应用数学和力学

A POD-Based Parameterization Model for Material Microstructure Representation and Its Application to Optimal Design of Material Effective Mechanical Properties

GUO Zhi-wen, XIAO Man-yu, XIA Liang

2017, 38(7): 727-742. doi: 10.21656/1000-0887.370279

Abstract(1403) PDF(1092)

Abstract:
With the increasing computing capability, numerical material simulation based on material microstructure images has attracted interest of more and more researchers. Within this context, an efficient numerical material parameterization model was proposed for the representation of material microstructures. First, the eigenvalue analysis of the material microstructure image data was carried out through the proper orthogonal decomposition (POD) to extract a common POD basis. The material microstructure image can be represented as a linear combination of the retained POD basis. Then, response surfaces of the POD projection coefficients with respect to the controlling parameters were built with the method of moving least squares. By means of this numerical parameterization model, the corresponding material microstructure image for arbitrary input controlling parameters can be reconstructed. Application of this model was demonstrated in view of a set of 2phase composite material snapshots. This parameterized material microstructure representation model can also been applied to the optimal design of material effective mechanical properties.

MLS-Based Postprocessing Procedure for Discontinuous Deformation Analysis

SUN Yue, FENG Xiang-chu, XIAO Jun, WANG Ying

2017, 38(7): 743-754. doi: 10.21656/1000-0887.370259

Abstract(1245) PDF(653)

Abstract:
The discontinuous deformation analysis (DDA) simulates fracture propagations by introducing fictitious joint meshes in blocks to generate sub-blocks. In order to obtain accurate stress distributions with this method, a stress recovery procedure was proposed based on the moving least squares (MLS) interpolation technique. With the MLS shape functions and their derivatives, the stress at any point within a block can be expressed by means of nodal displacements. Numerical examples were given to verify the accuracy and effectiveness of the proposed method. Comparison of the stress results between the analytical method, the averaging postprocessing method and the proposed MLS-based postprocessing procedure indicates that, the MLS-based stress recovery procedure is of high accuracy in providing more reliable block stress distributions.

A Constitutive Model for Polyether Ether Ketone (PEEK) in Various Mechanical States

ZHANG Heng, YAN Biao, YIN Hong-ling, XU Yong-cheng, PENG Xiong-qi, PENG Fu-jun

2017, 38(7): 755-761. doi: 10.21656/1000-0887.370283

Abstract(1449) PDF(1042)

Abstract:
Polyether ether ketone (PEEK) with its excellent performances is widely used in advanced machinery, nuclear engineering, aviation, aerospace and other scientific & technological fields. In order to describe the mechanical behaviors of PEEK in view of coupled effects of strain, strain rate and temperature, based on the famous JC (Johnson-Cook) constitutive model, a piecewise JC constitutive model was established for PEEK in 3 mechanical states at different temperatures. Compared with the traditional JC model and a modified one in previous literatures, the proposed piecewise JC constitutive model can better predict the flow behaviors of PEEK at high temperatures. It provides a theoretical foundation for the numerical simulation and engineering application of PEEK in composites in the future.

Dynamic Modelling and Symplectic Solution of Coupled Orbit & Attitude for Solar Sail Towers

WEN Fen-qiang, DENG Zi-chen, WEI Yi, LI Qing-jun

2017, 38(7): 762-768. doi: 10.21656/1000-0887.370321

Abstract(1215) PDF(578)

Abstract:
A simplified model for solar sail towers was established. Firstly, the dynamic equations for the system were transformed from the Lagrangian system into the Hamiltonian system, and the canonical constrained Hamiltonian equations were obtained. Then the dynamic characteristics of the coupled orbit-attitude system of the solar sail tower were analyzed with the symplectic Runge-Kutta method and the Zu-class method. Energy and constraint conservation problems of the schemes were also investigated. Finally, the dynamic characteristics of the system were numerically simulated. The results illustrate the effectiveness of the proposed method.

Flutter Characteristics Analysis of 2D Rigid Airfoils With Control Surface Based on the Arc-Length Numerical Continuation Method

CHEN Heng, WANG Yang-yu, JIN Jiang-ming

2017, 38(7): 769-779. doi: 10.21656/1000-0887.370223

Abstract(1452) PDF(640)

Abstract:
A 3-DOF aeroelastic model was built for 2D rigid airfoils with control surface. This model was simplified with cubic nonlinear stiffness in heave and pitch, where the freeplay control surface was replaced with bilinear stiffness. According to the quasi-steady aerodynamic theory, the motion equations for the system was established. The peak-to-peak value diagram was used to depict the global dynamic properties of the airfoil at different flow velocities, and the arc-length numerical continuation method together with the Floquet multiplier was applied to construct the bifurcation diagram and study the aerodynamic stability. The bifurcation diagram matched the peak-to-peak value diagram well. The results show there are various dynamic behaviors due to freeplay nonlinearity. The aeroelastic model yields complicated limit cycle oscillations, quasi-periodic motions and chaotic phenomena when the angular displacement of the control surface reaches the clearance limit.

LBM Simulation of Double Diffusive Mixed Convection in a Porous Medium Composite Cavity

LU Wei, WANG Ting-ting, XU Hong-tao, CHEN Jian, YANG Mo

2017, 38(7): 780-793. doi: 10.21656/1000-0887.370175

Abstract(1168) PDF(1077)

Abstract:
Based on the coupled lattice Bhatnagar-Gross-Krook (CLBGK) model, the lattice Boltzmann method was used and the concentration distribution function was introduced to investigate the double diffusive mixed convection in a lid-driven composite cavity composed of a porous medium layer and the rest space full of pure fluid. At Ri=1.0, Le=2.0, Gr=10⁴, Pr=0.7, ε=0.7, the influences of the porous layer locations and the buoyancy ratios（-5.0≤N≤5.0） on the double diffusive mixed convection in the porous medium composite cavity were studied at the pore scale. Results presented in the distribution diagrams of local and average Nusselt and Sherwood numbers at the high temperature and concentration wall of the cavity show the mixed convection rule.

Low-Dimensional Analysis and Numerical Simulation of Rotating Flow

WANG He-yuan, CUI Jin

2017, 38(7): 794-806. doi: 10.21656/1000-0887.360342

Abstract(1461) PDF(1489)

Abstract:
In order to explore the transition way of the Couette-Taylor flow from laminar flow to turbulence and the characteristics of chaotic attractors in turbulence, dynamic behaviors and numerical simulation of the Couette-Taylor flow were studied by means of the low-dimensional analysis method. The dynamic properties of the 3-model Lorenz-type system of the Couette-Taylor flow were discussed, including the stability of equilibrium points, the occurence of limit cycles, the evolution of bifurcation and chaos, as well as the global stability etc. Through linear stability analysis and numerical simulation, the dynamic behavior and evolution history of bifurcation and chaos of this low-dimensional model were presented. Consequently, successive transitions of the Couette-Taylor flow from laminar flow to turbulence in the experiment were explained. The numerical simulation results of bifurcation diagrams, Lyapunov exponent spectra, Poincaré sections, power spectra and return mappings of the system reveal the general features of the system chaos behaviors.

Effects of Surface Topography on Friction Noise Under Elastohydrodynamic Lubrication Condition

LI Zhi, CHEN Jian, SHEN Jin-long, LIU Xiao-jun

2017, 38(7): 807-817. doi: 10.21656/1000-0887.370231

Abstract(1101) PDF(1169)

Abstract:
The effects of surface topography on the friction noise were studied under the elastohydrodynamic lubrication (EHL) condition. 2 kinds of groove-textured surface topographies were fabricated by laser texturing on the surface of the metal disc specimen. Friction noises and friction characteristics of different surface topographies were tested on a modified JPM-1 2-disc tribo-tester. The effects of different operating conditions and surface topographies on the friction noise under line contact EHL conditions were analyzed, and the results were verified with the finite element analysis. The work shows that, variations of the load and the rotational speed have significant effects on the line contact friction noise. Since the line contact pairs usually work in a partial EHL condition, the friction noise characteristics are similar to those of dry friction: the surface with a larger friction coefficient will radiate stronger friction noise. Specific topographies can improve the lubrication characteristics of the surface, and effectively reduce the sound pressure level of the friction noise. The presence of groove textures can interrupt the stress distribution of the contact area and weaken the impact by surface asperities, thereby reducing the self-excited vibration. At the same time, the proper surface topography structure is also helpful in the formation of lubricating oil film, hence lowering the friction noise as well as the friction energy of the system.

Properties of Positive Solutions to a Class of Fractional Differential Equations With Parameters and Integral Boundary Conditions

FENG Hai-xing, ZHAI Cheng-bo

2017, 38(7): 818-826. doi: 10.21656/1000-0887.380124

Abstract(1275) PDF(545)

Abstract:
A class of boundary value problems of fractional differential equations with parameters were studied. Based on the fixed point theorem and the properties of the mixed monotone operator eigenvalue problems, some characteristics of positive solutions to the fractional differential equations depending on the parameters were obtained: existence and uniqueness, monotonicity, continuity and limitations. In the end, an example was given to illustrate the rationality of the main results.

Study of Semistrict-G-E-Semipreinvex Functions and Applications in Nonlinear Programming

PENG Zai-yun, SUN Jia-hui, LI Ke-ke, ZHANG Shi-sheng

2017, 38(7): 827-836. doi: 10.21656/1000-0887.370280

Abstract(1227) PDF(452)

Abstract:
A new class of generalized convex functions, namely the semistrict-G-E-semipreinvex functions were proposed, which are a class of very important generalized convex functions and make a true generalization of both the semistrict-G-semipreinvex functions and the semistrict-E-preinvex functions. Firstly, several examples were given to illustrate the existence of semistrict-G-E-semipreinvex functions and the dependence on the related generalized convex functions. Afterwards, the basic characteristics of the semistrict-G-E-semipreinvex functions were discussed. Finally, some applications of the semistrict-G-E-semipreinvex functions in nonlinear programming problems without constraint and with inequality constraints were studied respectively, and some optimality results were obtained; moreover, some examples were given to illustrate the correctness of the obtained results.

Solutions to the Gain Flux Coupling System of Laser Pulse Amplifiers

FENG Yi-hu, CHEN Huai-jun, MO Jia-qi

2017, 38(7): 837-844. doi: 10.21656/1000-0887.370208

Abstract(1020) PDF(465)

Abstract:
The solutions to the gain flux coupling system of laser pulse amplifiers were studied. Firstly, the system of the general model was discussed; secondly, the homotopic mapping was used and an artificial parameter was introduced with the property of the mapping, to transform the nonlinear problem to a series of linear problems, which were solved one by one. Then the approximate expressions of the solutions to the corresponding model were obtained. The expansion of solutions with the homotopic mapping method is analytic, where the analytic operations of the functions are kept and the approximate solutions are expressed with elementary functions, which are different from the numrically computed discrete solutions and can be further analytically computed. Thus the differential and integral operations can be implemented to obtain other physical behaviors of the gain flux for laser pulse amplifiers.

2017 Vol. 38, No. 7