应用数学和力学

2015 Vol. 36, No. 8

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The Bi-Potential Theory Applied to Non-Associated Constitutive Laws

ZHOU Yang-jing, FENG Zhi-qiang, NING Po

2015, 36(8): 787-804. doi: 10.3879/j.issn.1000-0887.2015.08.001

Abstract(1674) PDF(850)

Abstract:
The explicit integration algorithm based on the traditional plastic mechanics framework and the implicit integration algorithm proposed by Simo-Taylor were 2 classic constitutive integration algorithms widely used in solid mechanics. These 2 algorithms were reviewed respectively with the 2 correspon...

Multi-Scale Analysis of Piezoelectric Energy Harvesters With Magnetic Oscillators

ZHAO Jian, ZHANG Guo-ce, CHEN Li-qun

2015, 36(8): 805-813. doi: 10.3879/j.issn.1000-0887.2015.08.002

Abstract(1483) PDF(969)

Abstract:
A piezoelectric energy harvester with a magnetic oscillator was studied. The dynamic equation was derived via introduction of coordinate transform based on the equilibrium configuration. The Taylor series expansion method was employed to deal with the nonlinear function of the magnetic force. The mu...

Bandgap Properties of Periodic 4-Point Star-Shaped Honeycomb Materials With Negative Poisson’s Ratios

YUN Hao, DENG Zi-chen, ZHU Zhi-wei

2015, 36(8): 814-820. doi: 10.3879/j.issn.1000-0887.2015.08.003

Abstract(1678) PDF(1049)

Abstract:
The bandgap properties of the periodic 4-point star-shaped honeycomb materials with negative Poisson’s ratios were investigated. The in-plane wave propagation in the honeycomb material was analyzed with the finite element method and according to the Bloch theorem. Attention was devoted to determinin...

Elastoplastic Damage Analysis of Powder Metallurgy Superalloy Based on the Cosserat Continuum Theory

ZHANG Cheng-cheng, YANG Dong-sheng, REN Yuan, ZHANG Sheng

2015, 36(8): 821-832. doi: 10.3879/j.issn.1000-0887.2015.08.004

Abstract(1551) PDF(712)

Abstract:
The development of the powder metallurgy (PM) superalloy applied in turbine discs of high thrust-weight ratio aeroengines was reviewed. Based on the Cosserat continuum theory, the elastoplastic damage model for the PM superalloy was developed in which the microscopic properties were modeled with the...

Lie Group and Lie Algebra Modeling for Numerical Calculation of Rigid Body Dynamics

BAI Long, DONG Zhi-feng, GE Xin-sheng

2015, 36(8): 833-843. doi: 10.3879/j.issn.1000-0887.2015.08.005

Abstract(1931) PDF(1233)

Abstract:
The Lie group dynamics equation for rigid bodies was derived based on the exponent mapping equivalence relationship between the Lie group and Lie algebra. The discrete Lie group variational integrator was derived according to the discrete variation theory. The momentum conservation of the 2 Lie grou...

Study on the Transient Temperature Field Based on the Fractional Heat Conduction Equation for Laser Heating

XU Guang-ying, WANG Jin-bao, HAN Zhi

2015, 36(8): 844-854. doi: 10.3879/j.issn.1000-0887.2015.08.006

Abstract(1834) PDF(1489)

Abstract:
Based on the fractional Taylor series expansion principle, the 1st-order fractional approximate heat conduction constitutive equation was formulated through expansion of the single-phase lag model. Combined with the energy equation, the fractional heat conduction equations were built for short pulse...

Creep Analysis of Simply Supported-to-Continuous Box Girders Under Shear Lag Effect

SUN Yong-xin, LIN Peng-zhen

2015, 36(8): 855-864. doi: 10.3879/j.issn.1000-0887.2015.08.007

Abstract(1600) PDF(947)

Abstract:
To analyze how creep interacts with shear lag effect in concrete box girders, the calculation formulae for the creep secondary internal force and stress were derived with the energy variation method. With a simply supported-to-continuous box girder for example, the creep bending moment and stress we...

A Real-Time Identification Method for the Bottomhole Gas Invasion State in Managed Pressure Drilling

HE Miao, LIU Gong-hui, LI Jun, ZHANG Tao, LI Meng-bo, GUO Qing-feng

2015, 36(8): 865-874. doi: 10.3879/j.issn.1000-0887.2015.08.008

Abstract(1243) PDF(853)

Abstract:
Real-time identification of the bottomhole gas invasion state is the key to well control during managed pressure drilling (MPD), which is directly related to the selection of follow-up operations involving the gas circulation exhaust based on standpipe pressure control or the conventional shut-in pr...

A Reduced-Order Extrapolating FDM for Conserved High-Order Anisotropic Traffic Flow Models

LUO Zhen-dong, XU Yuan

2015, 36(8): 875-886. doi: 10.3879/j.issn.1000-0887.2015.08.009

Abstract(1866) PDF(988)

Abstract:
A reduced-order extrapolating finite difference method (FDM) with sufficiently high accuracy and very few degrees of freedom for conserved high-order anisotropic traffic flow models was established by means of the Godunov fluid method and the POD technique. The error estimate of the reduced-order ap...

A Numerical Method for the Solutions to Nonlinear Dynamic Systems Based on Cubic Spline Interpolation Functions

LI Peng-zhu, LI Feng-jun, LI Xing, ZHOU Yue-ting

2015, 36(8): 887-896. doi: 10.3879/j.issn.1000-0887.2015.08.010

Abstract(2234) PDF(1279)

Abstract:
The cubic spline interpolation function has good convergence, stability and 2nd-order smoothness. A numerical method for the solutions to nonlinear dynamic systems was constructed with the cubic spline interpolation functions. Advantages and disadvantages were compared between this method and the pr...