应用数学和力学

2016 Vol. 37, No. 10

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A Directional Shape-Preserving Topology Optimization Method With Multi-Point Constraints

ZHU Ji-hong, WANG Lin, LI Yu, ZHANG Wei-hong

2016, 37(10): 999-1012. doi: 10.21656/1000-0887.370255

Abstract(1404) PDF(963)

Abstract:
Shape preservation of aerodynamic surfaces and functional surfaces was an important aspect in aircraft stiffness design. An extended topology optimization method was presented with directional shape-preserving constraints, which suppressed the warping deformation of structural local domains in particular directions and generated required deformation patterns. On the one hand, artificial weak elements (AWEs) were established with respect to the finite control points in local shape-preserving domains. Multi-point constraints (MPCs) were further applied to transfer nodal displacements at the control points to nodes of the AWEs. Strain energy of the AWEs was then constrained to suppress the warping deformation. On the other hand, the MPCs were properly defined to transfer only the displacements of the specified degrees of freedom to be suppressed. Directional shape preservation was in turn achieved. The numerical examples and optimized designs prove the validity of the proposed method in maintaining directional shape preservation based on the stiffness maximization topology optimization. Compared with the existing shape-preserving topology optimization design method, the proposed directional shape-preserving one brings more flexibility in controlling the local structural deformation.

A Meshless Intervention-Point Method With h-p-d Adaptability

YANG Jian-jun, ZHENG Jian-long

2016, 37(10): 1013-1025. doi: 10.21656/1000-0887.370159

Abstract(1965) PDF(1322)

Abstract:
A truly meshless method, the meshless intervention-point (MIP) method, was presented. The moving least squares core (MLSC) approximation was applied to build the shape functions, and to help formulate a more simple and stable algorithm. Furthermore, a local intervention-point approximation technique for numerical discretization was introduced to endow the method with the h-p-d adapability, which meant higher flexibility and applicability in reality. The results from several numerical tests show that the proposed method is simple, efficient and accurate, and exhibits all-round potential for engineering computation.

Numerical Simulation of Impact Dynamic Responses and Interlayer Failure of CFRMLs Under Thermal Loads

TANG Xiao-jun, HUI Tian-li, WANG Zhen-qing, YANG Feng-long

2016, 37(10): 1026-1038. doi: 10.21656/1000-0887.370092

Abstract(1280) PDF(866)

Abstract:
To investigate the impact response characteristics of carbon fiber reinforced metal laminates (CFRMLs) and the effects of thermal loads on the impact performance of CFRMLs, the VUMAT user subroutine for composite progressive damage modes and the Johnson-Cook model based on ABAQUS/Explicit were employed to simulate the impact response process of carbon fiber reinforced epoxy resin matrix composite-stainless steel laminates under different ambient temperatures. The dynamic responses and damage evolution of CFRMLs were discussed. The effects of thermal loads on the kinetic energy absorption, the contact force and the failure modes of CFRMLs were analyzed detailedly. The results show that the main failure forms of CFRMLS under high-speed impact loads involve the brittle fracture of carbon fiber layers, the plastic deformation of metal layers and the delamination between carbon fiber layers and metal layers. The thermal load has significant effects on the impact performance of CFRMLs. The residual bullet velocity and the contact force between the bullet and CFRMLs are directly influenced by the thermal load. In general, with the rise of the ambient temperature, the contact force decreases while the residual bullet velocity increases. This indicates that the thermal load rise reduces the kinetic energy absorption capability of CFRMLs, and weakens the anti-impact performance of CFRMLs. The thermal load also has great effects on the global failure, fiber failure, matrix failure and delamination of CFRMLs during the impact process.

A Finite Element Method With Generalized DOFs for Stress Intensity Factors of Crack Groups

XU Hua, XU De-feng, YANG Lü-feng

2016, 37(10): 1039-1049. doi: 10.21656/1000-0887.370050

Abstract(1010) PDF(1176)

Abstract:
Stress intensity factors (SIFs) at crack tips of crack groups were solved by means of the finite element method with generalized DOFs. Firstly, based on the improved Williams series, the typical Williams elements in the singular region around the crack tip were set up. Then the global governing equations were formulated through intergration of the block matrices. Finally, with the undetermined parameters of the Williams series, SIFs at all the crack tips could be directly obtained. The influences of the parameters such as the distance between the centers of 2 adjacent cracks, and angle γ between the oblique crack and axis X on the calculation results were further analyzed through several examples. The results show that the proposed method can effectively overcome the defects of traditional finite element methods and it has higher accuracy and efficiency. Moreover, as for an infinite plate with multiple collinear horizontal cracks, when the ratio of the distance between the centers of 2 adjacent cracks to the half crack length is bigger than 9, the interaction among cracks can be ignored, so multiple cracks can be regarded as a single crack for calculation. For an infinite plate with an even number of axisymmetric oblique cracks, as angle γ increases, K_Ⅰ decreases, but K_Ⅱ first increases and then decreases.

Structure-Preserving Algorithm for Fluid-Solid Coupling Dynamic Responses of Saturated Poroelastic Rods

LIU Xue-mei, DENG Zi-chen, HU Wei-peng

2016, 37(10): 1050-1059. doi: 10.21656/1000-0887.370106

Abstract(945) PDF(579)

Abstract:
Based on the momentum balance equations for 3D fluid-solid mixture, the momentum balance equations for pore fluid and the balance equations of volume fraction, the fluid-solid coupling axial vibration equations for saturated poroelastic rods were established. With the orthogonal variables, a 1st-order multi-symplectic structure-preserving form of the axial vibration equations was built firstly, then the generalized multi-symplectic conservation law and the errors of the modified local momentum were derived. The axial displacement profile of the solid skeleton and the seepage velocity profile of the pore fluid were obtained, where the effect of the dissipation constant on the axial dynamic responses was also revealed numerically. Compared with the analytical solution derived with the variable-separating method, this generalized multi-symplectic structure-preserving scheme has excellent validity and high accuracy. The generalized multi-symplectic conservation law and its corresponding conditions were presented. Meanwhile, the numerical errors of the generalized multi-symplectic conservation law and the generalized multi-symplectic local momentum were both investigated for different dimensionless parameters. The results show that the proposed generalized multi-symplectic structure-preserving scheme has long-time numerical stability and good conservation properties.

Research on the Integration Method for Laser Beam Progagation in Turbulent Flows

XU Ling-fei, ZHOU Zhi-chao, REN Tian-rong

2016, 37(10): 1060-1072. doi: 10.21656/1000-0887.370065

Abstract(874) PDF(1135)

Abstract:
The integration method for the solution of the Maxwell equations with the Born approximation was less utilized in the aero-optic numerical simulation because of its difficulty in the discrete calculation. Combined with the generalized convolution-FFT (GCV-FFT) algorithm, the more accurate results were obtained from the numerical computation of the Rayleigh-Sommerfeld diffraction in the free space. With some modifications to the Green function and the sampling coefficients, the integration method can be used in the numerical simulation of aero-optics. The laser beam propagation through a supersonic boundary layer shows that the effects of aero-optics (beam break, beam shift, etc.) can be well simulated with the integration method combined with the generalized GCV-FFT algorithm. The numerical simulation results gotten with the proposed integration method would be closer to the problems’ physical essence due to its independence from the paraxial approximation.

Nonlinear Evolution of Stationary Crossflow Vortices in Swept-Wing Boundary Layers

LU Xue-zhi, ZHAO Lei, LUO Ji-sheng

2016, 37(10): 1073-1084. doi: 10.21656/1000-0887.370152

Abstract(1244) PDF(675)

Abstract:
The crossflow instability was one of the main forms of instability in sweptwing boundary layers. Previous investigations indicated that the stationary crossflow vortex underwent a period of nonlinear saturation before the transition, so the linear stability theories couldn’t effectively predict the transition process caused by the crossflow instability and it was essential to study the nonlinear evolution of stationary crossflow vortices. A 45°-sweepback and -4°-attack-angle NLF(2)-0415 airfoil under the condition of Ma=0.8 was studied. The nonlinear evolution of stationary crossflow vortices was computed with disturbance equations. The results illustrate that the nonparallelism plays a more unstable role. The nonlinear interaction begins to be obvious when the amplitude of the 1st order wave reaches around 0.1. The crossflow vortex undergoes a procedure of amplitude saturation, and the vortex shape is like a half-mushroom structure. The vortex axis is parallel to the inviscid potential flow direction. These vortices distort the velocities, and make the streamwise and spanwise velocity profiles go through inflection points.

Supersonic Flutter Analysis for Aeroelastic Multibody Systems

XU Bin, ZHANG Wen, MA Jian-min

2016, 37(10): 1085-1099. doi: 10.21656/1000-0887.370114

Abstract(1254) PDF(1048)

Abstract:
The supersonic flutter of aeroelastic multibody systems was investigated. Based on the theory of multibody dynamics and the piston theory for unsteady aerodynamic forces, the governing differential algebraic equations (DAEs) for the aeroelastic multibody system were established. The supersonic flutter analysis was conducted through solution of the eigenvalue problem in the form of DAEs to discuss the stability of the perturbed motion and the equilibrium of the multibody system. The approach was used for the supersonic flutter problems of a plate wing and a wing with control surfaces. The flutter speed of the wing was obtained with the control surfaces in different positions. The agreement between the simulation results and the experimental ones shows that, the present method has high computational accuracy, and is suitable for the flutter analysis of engineering structures consisting of multiple components.

Coherent Disturbance Structures and Bed Topography Responses in Large Depth-to-Width Ratio River Bends With Constant Curvatures

GAO Shu-xian, XU Hai-jue, BAI Yu-chuan

2016, 37(10): 1100-1117. doi: 10.21656/1000-0887.370094

Abstract(1003) PDF(468)

Abstract:
The bed topography is the result of the dynamic response of a complex meandering river system, and is an important factor influencing the further river development. Based on meandering rivers characterized by large depth-to-width ratios, the relation between the hydraulic structure and the bed topography was explored. The flow characteristics and bed topography responses were discussed through coupling of the N-S equations, the sediment transport equations as well as the bed deformation equations, and with the perturbation method. Research results show that shallows and deep grooves present regular responses under the effects of 2D flow disturbances. For a zero curvature, the bed topography shows an anti-symmetric distribution about the channel centerline; while for a non-zero curvature, the channel centerline deviates toward the concave bank. Finally, the criteria for the judgement on the stability of the bed topography influenced by the Reynolds number, the disturbance wave number and the decay ratio of the bed topography, are given.

Oscillating Flow in Annular Microchannels With Sinusoidally Corrugated Walls

CHANG Long, LIU Quan-sheng, JIAN Yong-jun, Burenmandula, SUN Yan-jun

2016, 37(10): 1118-1128. doi: 10.21656/1000-0887.370116

Abstract(1320) PDF(517)

Abstract:
Oscillating flow in annular microchannels with sinusoidal wall roughness was investigated. The oscillating flow of incompressible viscous fluid was driven by a time-periodically oscillating pressure gradient. Approximate solutions of the velocity and flow rate in the annular microchannel were obtained through computation of the momentum conservation equations in the cylindrical coordinate system with the perturbation method. Based on these approximate solutions, the effects of the relevant nondimensional parameters, such as Reynolds number Re, pressure gradient amplitude A, sinusoidal roughness amplitude ε, ratio of the inner radius to the outer radius α, phase difference β and wave number λ, on velocity u and flow rate Φ_m, were analyzed. The results show that the velocity increases with A and decreases with Re, and phase lag χ increases with Re.