应用数学和力学

2021 Vol. 42, No. 4

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A Variational Principle and Applications for a Class of Specified Stress Problems

WANG Jialin, ZHANG Junbo, HE Lin, CHEN Zhuo

2021, 42(4): 331-341. doi: 10.21656/1000-0887.410173

Abstract(1256) PDF(666)

Abstract:
To solve some problems in the finite element analysis with specified conditions for stresses or internal forces, the inelastic strain as an additional unknown to meet the specified stress condition was introduced. The elastic mechanics governing equations meeting the specified stress conditions were described under the small deformation assumption. The potential variational principle and the virtual work equation were established with the displacements and unknown inelastic strains as independent variables. Then a generalized variational principle with 4 types of independent variables of the displacement, the elastic strain, the unknown inelastic strain and the stress, was presented. Based on the variational principle, the specified axial forces and the required adjustment quantities were arranged in a dual form in the equations for truss and beam elements. The ordinary stress analysis was realized under the condition with known adjustment quantities, and the required adjustment quantities were obtained with specified axial force conditions. The effects of material stiffness and internal force of a structure were considered in the new method with the prestressing reinforcement simulation improved based on the equivalent load method or the real physical reinforcement method. The method applies to the optimization and adjustment of cable forces in related structures. Numerical simulations of displacement optimization and cable tension adjustment for a cablestayed structure demonstrate the feasibility and accuracy of the presented theory and algorithm.

Analytical Analysis of Non-Circular Hydraulic Lined Tunnels Under Smooth Contact With Transversely Isotropic Rock Mass

WANG Shaojie, ZENG Xiangtai, Lü Aizhong

2021, 42(4): 342-353. doi: 10.21656/1000-0887.410182

Abstract(1206) PDF(368)

Abstract:
An analytical method for non-circular hydraulic lined tunnels in transversely isotropic rock mass was proposed, with the lining under the smooth contact condition with surrounding rock mass. Based on the complex variable theory, continuous conditions for stresses and displacements at the contact boundary and water pressure boundary condition at the lining free boundary were established. In view of the lining support delay effect and with the power series method, the analytical solution was acquired. Aimed at a horseshoe-shaped lined tunnel constructed in transversely isotropic rock mass with inclined structural face, the correctness of this method was validated by analytical check and numerical comparison. Distributions of stress and displacement at the contact boundary and lining free boundary under the effects of anisotropic property and water pressures were discussed.

Analytical Solution of Heat Exchanger Tubesheet Deformation Under Temperature Load

HE Jinyuan, WEI Yongtao, TANG Xin>, ZHANG Yuming, GAO Cheng, LUO Dingming

2021, 42(4): 354-362. doi: 10.21656/1000-0887.410282

Abstract(1136) PDF(360)

Abstract:
A mechanical model for calculating tubesheet deformation was established according to the structure of the heat exchanger. The effective elastic constant of the tubesheet was calculated with reference to code ASME Ⅷ-1, the outer cylinder and the heat exchange tube bundle were respectively equalized to springs and elastic foundations axially deforming due to temperature and pressure loads. An analytical solution of tubesheet deflection was obtained with the Ritz method, and compared with the numerical simulation results of 3 heat exchangers of different scales. The results show that, the analytical solution is in good agreement with the numerical simulation results, which verifies the correctness of the derived analytical solution of tubesheet deformation. The research work has guiding significance for the design of fixed tubesheet heat exchangers.

Optimization of Wheel Weight Distribution for EMU Vehicles Based on the SAGA Hybrid Algorithm

MENG Jianjun, MENG Gaoyang, LI Decang

2021, 42(4): 363-372. doi: 10.21656/1000-0887.410107

Abstract(1732) PDF(412)

Abstract:
Aimed at the wheel weight deviation of EMU vehicles before leaving the factory, a mechanical model for wheel weight adjustment was established. An SA-GA hybrid algorithm proposed with the mechanism of the simulated annealing (SA) algorithm and the non-uniform mutation idea of the genetic algorithm (GA), and the mechanical model for vehicle wheel weight adjustment was numerically solved with this hybrid algorithm. The results show that, the wheel weight deviation can be reduced to less than 1.2%, which conforms to the regulations of GB/T 3317-2006. At the same time, the simulation results were compared with the numerical calculation results from the Simpack software. The comparison shows that, the calculation results based on the SA-GA hybrid algorithm are correct, and the work provides an effective calculation method for quickly optimizing the wheel weight distribution.

Thermomechanical Responses of 3D Media Under Moving Heat Sources Based on Fractional-Order Strains

HUANG Fei, MA Yongbin

2021, 42(4): 373-384. doi: 10.21656/1000-0887.400346

Abstract(1234) PDF(393)

Abstract:
Based on the theory of fractional-order strains, the thermomechanical dynamic responses of 3D elastomers under moving heat sources were studied. The governing equations under the theory of fractional-order strains were applied to the 3D semi-space model, and solved by means of the Laplace transform, the double Fourier transform and its numerical reverse transform. The distributions of non-dimensional temperatures, stresses, strains and displacements were obtained under different heating source velocities and different fractional-order parameters. The results show that, the fractional-order strain parameters have significant effects on mechanical waves but minor effects on heat waves, and the heat source velocity has significant effects on thermomechanical waves.

An Iterated Sinh-Sigmoidal Combined Transformation Method for Calculating Nearly Singular Integrals of Boundary Elements

LIU Jing, YAO Qishui, YANG Wen, ZHOU Fenglin, YU Jianghong

2021, 42(4): 385-393. doi: 10.21656/1000-0887.410167

Abstract(1391) PDF(393)

Abstract:
Accurate and effective elimination of the near singularity of integrals is the primary problem in engineering application of 3D BEM. Nearly singular integrals will appear when the distance between source points and the triangle integral element approaches zero indefinitely. The shape of the integral element and the position of the projection points are both important factors influencing the computation accuracy of nearly singular integrals. Most of the existing nonlinear transformation methods only focus on the near singularity of integrals in the radial direction, ignoring the angular direction and the shape of triangular integral elements, so the calculation accuracy is always unsatisfactory and very sensitive to the shape of the integral elements of subtriangles in the case of projection points near the boundary. An improved iterated sinhsigmoidal combined transformation method based on the adaptive partitioning technology and different coordinate transformations was proposed to eliminate the near singularity of integrals in radial and angular directions respectively, which can greatly reduce the calculation scale while ensuring the calculation accuracy. Numerical examples were presented to verify the proposed method.

An Improved 3rd-Order WENO-Z Type Scheme

WANG Jianling, LI Xiaogang, WANG Wenshuai

2021, 42(4): 394-404. doi: 10.21656/1000-0887.410203

Abstract(1265) PDF(370)

Abstract:
Based on the high-order global smoothness factor, a low-dissipation and high-resolution 3rd-order WENO difference scheme was obtained under the WENO-Z scheme framework. A parameter was introduced in the nonlinear weight, the parameter range was determined by convergence analysis, and the optimal parameter value was obtained with combined accuracy and non-oscillation. The scheme can maintain expected 3rd-order accuracy at the 1st-order extremum of the function. Finally, the accuracy recovery of the scheme at various extremum points was verified with exact solution examples, and the low-dissipation and high-resolution characteristics of the scheme were tested with the 1D and 2D Euler equations. The results show that, the proposed scheme is a good shock-capturing method.

A Combined Predicting Model for Expressway Travel Time Based on EMD-GRU

PENG Yong, ZHOU Xin, SONG Qiankun, XIANG Zhonghua

2021, 42(4): 405-412. doi: 10.21656/1000-0887.410165

Abstract(1237) PDF(514)

Abstract:
In view of the variety of influential factors on the expressway travel time and the significance of nonlinear and non-stationary characteristics of the travel time series, a combined expressway travel time predicting model was designed based on the empirical mode decomposition and the GRU neural network. First, the time information of vehicles entering and exiting the expressway in toll data was used to obtain the travel time series of the road segments; then, the empirical mode decomposition algorithm was applied to decompose the complex travel time series into a number of relatively stable and different-time-scale eigen modal function components as well as residual components; then, the GRU neural network was used to predict and integrate the intrinsic modal function components and residual components. The example analysis shows that, the empirical mode decomposition can effectively improve the prediction accuracy of the LSTM and the GRU neural networks; under the same parameter settings, the prediction accuracy of the GRU neural network is better than that of the LSTM neural network.

Research on the Spread of COVID-19 Based on the SEIR Model for Susceptible Populations With Basic Medical History

ZHAI Yijiang, LIN Xiaolin, LI Jianquan, LIANG Weiping

2021, 42(4): 413-421. doi: 10.21656/1000-0887.410313

Abstract(1498) PDF(484)

Abstract:
Based on the classic SEIR infectious disease model, a new type of new coronary pneumonia transmission model containing a population with a history of basic diseases was established, the basic reproduction number of its transmission was obtained, and the existence of the equilibrium of the model was determined. Through construction of the Lyapunov function and with the LaSalle invariance principle, the global stability of the equilibrium was proved, and the theoretical research results were also verified by numerical simulation. At the same time, the influence of the transformation rate coefficient from no basic medical disease to basic disease on the disease transmission was discussed. It is found that, the mathematical model considering no basic disease will underestimate the basic reproduction number of disease transmission and the scale of infection. Numerical simulations also show the definite impact of the transformation rate coefficient from no basic disease to basic disease on the peak number of the infected population.

Active TimeDelay Control of Networked Control Systems With Aperiodic Sampling: a Stochastic Impulsive Switched System Approach

HE Yanjun, MA Weiwei, CHI Xiaobo

2021, 42(4): 422-430. doi: 10.21656/1000-0887.410213

Abstract(1300) PDF(598)

Abstract:
The stabilization problem for a class of networked control systems with aperiodic sampling and stochastic packet dropouts was studied. Other than the traditional view that a time delay was often a negative factor of system stability, the positive effect was considered and a novel active timedelay control method was proposed to stabilize the systems. To analyze the positive effects of the time delay control and to obtain some less conservative conclusions, the aperiodic sampleddata system with stochastic packet dropouts was firstly modeled as a stochastic impulsive switched system with a fixed switching law. Then a new separation lemma was presented in a mean square sense to analyze the stability of the stochastic impulsive switched system. Based on the loopfunctional method and the proposed separation lemma, the mean square stability criterion for the stochastic impulsive switched system was obtained in terms of linear matrix inequalities. Furthermore, the refined mean square stability criterion was given with an interval segmentation technique. Finally, a classical numerical example illustrates the validity of the obtained stability criteria and the advantages of the proposed method.

Spatial Alternative and Stability of Type Ⅲ Thermoelastic Equations

LI Yuanfei, XIAO Shengzhong, CHEN Xuejiao

2021, 42(4): 431-440. doi: 10.21656/1000-0887.410270

Abstract(1248) PDF(368)

Abstract:
The spatial alternative of type Ⅲ thermoelastic equations in a semi-infinite region was considered. The equations were assumed to satisfy certain initial and boundary conditions, and the solution was proved to grow exponentially or alternatively decay exponentially respectively, with spatial variables on a semi-infinite cylinder with the energy analysis method. The continuous dependence of solutions on the coefficients of equations was established.