应用数学和力学

On the Stress Prediction of Key Components in Steam Turbine Rotors Based on the NARX Neural Network

ZHANG Chaodong, ZHAO Xiang, RU Dongheng, WANG Peng, WU Hao, GAN Lei

2021, 42(8): 771-784. doi: 10.21656/1000-0887.410372

Abstract(780) PDF(113)

Abstract:
Stress prediction of steam turbine rotors during startup processes is of great significance. To predict the stresses of key components in a 350 MW supercritical steam turbine rotor, a NARX neural network-based method was proposed with a 2D axisymmetric finite element model established according to the actual dimensions of the rotor. Appropriate boundary conditions were applied to the model and the temperature and stress distributions under cold startup conditions were calculated. The simulated results were experimentally verified and the danger points of the rotor were then determined after 288 finite element calculations according to typical startup conditions. The stresses calculated near the danger points as well as several user-selected operating parameters were used to establish the neural network sample dataset. An effective NARX neural network was employed to estimate the stresses at the danger points. The results show that, the proposed method can accurately predict the stresses with their tendency. The stresses predicted by the NARX neural network are in good agreement with the finite element simulated results, and can meet the requirements for rotor stress monitoring.

Application of the Base Force Element Method to Spacial Geometrically Nonlinear Problems

GONG Linqi, CHEN Xiyun, GUO Qing, PENG Yijiang

2021, 42(8): 785-793. doi: 10.21656/1000-0887.410341

Abstract(568) PDF(55)

Abstract:
Based on the base force element method (BFEM) and the principle of complementary energy, a 6-node spatial solid unit was proposed for spacial geometrically nonlinear calculation, and the Euler angles were used to describe the displacement. MATLAB was used to program and simulate the elastic large deformation problem of typical beam and plate structures. The calculation results show that, the finite element model based on the BFEM and the complementary energy principle has good calculation accuracy for the spatial geometrically nonlinear components. Compared with the traditional finite element method, the model has the characteristics of smaller mesh size effects and stronger anti-distortion ability.

Monte-Carlo Simulation of Particle Reinforced Composites Based on Hybrid Stress Elements

WANG Wei, GUO Ran

2021, 42(8): 794-802. doi: 10.21656/1000-0887.420016

Abstract(533) PDF(41)

Abstract:
Based on the assumed high-order stress field, the hybrid stress finite element method has higher calculation accuracy with sparse grids. The quadtree meshes were used to discretize heterogeneous computing domains with advantages of the displacement coordination conditions for hanging nodes automatically satisfied. Moreover, all quadtree elements can be divided into a limited number of types, and the stiffness matrices of these elements can be pre-computed and stored in the memory, retrieved and scaled as required during computations, which greatly improves the computational efficiency. In view of the randomness of inclusions, the effects of the volume ratio, the number and the aspect ratio of random inclusions on the homogeneous equivalent modulus of the composite were discussed with the Monte-Carlo method and the homogenization method. The results show that, the equivalent elastic modulus of the composite increases with the volume ratio, the number and the aspect ratio of inclusions, and is most sensitive to the volume ratio.

Research on Failure Characteristics and Failure Models for Superalloy GH4169

TAN Xueming, WANG Ruifeng, GUO Xiaojun, MENG Weihua, GUO Weiguo

2021, 42(8): 803-812. doi: 10.21656/1000-0887.410299

Abstract(671) PDF(66)

Abstract:
The material property tests of superalloy GH4169 were carried out under different stress triaxialities (-0.33~0.33), different strain rates (0.001~5 000 s^{-1^{) and different temperatures (293~1 073 K). Under the framework of the Johnson-Cook (JC) failure model, the uncertainty of fitting results of the stress triaxiality term in the JC failure model and the limitation of the linear relationship description between the strain rate and the failure strain in the modified form proposed in previous literatures were studied. With the proposed method of calibrating specific parameters and the strain rate effect index function of coupled stress triaxiality, a phenomenological modified failure model was established. Based on the test results of superalloy GH4169, the parameters of the modified failure model and the JC model were calibrated. The results show that, the failure strain of GH4169 exhibits different strain rate effects under different stress triaxialities; the modified failure model can better describe the failure behavior of GH4169 than the traditional JC model; at the same time ensure non-negativity of the failure strain.}}

Triple-Shear Elastoplastic Constitutive Models for Normally Consolidated Unsaturated Soils Based on the Coordinate Translation Method

HU Xiaorong, CAI Xiaofeng, QU Peng

2021, 42(8): 813-831. doi: 10.21656/1000-0887.410288

Abstract(527) PDF(51)

Abstract:
The unified triple-shear strength criterion for unsaturated soils was established with the single-stress variable method and the double-stress variable method, and the corresponding triple-shear failure stress ratios were derived with the coordinate translation method. Then the triple-shear failure stress ratios were combined with the modified Cambridge model for unsaturated soils, the triple-shear elastoplastic constitutive models for normally consolidated unsaturated soils under the single-stress variable and double-stress variable were built, and the secondary development of ABAQUS was carried out. With the Nanchang unsaturated remolded clay as the research object, the consolidation and drainage (CD) test verification and true triaxial CD test simulation of unsaturated soils were done, and the effects of intermediate principal stress influence coefficient b and matrix suction s on the calculation model for the gravity retaining wall were studied. The results show that, the proposed 2 constitutive models can well describe the deformation characteristics of normally consolidated unsaturated soils in CD tests, and the simulation results of the coordinate translation method under double-stress variables are more close to the real test data. In the simulation of true triaxial CD tests, the shear stress and the volume strain obtained with the double-stress variable method are more close to the results of the single-stress variable method. With the increase of intermediate principal stress influence coefficient b, the shear stress and the volume strain of the 2 constitutive models will also increase. The gravity retaining wall calculation model with the double-stress variable method is more stable. With the increase of intermediate principal stress influence coefficient b or matrix suction s, the soil displacement of the retaining wall model will decrease, while the strength and stability of the soils behind the wall will increase.

An Efficient Numerical Algorithm for Fractional Cahn-Hilliard Equations

WANG Jingying, ZHAI Shuying

2021, 42(8): 832-840. doi: 10.21656/1000-0887.420008

Abstract(791) PDF(108)

Abstract:
An efficient numerical algorithm for the time-space fractional Cahn-Hilliard equation was proposed. Firstly, the time-space fractional Cahn-Hilliard equation was converted into the spatial fractional Cahn-Hilliard equation through the Laplace transform. Then, by means of the Fourier spectral method combined with the finite difference method, an efficient numerical scheme with 2nd-order convergence in time and spectral accuracy in space was obtained. Finally, the validity of the proposed algorithm was verified by numerical experiments. The algorithm satisfies the energy dissipation law and the mass conservation law.

Stabilization of Nonlinear Stochastic Delay Differential Equations Driven by G-Brownian Motion

LI Guangjie, YANG Qigui

2021, 42(8): 841-851. doi: 10.21656/1000-0887.410332

Abstract(532) PDF(51)

Abstract:
The stabilization problem of a class of nonlinear stochastic delay differential equations driven by G-Brownain motion (G-SDDEs) was studied. Firstly, a delay feedback control was designed in the drift term of an unstable nonlinear G-SDDE, and the controlled system was therefore obtained. Then, with the Lyapunov technique, sufficient conditions for the asymptotical stability of the controlled system were given. Finally, two examples were presented to illustrate the obtained results.

Homoclinic Breathing Wave Solutions and High-Order Rogue Wave Solutions of (3+1)-Dimensional Variable Coefficient Kudryashov-Sinelshchikov Equations

ZHANG Shijie, TAOGETUSANG

2021, 42(8): 852-858. doi: 10.21656/1000-0887.410387

Abstract(655) PDF(52)

Abstract:
Based on the Hirota bilinear method, the homoclinic breathing wave solutions to the (3+1)-dimensional variable coefficient Kudryashov-Sinelshchikov (K-S) equations were obtained by means of the extended homoclinic breathing test method. Homoclinic breathing waves with different structures were given through selection of appropriate values for the parameters of the solution, and the rogue wave solutions to the equation were derived under the limit of the periodicity of the homoclinic breathing wave solutions. Finally, a special high-order polynomial was constructed as a test function to obtain the 1st-order and the 2nd-order rogue wave solutions.

Existence of Solutions for a Class of Kirchhoff Type Equations With SignChanging Potential

LEI Jun, SUO Hongmin, PENG Linyan, WU Deke, MENG Lu

2021, 42(8): 859-865. doi: 10.21656/1000-0887.410283

Abstract(580) PDF(42)

Abstract:
The Neumann boundary value problem about a class of Kirchhoff type equations with sign-changing potential terms was studied. By means of the variational method and the decomposition process for the underlying space, the energy functional was proved to satisfy the mountain pass geometry. Then, the energy functional (PS) sequence was proved to have a strongly convergent subsequence. Finally, the existence of two nontrivial solutions was obtained by Ekeland’s variational principle and the mountain pass lemma.

Dynamic Analysis of an Epidemic Model With Infectivity in the Incubation Period

ZHANG Lijuan, WANG Fuchang, WAN Yongge, LI Zhengang

2021, 42(8): 866-873. doi: 10.21656/1000-0887.410251

Abstract(633) PDF(117)

Abstract:
A transmission model for infectious diseases with infectivity in the latent periods was established. According to the law of disease transmission, the basic regeneration number, as the threshold of disease disappearance and spread, was solved. The stability of the system was discussed and the stability condition for the system was obtained. With the COVID-19 pandemic as an example, the effects of various measures for disease control were studied. The spread of the pandemic was discussed and predicted. The work makes a reference for epidemic disease control.

Solutions to Space-Time Fractional Complex Ginzburg-Landau Equations With the Complete Discrimination System for Polynomial Method

HU Yan, SUN Yuhuai

2021, 42(8): 874-880. doi: 10.21656/1000-0887.410392

Abstract(717) PDF(66)

Abstract:
The space-time fractional complex Ginzburg-Landau equation was studied. Firstly, the space-time fractional complex Ginzburg-Landau equation was transformed into the ordinary differential equation through the fractional complex transform. Secondly, the ordinary differential equation was reduced to an elementary integral form. Finally, a series of exact solutions including solitary wave solutions, rational function type solutions, triangle function type periodic solutions, and Jacobian elliptic function doubly-periodic solutions, were constructed with the complete discrimination system for polynomial method.

2021 Vol. 42, No. 8