应用数学和力学

2019 Vol. 40, No. 5

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A Non-Iterative Method for Dynamic Load Identification

YU Bo, WU Yue, NIE Chuanbao, GAO Qiang

2019, 40(5): 473-489. doi: 10.21656/1000-0887.390211

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Abstract:
To identify the load states of structures under complex environment quickly and accurately, a noniterative inversion method was proposed based on the finite element method and the Newmark-β method, and used to identify dynamic loads on structures. The relationship between the measurement information and the parameters to be identified was found out, and the error function was established. With the least squares method, the proposed method can estimate the dynamic load directly without iteration. What’s more, the basis function expansion was applied to inverse the distributed loads and help overcome the illposedness of the algorithm. Meanwhile, the singular value decomposition method was used to solve illconditioned equations. The effects of the measurement noise, the number of measurement points, the basis function expansion, the locations of measurement points and the time step on the inversed results were discussed in numerical examples. The results show that, the proposed method has high accuracy and efficiency for dynamic load identification problems.

Equivalent Stiffness of Sinusoidal Periodic Dimpled Plates

FENG Yan, DU Guojun, SHEN Zhenxing, WANG Mixiao

2019, 40(5): 490-497. doi: 10.21656/1000-0887.390160

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Abstract:
The equivalent stiffness of sinusoidal periodic dimpled plates was derived according to the classical elastic thin plate theory, in view of the analysis of the mechanical properties of the unit cell structure and the homogeneous distribution of unit cells over the plate. The sinusoidal periodic dimpled plate with 4 sides simply supported under a concentrated load was taken as an example, the analytical results were compared with those of the finite element method (FEM), and the rationality and accuracy of the analytical equivalent stiffness were verified. Finally, the effects of some structural parameters on the equivalent stiffness of the dimpled plate were analyzed. The results show that, the presented method can effectively calculate the equivalent stiffness of the sinusoidal periodic dimpled plate. The bending stiffness and torsional stiffness of the dimpled plate are obviously higher than those of the basic plate, for the geometric change of the dimpled plate. The work has important meanings for the research on statics and dynamics of dimpled plates and the engineering application.

Dynamical Behavior Analysis of Micro Beams Conveying Fluid in Longitudinal Magnetic Fields

JIANG Pengfei, YAN Yan, WANG Wenquan

2019, 40(5): 498-507. doi: 10.21656/1000-0887.390185

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Abstract:
Such nonlinear characteristics as mechanics, magnetics and fluidstructure interactions exist in the microelectromechanical system (MEMS) driven by the magnetic field, which will affect the safety and reliability of the system. Based on the nonlocal Eulerian beam model, the dynamical behaviors of fluidconveying micro beams (a kind of MEMS) in magnetic fields were studied. The dynamical system bifurcation theory and the harmonic balance method were used to study the stability and amplitudefrequency characteristic curves of the pinnedpinned micro beam system. The results show that, the frequency of the beam can be adjusted through changes of the magnetic field intensity, the flow velocity and the system damping. The smallscale effects tend to change the critical velocity and the existence of damping can change the number of critical velocities and the type of bifurcation.

Geometrically Nonlinear Analysis of Functionally Graded Beams Under Thermomechanical Loading

WANG Xue, ZHAO Weidong

2019, 40(5): 508-517. doi: 10.21656/1000-0887.390201

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Abstract:
Based on the classical beam theory, the geometric nonlinear governing equations for FGM beams under uniform temperature field and uniform transverse loading were derived according to the principle of virtual work and the variational method. In view of the immovably clamped boundary conditions, the 2-point boundary value problem was solved with the shooting method. For the zero uniform transverse loading, the thermal buckling critical temperature and equilibrium path of the FGM beam were investigated. The load-deflection curves of the FGM beam were given for the nonzero uniform temperature and the nonzero transverse uniform loading. The numerical results show that, the dimensional thermal buckling critical temperature of the beam decreases significantly and the post-buckling deformation increases significantly with the material volume fraction index increases, and the temperature variation has a heavy influence on the load-deflection curves. The bistable configurations and the switch of the FGM beam were found. The final equilibrium shape of the beam is not only related to the variable temperature and loading parameters, but also to the loading process.

Improved Noncompatible Generalized Mixed Elements and Performance Analysis

ZHAO Zhiqin, QING Guanghui

2019, 40(5): 518-526. doi: 10.21656/1000-0887.390146

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Abstract:
The coefficient matrix of traditional mixed elements has zero values on the principle diagonal. The most prominent feature of noncompatible generalized mixed elements is that they avoid this problem. Thus, the convergences of the displacement and the stress are stable. Combined with the enhanced assumed strain (EAS) method, a new type of 8-node noncompatible generalized mixed elements was established based on the minimum potential energy principle and the H-R variational principle. The element retains all the advantages of existing noncompatible generalized mixed elements. Meanwhile, the integral calculation is more simple. Numerical examples show that, the improved noncompatible generalized mixed element gives highly accurate results, and has a faster computation speed and less sensitivity to the geometric distortions.

Creep Lifetime Evaluation of Muddy Salt Rock

XU Hongfa, MA Yuqing, YANG Yaoran, Lü Yaru, GENG Hansheng

2019, 40(5): 527-535. doi: 10.21656/1000-0887.390230

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Abstract:
The creep life is an important problem in the research of rock rheology. For the lack of long-term creep experiment data, the creep rupture time is difficult to estimate. The complete stress-strain uniaxial compression experiment of the muddy salt rock was conducted, and the uniaxial creep test with the Chen method was done. The creep curve cluster under different stress levels was gained through processing of the creep curves, thereby the isochronal stress-strain curve cluster was obtained. Based on the fitting analysis, the variation law for the secant modulus of isochronal stress-strain curves with time and the mathematical model for isochronal stress-strain curves were established. The relationship between isochronal stress-strain curves and the complete stress-strain curve was considered to get the mathematical expressions of the creep failure strength and failure strain with the creep lifetime respectively. The research results can be used to estimate the creep lifetime, the long-term strength, the long-term elastic modulus, the creep failure line and the termination line of muddy salt rock, also make a reference for the estimation of the creep lifetime of similar rocks.

Singularly Perturbed Solutions of NonFourier Temperature Field Distribution in Single-Layer Materials

BAO Liping, LI Wenyan, WU Liqun

2019, 40(5): 536-545. doi: 10.21656/1000-0887.390112

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Abstract:
A temperature field model for single-layer materials was constructed with the non-Fourier heat conduction law, i.e. a type of singularly perturbed hyperbolic equations with small parameters in an unbounded domain. The asymptotic solution to the problem was obtained with the singularly perturbed expansion method. Firstly, the singular perturbation method was used to obtain the external solution and boundary layer correction terms of the problem. Through estimation of the maximum norms of the internal solution and the external solution, and the maximum norms of the time derivative, and under the theory of linear parabolic equations, the existence and uniqueness of the internal and external solutions were obtained, and the formal asymptotic expansion of the solution was obtained. The L² estimator of the asymptotic solution was given with the remainder estimator. The uniform validity of the asymptotic solution and the distribution of the temperature field in the unbounded domain were got. Through singular perturbation analysis, the relationship between the non-Fourier temperature field and the Fourier temperature field was given, and the specific behaviors of the non-Fourier temperature field were described.

A Conserved HighOrder Traffic Flow Model With Discontinuous Flux and Its Numerical Simulation

QIAO Dianliang, LI Xiaoyang, GUO Mingmin, ZHANG Peng

2019, 40(5): 546-561. doi: 10.21656/1000-0887.390277

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Abstract:
Under inhomogeneous road conditions, a conserved high-order (CHO) anisotropic traffic flow model was extended to obtain a CHO model with discontinuous fluxes. Based on the property of the Riemann invariant for the CHO model with discontinuous fluxes, the first-order Godunov, EO (Engquist-Osher) and LF (Lax-Friedrichs) numerical schemes for this model were designed with the local simplification method and the δ mapping algorithm. The numerical simulations show that, the CHO model with discontinuous fluxes is reasonable and effective. It can describe equilibrium and non-equilibrium traffic flows, and can better describe the actual traffic phenomena compared with the LWR (Lighthill-Whitham-Richards) model with a discontinuous flux.

Transient Pressure Analysis of Bi-Zone Composite Horizontal Wells With Non-Newtonian and Newtonian Power-Law Fluid Flow

JI Anzhao

2019, 40(5): 562-573. doi: 10.21656/1000-0887.390252

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Abstract:
Polymer flooding plays an important role in enhancing oil recovery and the horizontal well has great advantages in the development of thin reservoirs. Based on the physical process of polymer flooding, a well-test mathematic model for horizontal wells in Newtonian-non-Newtonian bi-zone composite reservoirs was established with the basic theory for point source functions. The analytical solution of the well-test model for horizontal wells was obtained through the Laplace integral transform and the Fourier finite cosine integral transform. The well-test curves of the pressure and the pressure derivative were got with the Stehfest numerical inversion algorithm. The results show that, the smaller the power law index is, the steeper the curves of the pressure and the pressure derivative will be in the outer zone, like a line with a slope of (1-m)/(3-m).When the power law index is 1, the model can be reduced to the traditional model for horizontal wells in bi-zone reservoirs. The longer the horizontal section of the horizontal well is, the earlier the radial flow stage will end. The larger the flow ratio is and the smaller the inner radius is, the higher the positions of the pressure and the pressure derivative curves will be in the outer zone, where the pressure derivative curve keeps as a line with a slope of (1-m)/(3-m).

Research on Pressure Strain Correlation Terms in the Reynolds Stress Model for Spiral Flow in Reducing Pipes With Rotating Wall

ZHANG Jinglong, WANG Zunce, XU Yan, XU Dekui

2019, 40(5): 574-582. doi: 10.21656/1000-0887.390325

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Abstract:
The characteristics of flow field in reducing pipes were analyzed. It was determined that the inner vortex in the tangential velocity field is an elliptic flow dominated by the rotation of fluid micelle. The outer vortex is a hyperbolic flow dominated by deformation of fluid micelle and influenced by wall rotation. With the tensor invariant theory, an invariant integrating the rotation rate tensor and the strain rate tensor was introduced as the model coefficient. Then the modified model for pressure and strain terms in the Reynolds stress, which is applicable to flow dominated by rotation, was extended to hyperbolic flow. Ultimately, the model was applied to the flow field simulation of the reducing pipe with rotating wall. Comparison between numerical results and measured ones proves the effectiveness of the modified model.