equations. Prior estimates of the solutions, combined with energy estimation and the differential inequality technique, were used to control steam ratios. The results prove the continuous dependence of the solutions to the large-scale wet atmosphere original equations on boundary parameters.

Solution and Application of the Transient Phreatic Flow Motion Model Under General Function Boundary

LIU Nengsheng, CAO Hengming

2020, 41(9): 1048-1056. doi: 10.21656/1000-0887.400371

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Abstract:
In view of the limitations on the generalization of the canal water level boundary conditions for the classic transient phreatic flow motion model near the semi-infinite domain canal, and based on this model, the water level change process of the canal was generalized into a general function form, and the Laplace transform method was used to process the model. Combined with the differential theorem and convolution theorem in the Laplace transform, the analytical solution of the model was given. To explore the application of the solution to practical problems, the water level change process of the canal was analyzed by the Lagrange interpolation, and the MATLAB software was used to solve the aquifer parameters with the relevant measured water level data. The results show that, the analytic general function form model under the river channel water level boundary conditions is relatively simple, and the composition of the solution includes all conventional functions. Combined with the interpolation functions, the proposed model works well in solution of the aquifer parameters with high precision and apparent simplicity, and has good popularization values.