应用数学和力学

2014 Vol. 35, No. 5

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An Anisotropic Hyperelastic Constitutive Model With Fibre Bending Stiffness for Cord-Rubber Composites

SUN Shu-lei, MAO Jian-liang, PENG Xiong-qi

2014, 35(5): 471-477. doi: 10.3879/j.issn.1000-0887.2014.05.001

Abstract(1334) PDF(1161)

Abstract:
Based on the invariant theory of continuum mechanics by Spencer, an anisotropic nonlinear hyperelastic constitutive model involving fibre bending effect was developed for cord-reinforced rubber composite materials. Through introduction of the gradient of fiber vector after deformation, the unit-volume strain energy function was decomposed into four parts: volumetric, isochoric, anisotropic and bending deformation energy terms, which were convenient for parameter identification. Both the theoretical analysis and experimental study indicate that the traditional finite deformation theory based on the continuum mechanics for fibre-reinforced composite materials is not suitable for bending deformation. With the fibre bending stiffness taken into consideration, the present constitutive model’s correctness is validated by the numerical bending simulation of a previous test.

Effects of Nonlocal Shear Factor on Flexural Wave Dispersion in Double-Walled Carbon Nanotubes

WANG Bi-rong, DENG Zi-chen, XU Xiao-jian, WANG Yan

2014, 35(5): 478-486. doi: 10.3879/j.issn.1000-0887.2014.05.002

Abstract(1352) PDF(872)

Abstract:
The effects of nonlocal factors on the wave dispersion in the doublewalled carbon nanotube(DWCNT) were analyzed with the modified Timoshenko beam model modified based on the stress gradient theory. Coupling with Van der Waals force, the dispersion characteristics, such as phase velocity, frequency, critical frequency and amplitude ratio of outer tube to inner tube, were studied. The results show that: for a given wave number, both the first 4 modes’phase velocities and frequencies of the DWCNT decrease with rise of the nonlocal shear factor, in which no obvious linear law is found. It is notable that for the 3rd and 4th modes the amplitude ratios do not decrease with the rise of the nonlocal shear factor. Meanwhile, the nonlocal shear factor has prominent effects on the wave dispersion characteristics of the DWCNT especially at relatively higher wave numbers.

Numerical Investigation on Galloping Characteristics of Continuous Multi-Span Iced Quad Bundle Conductor Lines

ZHAO Li, YAN Bo, CAI Meng-qi, WU Chuan

2014, 35(5): 487-497. doi: 10.3879/j.issn.1000-0887.2014.05.003

Abstract(892) PDF(931)

Abstract:
Finite element models of iced quad bundle conductor lines were set up and galloping processes of these lines were numerically simulated by means of ABAQUS software. Based on the analysis of the dynamic characteristics of the conductor lines and the galloping responses, the galloping vibration modes, frequencies and amplitudes of the continuous multi-span lines with different span lengths and span numbers were investigated and compared with those of the single-span dead-end lines. It is shown that the galloping modes and frequencies of the two end-spans of the multi-span lines are different from those of the intermediate spans, and the galloping characteristics of the multi-span lines are different from those of the single-span lines, which have to be taken into account in the development of anti-galloping technology.

Geometric Nonlinear Spatial Beam Elements With Curvature Interpolations

QI Zhao-hui, FANG Hui-qing, ZHANG Zhi-gang, WANG Gang

2014, 35(5): 498-509. doi: 10.3879/j.issn.1000-0887.2014.05.004

Abstract(1738) PDF(1034)

Abstract:
Beam elements with absolute nodal coordinates played an important role in the geometric nonlinear analysis of structures and dynamics of flexible multibody systems. One of such elements was the beam element based on the exact geometric beam model, in which the process of obtaining internal nodal forces involved interpolations of rotational angles, resulting in some numerical difficulties. Another such element proposed by Shabana, avoided the angular interpolations by replacing the nodal rotation parameters with many newly introduced nodal parameters. In accordance with the exact virtual power equations for beams with large deformations and the relationships between tangents of the beam centroid line and curvatures of the beam sections, a new spatial beam element with absolute nodal coordinates was presented. The nodal parameters of the presented element are the same with those of the element based on the exact geometric beam model, but the internal forces can be obtained without angular interpolations. Numerical examples verify its validity through comparison with the analytical results.

Dynamic Buckling of Cylindrical Shells Under Coupled Impact Loads

MA Jian-qing, XU Xin-sheng

2014, 35(5): 510-522. doi: 10.3879/j.issn.1000-0887.2014.05.005

Abstract(1107) PDF(1419)

Abstract:
In consideration of the stress wave propagation under axial-torsional coupled impact loads, the dynamic buckling of elastic long cylindrical shells was investigated. The Hamiltonian system for the problem was established firstly. Then, accordingly, the critical buckling loads and buckling modes were converted to a problem of eigenvalues and eigensolutions in the symplectic space. By means of the Hamiltonian system a perfect buckling space was given, and the relations of how the critical loads and buckling modes corresponded to the symplectic eigenvalues and eigensolutions in the symplectic space were revealed. Due to the different propagation velocities of the axial stress wave and torsional stress wave, progress and reflection of the longitudinal wave and transverse wave were not synchronous within a cylindrical shell. So the cylindrical shell was divided into three regions with respective different stress, displacement and boundary conditions. The numerical results of critical load curves and buckling modes under clamped and simple boundary conditions were given. Especially, the different first-order buckling modes were discussed detailedly.

Micro Numerical Simulation of Creep Mechanical Behavior of Aluminum Silicate Short Fiber-Reinforced AZ91D Magnesium Matrix Composite

TIAN Jun, CHEN Zhou-quan, ZHONG Shou-yan

2014, 35(5): 523-532. doi: 10.3879/j.issn.1000-0887.2014.05.006

Abstract(1199) PDF(845)

Abstract:
A research was conducted on the micro mechanism of the creep mechanical behavior of aluminum silicate short fiber-reinforced AZ91D magnesium matrix composite. The unit cell model was applied together with the finite element method (FEM) of ABAQUS to simulate the composite. The FEM results show that the distribution of stress and strain in the fiber and matrix is roughly uniform in each segment, the fiber assumes far higher equivalent Mises stress than the matrix, and there is distinct stress concentration around the interface between the matrix and the fiber. The creep fracture of the composite goes through three microscopic processes. With the increase of creep deformation, the short fiber bears and transfers the load with various damages, fracture and multiple fracture, which strengthens the creep resistance of the matrix. The micro-cracks generated at the weak interface continue to expand, causing sharp fall of the creep resistance and in turn fracture of the composite.

A Calculation Method for Structural Dynamic Responses Based on the Approximation Theory of Radial Basis Function

XU Ji-qing, LI Zheng-liang, WU Lin-jian

2014, 35(5): 533-541. doi: 10.3879/j.issn.1000-0887.2014.05.007

Abstract(1594) PDF(1058)

Abstract:
A new numerical calculation method for structural dynamic responses was proposed based on the approximation theory of radial basis function (RBF) and weighted residual collocation point method, with the time interval to replace the space distance as the independent variable of RBF for the first time. Aimed at the numerical characteristics of structural dynamics, a new RBF expression of joint interpolation combining displacement, velocity and acceleration was developed, and the concept and standard for precise calculation put forward. According to the numerical examples, the new method has significant advantages in solving strong stiff dynamic equations and structural transient-phase dynamic responses, compared with the Newmark method, Wilson-θ method and Runge-Kutta method. Its calculation accuracy is equivalent to that of the precise time-integration method. This new calculation method is independent of the computation efficiency-related dynamic eigen-matrix and the degrees of freedom of a problem. It has good applicability to some large-scale problems, and makes a promising way to the calculation of structural dynamic responses.

A Second-Order Rotated-Hybrid Scheme for Solving Multi-Dimensional Compressible Euler Equations

LIU You-qiong, FENG Jian-hu, REN Jiong, GONG Cheng-qi

2014, 35(5): 542-553. doi: 10.3879/j.issn.1000-0887.2014.05.008

Abstract(1418) PDF(1460)

Abstract:
A second-order Euler flux function based on the rotated Riemann solver approach was presented. This scheme was different from the grid-aligned finite-volume method or the finite-difference method based on dimensional splitting. It was a hybrid numerical scheme developed through particular combination of the HLLC scheme and HLL scheme. The HLL scheme was applied in the direction normal to shock waves to suppress the carbuncle phenomenon and the HLLC scheme was applied across shear layers to avoid excessive numerical dissipation. Numerical experiments show that the new rotated-hybrid scheme is extremely simple, carbuncle-free and highly efficient.

Numerical Simulation of Flow Fields in Circularly Lobed Ejectors With/Without Central Plug Sudden Expansion

LUO Hu, JIN Jie, DU Gang

2014, 35(5): 554-564. doi: 10.3879/j.issn.1000-0887.2014.05.009

Abstract(1202) PDF(789)

Abstract:
The models of lobed ejectors with/without central plug sudden expansion were built. The flow fields by CFD simulation were compared and analyzed with focuses on the sizes and distributions of the downstream streamwise vorticities. Thermal mixing efficiency and total pressure recovery coefficient were used to judge the performances of the two kinds of ejectors. The results show that the central plug with sudden expansion can effectively reduce flow loss and significantly improve the total pressure recovery coefficient. As the central plug sudden expansion causes the mainstream velocity to slow down, the vorticity of the ejector declines in the downstream flow field; but on the other hand, the central plug sudden expansion brings additional flow disturbances to the flow field and makes the mixing efficiency of the whole field increase.

Energy Conservation and Resonance Conditions for Interactions of an Infinite Number of Ocean Surface Waves

HUANG Hu

2014, 35(5): 565-571. doi: 10.3879/j.issn.1000-0887.2014.05.010

Abstract(1286) PDF(912)

Abstract:
Based on the energy conservation law and the existing wave-wave resonance conditions for ocean surface waves, a typical group of resonance conditions for the 3-4-5-6-7 wave interactions was put forward through expansion of the Hamiltonian energy functional into a 7-order symmetrical integro-power series, therefore a general group of resonance conditions for an infinite number of wave interactions was induced and deduced. The work may make a great improvement in the present structure of the fundamental wave turbulence theory.

Research on the Throttle Valve Opening Degree Control to Keep Bottomhole Pressure in Balance When Gas Influx Occurs During Drilling Operations

KONG Xiang-wei, LIN Yuan-hua, QIU Yi-jie, YUAN Ji-ming

2014, 35(5): 572-580. doi: 10.3879/j.issn.1000-0887.2014.05.011

Abstract(1578) PDF(1222)

Abstract:
Based on the micro control body equations of multiphase flow for drilling operation, a model for compensation balance control of back pressure was proposed to adjust the throttle valve in real-time through compensation for gas slippage pressure drop, which can maintain balance between bottomhole pressure and formation pressure. Results show that the earlier the gas influx is detected, the easier the balance of bottomhole pressure can be achieved. The early detection of gas influx relies on the downhole detection tools. When gas influx occurs in the bottomhole, the throttle valve opening degree should be adjusted sharply to balance the formation pressure rapidly with the back pressure. Adjustment of the throttle valve opening degree depends on the change of pressure difference in the bottomhole. As the gas migrates upwards along the annulus, the throttle valve should be adjusted slightly in real-time to balance the pressure drop generated by gas slippage according to the compensation balance control model. When the gas flow away from the wellhead with the circulation, 0 gas flow appears in the annulus, and the throttle valve opening degree and back pressure tend to be stable.

Theoretical Model and Numerical Simulation of Vortex Induced Flexible Tube Vibration

FENG Zhi-peng, ZANG Feng-gang, ZHANG Yi-xiong, YU Xiao-fei, YE Xian-hui

2014, 35(5): 581-588. doi: 10.3879/j.issn.1000-0887.2014.05.012

Abstract(1063) PDF(851)

Abstract:
In order to predict vortex induced vibration (VIV) of flexible tubes, the flexible tube was modeled as an Euler-Bernoulli type beam and the equations of motion for the tube under VIV were derived based on the fluid force coefficients obtained through fluid-structure interaction simulation and the wake oscillator model respectively. Two theoretical models for predicting VIV of the flexible tube were presented. Firstly, the infinite-dimensional model was discretized with the 4-order Galerkin technique. The tube vibration responses induced by cross flow was predicted successfully with the fluid force coefficients obtained through fully fluid-structure coupling simulation. Then, the results predicted by the wake oscillator model were compared with those by the fluid-structure interaction simulation. The research shows that, the vibration amplitudes predicted by the harmonic fluid force model is smaller than that predicted by the fluid-structure interaction simulation. However, the wake oscillator model properly simulates the vortex induced vibration characteristics of the tube, which agrees well with the fluid-structure interaction numerical results. That indicates the wake oscillator model is a feasible way to predict the vortex induced flexible tube vibration.