应用数学和力学

2024 Vol. 45, No. 5

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Solid Mechanics
Fluid Mechanics

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2024, 45(5)

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Comments of the Chief Editor

The Greatness of a University Lies in Its Excellence

LU Tianjian

2024, 45(5): 509-517. doi: 10.21656/1000-0887.450105

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Abstract:
The core of a great university lies not only in the improvement of its hardware facilities, but also in the profound academic atmosphere, educational philosophy, and cultural heritage it embodies. Based on the author's academic and work experiences at universities such as Cambridge, Harvard and Xi'an Jiaotong University, this article elaborates on the core elements that a great university should possess (good place, good constitution, good inheritance, good teachers, and good students), as well as how these elements can effectively promote the cultivation of high-quality talents and scientific innovation, providing reference and inspiration for the construction of first-class universities.

Solid Mechanics

Analogic Analysis of Orthotropic Plate Bending Problems With Gridwork Systems

YUAN Quan, YUAN Si

2024, 45(5): 518-528. doi: 10.21656/1000-0887.440232

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Abstract:
Orthotropic plates were analogized to gridwork systems, and the compatibility and incompatibility between these 2 structure types in static and dynamic analyses were discussed. The results show that, the gridwork results converge to the theoretical solution of plates through the grid refinement for compatible problems with simply supported and/or clamped boundaries. All the formulas for calculation of various internal forces were derived, and the algorithms required in solving the gridwork systems were proposed by means of the 3D structural mechanics solver. A wide range of numerical examples, including rectangular and circular plates, were given to verify the validity of the proposed theory and algorithms.

Structure Optimization of Holding Poles Based on the Improved Sine Cosine Algorithm

YANG Xiaomeng, LI Liang, HU Xiongfei, ZHOU Huanlin

2024, 45(5): 529-538. doi: 10.21656/1000-0887.440354

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Abstract:
The holding pole is a special lifting device for the construction of transmission towers. The optimization design model for the holding pole was established. The minimum mass was set as the optimization objective. The cross-section sizes of members, the connection modes of auxiliary members and the coordinates of the rocker joint were set as the optimization variables. The allowable stress, displacement and buckling coefficient were taken as the constraining conditions. An improved sine cosine algorithm (ISCA) was proposed to carry out the size, shape and topology optimization designs of the holding pole. For the ISCA, the Lévy flight was introduced to enhance the global search ability, elite guidance strategy was applied to enhance the local search ability, and the greedy selection strategy was used to update the optimal solution. The example shows that, the ISCA can effectively solve the optimization design problems of spatial truss structures.

Linear Bending Analysis of Functionally Graded Sandwich Shells With the Meshless Method Based on the Layer-Wise Theory

CHEN Wei, TANG Zhihong, PENG Linxin

2024, 45(5): 539-553. doi: 10.21656/1000-0887.440262

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Abstract:
Based on the 3D continuous shell theory and the 1st-order shear deformation theory, a moving least squares meshless method was proposed for solving the linear bending problem of functionally graded sandwich shells with the layered method. With the mapping technology, the 2D meshless node information on the convected coordinate system was mapped on the 3D shell, and the shape function of moving least squares (MLS) approximation was formed on the convected coordinate system. Due to the inability of shell numerical solutions based on the 3D continuous shell theory to provide an explicit expression for the thickness direction of a specific shell, the portion of material parameter changes in the functionally graded sandwich material shell structure was divided into several layers, and the material parameters of each layer were obtained as constants. The governing meshless equation for linear bending of functionally graded sandwich shells was derived under the principle of minimum potential energy. Through introduction of a linear transformation in the thickness direction, the Gaussian integral in the thickness direction of each layer was bounded within the range of -1 to 1, without violation of the 1st-order shear deformation theory (FSDT). The essential boundary conditions were employed with the complete transformation method. Finally, the effects of different gradient coefficients, diameter to thickness ratios, and curvature radii on numerical results were discussed through examples of functionally graded sandwich plates, cylindrical shells, and hyperbolic shallow shells with classical geometric shapes. The calculated results were compared with the literature solutions. The results show that, the proposed method has the characteristics of good convergence and high computation accuracy in solving linear bending problems of functional graded sandwich shells with different shapes.

Analytical Solution of the Concrete Homogenization Method Based on the ANN

LIU Yifan, MA Xiaomin, WANG Zhiyong, WANG Zhihua

2024, 45(5): 554-570. doi: 10.21656/1000-0887.440106

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Abstract:
By means of the self-defined artificial neural network (ANN) and its excellent function fitting function, aimed at aggregate-mortar matrix 2-phase concrete, the analytical solutions of the highly nonlinear coupling differential equation of the differential method in the indirect homogenization theory were given, the functional relations between the volume modulus and the shear modulus of concrete and the volume fractions of aggregate were obtained respectively, and the results were compared with those of numerical simulation. The results show that, the method based on the ANN is fast and has higher precision. In addition, the method of deconstructing ANN provides the formula of calculating the elastic modulus of aggregate-mortar matrix-pore 3-phase concrete directly from aggregate volume fractions and initial porosities under constant meso-mechanical parameters. For concrete samples with different aggregate volume fractions and initial porosities, the formula has higher calculation accuracy, and avoids the complex analysis and many assumptions of the traditional homogenization method. The work provides a new idea of homogenization method for composite materials.

Structural Parameter Identification Based on the Interval Mathematics Method

SONG Haiyang

2024, 45(5): 571-581. doi: 10.21656/1000-0887.440319

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Abstract:
The statistical energy analysis (SEA) method was popularly employed to handle the high-frequency dynamics problems in many engineering fields such as aerospace and shipping. The damping loss factor and coupling loss factor were the major parameters in the SEA theory, and they can usually be identified with the measured external input power and structural modal energy. The measurement errors of the input power and modal energy were not considered in the traditional parameter identification, where the accuracy of the identified results was relatively low. The interval mathematics method was applied to the parameter identification in this study, and the measurement errors of the input power and modal energy were fully considered. The effects of the measurement errors on the parameter identification were revealed, and the accuracy of the identified results was improved. The work can be helpful for the structure design and safety analysis.

Research on Anti-Seismic Performances of Interlayer Isolation Structures With Lateral Stopping Viscoelastic Dampers

ZHAO Liju, WANG Shanku, WANG Xiaolin, GE Xinguang

2024, 45(5): 582-593. doi: 10.21656/1000-0887.440194

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Abstract:
Anti-seismic performances of the hybrid energy dissipation structure (HEDS) composed of an isolation interlayer with lateral stopping viscoelastic dampers (VEDs) under random excitation were systematically investigated. Firstly, the seismic motion equations for the HEDS subjected to the double-filtered white noise excitation (DFWNE) were established, and the filtering equation of the DFWNE was used to accurately transform the dynamic calculation of the HEDS based on the DFWNE into white noise excitation problems to be easily tackled with concise closed-form solutions. Secondly, based on the complex mode method and the properties of the Dirac function for white noise excitation, a concise closed-form solution of the variance and 0th-to 2nd-order spectral moments of the series of responses (structural displacements, interlayer displacements, and damper damping forces) of the HEDS, was derived. Finally, based on the verification of the correctness of the proposed closed solution through numerical examples, the influencing factors on the seismic performances of the HEDS were studied. The results show that, the structural responses of floors above the isolation layer increase with the stiffness of the isolation layer; while the damping parameter of the VED have different effects on the interlayer displacement and structural displacements of floors above the isolation layer, i.e., the structural displacement can reach the minimum under certain damping parameter of the VED, but the interlayer displacement increases with the damping parameter of the VED. This study can provide reference for the design of HEDSs.

Fluid Mechanics

Experimental Study on Flow and Heat Transfer Characteristics of Ambient Air in NACA0021 and NACA4822 Airfoil-Fin Channels

LI Yong, ZHANG Yingchun, FU Yu, ZHOU Qirun, ZHAO Yufei, YANG Senjie, MA Suxia

2024, 45(5): 594-605. doi: 10.21656/1000-0887.440331

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Abstract:
The active regenerative cooling technology faces the bottleneck problem of insufficient heat transfer capacity when the scramjet flies at a higher Mach number. It is proposed to strengthen the heat transfer performance of the regenerative cooling channel with airfoil-fins. To verify the enhanced heat transfer effect of the airfoil-fin channel in principle, an experimental test platform for flow and heat transfer of ambient air in NACA0021 symmetrical airfoil-fin channels and NACA4822 asymmetric airfoil-fin channels (with cross-section sizes of 50 mm × 50 mm) was built. The Nusselt number of the heated surface was obtained based on the steady-state liquid crystal technique. The results show that, the heat transfer intensities of NACA0021 symmetrical airfoil-fin channels and NACA4822 asymmetric airfoil-fin channels improve by 0.17%~17.1% and 18.4%~52.1%, respectively. Correspondingly, PECs are 1.04 and 1.24, respectively, with the volume flow of ambient air at 50 m³/h. The NACA4822 asymmetric airfoil-fin channel can enhance the heat transfer performance of the middle heating surface under the condition of a large flow rate. The flow pressure drop in the airfoil-fin channels also increases correspondingly, where the pressure drop in the NACA4822 airfoil-fin channel is the largest. The asymmetry of the airfoil-fin causes the continuous accumulation of flow turbulence intensity, resulting in a significant increase in the downstream pressure drop. The work is helpful for further research on the flow and heat transfer characteristics of supercritical fluids in airfoil-fin channels, and broadens the application temperature range of the active regenerative cooling technology for scramjets.

Finite Difference Solution of the Modified Mild Slope Equation for Wave Reflection by a Slope With Superimposed Undulating Seabed

NI Yunlin, ZHANG Xijiang, YU Jiangmei, SHEN Liangduo

2024, 45(5): 606-621. doi: 10.21656/1000-0887.440255

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Abstract:
A finite difference model was established to solve the modified mild slope equation, and the reflection of waves on the slope with superimposed undulating seabed was studied. Firstly, the reflection problems of incident waves on straight slope terrain, singly periodic sinusoidal sand ripples and doubly periodic sinusoidal sand ripples superimposed on the horizontal seabed, were verified in excellent agreement with the numerical and analytical solutions and experimental data of others, to prove the correctness of the model. Then, the influences of the upper convex height and lower convex depth of the slope with superimposed parabolic terrain, the number, height, and length of the slope with superimposed singly periodic sinusoidal sand ripples, and the height of the slope with superimposed doubly periodic sinusoidal sand ripples on wave reflection coefficients, were explored. The results show that, the reflection coefficient decreases with the upper convex height and increases with the lower convex depth on the parabolic slope. The law of wave reflection of slope with superimposed singly periodic sinusoidal sand ripples is the same as that of the horizontal seabed. Compared with the horizontal seabed, where the amplitude of the resonance phase downshift decreases with the number of sand ripples and then stays unchanged, the amplitude of the resonance phase downshift of the slope with superimposed sand ripples firstly decreases and then increases with the number of sand ripples. In the slope with superimposed doubly periodic sinusoidal sand ripples terrain, the peaks of the Bragg resonance increase with the heights of the 2 superimposed sand ripples, respectively, where the resonance bandwidth is almost unaffected, and the phase downshift amplitude of the peak Bragg primary resonance decreases, which is contrary to the situation that the amplitude of resonance phase downshift increases with the height of the singly periodic sand ripples. With the fixed number, length, and height of sand ripples, the reflection intensity of doubly periodic sinusoidal sand ripples on waves and the resonance bandwidth excited by them are larger than those of singly periodic sinusoidal sand ripples, and the amplitude of resonance phase downshift is smaller than that of singly periodic sand ripples, despite the horizontal seabed or the slope seabed. Moreover, the reflection intensity of the slope with superimposed sinusoidal sand ripples is greater than that of the horizontal seabed, the phenomenon of zero reflection no longer exists, and the phase downshift amplitude of the peak Bragg primary resonance is larger than that of the horizontal seabed.

Periodic Electroosmotic Flow of the Jeffrey Fluid in Microchannel Between Two Sinusoidally Wavy Walls

CHANG Long, BUREN Mandula, SUN Yanjun, JIAN Yongjun

2024, 45(5): 622-636. doi: 10.21656/1000-0887.440333

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Abstract:
The periodic electroosmotic flow of the Jeffrey fluid in microchannel between 2 sinusoidal wavy walls was studied. The momentum equation was solved with the perturbation expansion method, to give the approximate analytical velocity and volume flow rate of the periodic electroosmotic flow of the Jeffrey fluid in the parallel-wall microchannel. The influences of relevant dimensionless parameters, such as oscillation Reynolds number Re_Ω, pressure gradient G, Deborah number De, retardation time λ₂ω, electric width K, small wavy amplitude δ, phase difference θ and wave number λ on mean velocity u_m(t) and amplitude |U_m| of the mean velocity, were investigated. The study reveals a distinct difference in the velocity amplitudes between Newtonian, Maxwell, and Jeffrey fluids. The velocity distribution of the Jeffrey fluid is significantly influenced by wavy surface, exhibiting pronounced fluctuations. Furthermore, the velocity distribution depends on phase difference θ of the upper and lower wavy surfaces. As oscillation Reynolds number Re_Ω increases, the AC EOF velocity and mean velocity u_m(t) exhibits rapid oscillations, with the amplitude becoming increasingly smaller. Similarly, Deborah number De plays a role similar to Re_Ω, facilitating the AC EOF velocity profile to oscillate easily under the action of an external electric field. An increase in retardation time λ₂ω results in decrease in the amplitude of the AC EOF velocity profile and mean velocity amplitude |U_m|. For a given Re_Ω, phase lag χ (representing the phase difference between the electric field and the mean velocity) exhibits a significant increase or decrease with θ. Phase lag χ decreases with G, λ₂ω, and θ. However, for larger λ values (such as λ>3.4), there is almost no change of phase lag χ.

Effect of Shear Thinning Rheological Properties on Particle Migration in Microchannels

SHEN Yang, WANG Qikun, LIU Tangjing

2024, 45(5): 637-650. doi: 10.21656/1000-0887.440326

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Abstract:
A relative motion model was used to numerically simulate the phenomenon of particle aggregation in shear thinning fluids. To understand the shear thinning effects on particle mechanical properties in microfluidics, the shear thinning matching was performed with viscoelastic and non-viscoelastic fluids. The research results indicate that, shear thinning characteristics can significantly alter the mechanical properties of particles. In non-viscoelastic fluids, shear thinning can cause the aggregation position of particles to move towards the wall, and has an incentive effect on the aggregation speed of particles. In viscoelastic fluids, the occurrence of shear thinning will bring a decrease of the fluid elasticity, resulting in particle convergence from the center to the wall.