应用数学和力学

2013 Vol. 34, No. 8

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Nonconforming Isogeometric Analysis With FETI Method

ZHU Xue-feng, HU Ping, MA Zheng-dong, LIU Wei

2013, 34(8): 771-781. doi: 10.3879/j.issn.1000-0887.2013.08.001

Abstract(2252) PDF(1889)

Abstract:
Nonconforming isogeometric analysis (NIGA) with FETI method was proposed. The major purpose was to enable applying the isogeometric analysis directly to the NURBS models with trimmed patches for more general and practical engineering applications. The basic idea was to use the NURBS version of FETI to replace the zero space algorithm. The present method can deal with large scale engineering problem rapidly and is suitable for parallel computing. Numerical examples for patch tests and a car body analysis are presented to verify the efficiency of this method.

Legendre Series Solution to Rayleigh Stability Equation of Mixing Layer

GUO Xin, WANG Xian, XU Ding, XIE Gong-nan

2013, 34(8): 782-794. doi: 10.3879/j.issn.1000-0887.2013.08.002

Abstract(1580) PDF(1152)

Abstract:
Based on the fixed point concept in functional analysis, the fixed point method (FPM) was used to analyze the invisicd stability equation of the mixing layer, and an explicit semi-analytical solution in Legendre series form was obtained. It is different from other existing analytical methods, such as the well-known perturbation technique, because FPM can obtain a uniformly convergent solution in the full infinite flow domain. Meanwhile, the present Legendre series solution is valid to all wave numbers. What’s more, in the framework of FPM, the eigenvalue can be determined by the solvability condition in a straightforward manner. Finally, the comparison between FPM and other numerical methods shows that FPM is of high accuracy and efficiency.

Symplectic Conservative Approach for Solving Nonlinear Closed-Loop Feedback Control Problems Based on Quasilinearization Method

JIANG Xin, PENG Hai-jun, ZHANG Sheng

2013, 34(8): 795-806. doi: 10.3879/j.issn.1000-0887.2013.08.003

Abstract(1620) PDF(1065)

Abstract:
A symplectic approach was proposed to solve the nonlinear closed-loop feedback control problems. First, the optimal control problems of the nonlinear system were transformed into the iteration form of linear Hamilton system’s two-point boundary value problems. Second, a symplectic numerical approach was deduced based on dual variable principle and generating function. This method can keep the symplectic geometry structure of the Hamilton system. Last, with the state vector updated and input controlted by the forwarding of time steps, the goal of closed-loop control was achieved. The numerical simulation shows that the proposed symplectic method has high precision and fast iteration speed. In addition, the closed-loop feedback control and open-loop control were used separately to analyze the inverted pendulum control system. The results show that in the case of the presence of initial errors, open-loop control will result in the failure of the stability control tasks, while closed-loop feedback control will eliminate the initial errors after a certain period of time and lead the system to a stable state.

A Novel High-Order Immersed Boundary Method Based on Filter and Deconvolution Operation

FANG Le1

2013, 34(8): 807-814. doi: 10.3879/j.issn.1000-0887.2013.08.004

Abstract(1739) PDF(1208)

Abstract:
The traditional immersed boundary method has only first-order accuracy near boundary. Existing improvements need additional jump conditions thus are not general. A novel method based on filter and deconvolution was introduced. It improved the accuracy, and avoided the problems of jump conditions. A simple 1-D case was performed to proove that the accuracy was nearly second order. It is found that the exact order value depends on the boundary continuity of the inverse kernel function chosen in deconvolution.

Algorithm of Super-Convergent in Two-Dimensional Finite Element of Lines Based on Improved Displacement Mode

TANG Yi-jun, LUO Jian-hui

2013, 34(8): 815-823. doi: 10.3879/j.issn.1000-0887.2013.08.005

Abstract(1902) PDF(1217)

Abstract:
Algorithm of super-convergent in two-dimensional finite element of lines (FEMOL) based on improved displacement mode is presented. An explicit analytical formula of super-convergent calculating was derived with the conditions of equilibrium equations stuictly met within the element, of which the displacement mode of high-order finite element of lines solution was expressed with that of a conventional finite element of lines solution. The new displacement mode was constructed with the sum of the displacement mode of conventional finite element of lines solution and that of high-order finite element of lines solution. Based on the linear shape function, the improved ordinary differential equations for FEMOL solution were derived in the rariation form. The super-convergent formula was used for this algorithm in both the pre-processing and post-processing to improve the accuracy of the solution and reduce the residual of balance equation, with the higher-order trial function added the original trial function. A calculation example is presented for Poisson’s equation of a two-dimensional problem, the convergence accuracy of the displacement and derivative at nodes and in elements is greatly improved.

Wind Resistant Optimization of Spatial Truss Structures Under Multi-Constraints

HUANG You-qin, LIN Jun-hong, FU Ji-yang, WU Jiu-rong

2013, 34(8): 824-835. doi: 10.3879/j.issn.1000-0887.2013.08.006

Abstract(1718) PDF(1066)

Abstract:
The existing wind resistant optimization research on wind-sensitive structures mostly focused on high-rise buildings, and large span roof structures were seldom involved. The wind resistant optimization problem under multi-constraints like strength, stiffness and geometric dimensions, was converted to an unconstrained problem based on the principle of virtual work and Lagrange multiplier. A numerical program including finite element computation and optimization analysis was then developed to optimize a real double-layer cylindrical reticulated shell with 10 080 bars, followed by discussion of the influences of design variable feasible regions, design variable initial values and adjusting steps on the optimum results. Studies show that wind resistant performance of spatial truss structures under multi-constraints can be efficiently optimized by the proposed approach, and total weight of the shell is decreased by 37%. Lower limits of the design variables are necessary owing to non-uniform distribution of wind-induced responses, and different choices of initial design variables and adjusting steps could hardly influence the final optimum results.

Semistrict-G-Semi-preinvexity and Optimization

PENG Zai-yun, LI Yong-hong

2013, 34(8): 836-845. doi: 10.3879/j.issn.1000-0887.2013.08.007

Abstract(1629) PDF(1100)

Abstract:
A class of new generalized convex function——semistrict-G-semi-preinvex functions is given.It is an important class of generalized convex function. It is a true generalization of semistrict preinvex functions and semistrict-G-preinvex functions. First, an example was given to show that there exist semistrict-G-semi-preinvex functions. At the same time, examples were given to show that the semistrict-G-semi-preinvex functions were different from G-semi-preinvex functions. Then, some properties of the semistrict-G-semi-preinvex functions were discussed. Finally, some optimality results were obtained in nonlinear programming problems without constraint and with inequality constraint, and examples were given for illustration of the corresponding results.

Research on the Calculation Method of Pressure Field Caused by the Ship Moving at Subcritical Speed in Shallow Water

DENG Hui, ZHANG Zhi-hong, LIU Ju-bin, GU Jian-nong

2013, 34(8): 846-854. doi: 10.3879/j.issn.1000-0887.2013.08.008

Abstract(1852) PDF(1363)

Abstract:
A mathematical model for pressure field caused by the ship moving at subcritical speed in shallow water was established, based on the shallow water wave potential flow theory and slender ship assumption. The pressure field caused by the ship moving at subcritical speed in shallow water was calculated by the finite difference method.The effects of channel wall, depth Froude number and dispersion characteristics on the ship hydrodynamic pressure field were analyzed.The calculation results were improved by the virtual length method.The computed results were compared with the ones calculated by source distribution method,Fourier integral transform method and experimental results. The mathematical model and the calculation method were validated.

Fluid Flow and Heat Transfer Analysis of Single-Phase Steady Laminar Flow in Rectangular Micro-Channel Heat Sinks

WANG Li-feng, SHAO Bao-dong, CHENG He-ming, TANG Yan-jun

2013, 34(8): 855-862. doi: 10.3879/j.issn.1000-0887.2013.08.009

Abstract(1654) PDF(1489)

Abstract:
Fluid flow and heat transfer of single-phase steady laminar flow in a rectangular micro-channel were investigated by analytic method. Based on the assumption of constant flow velocity and heat transfer along y-direction, flow velocity and heat transfer equations for fluid flow in the rectangular micro-channel were set up. Then the theoretical expressions of Nusselt number and Poiseuille number were derived. The computed results show that the analytic solutions derived coincide well with the results of other literatures. When the aspect ratio of cross section tends to infinity, Nusselt number and Poiseuille number tend to be 8.235 and 96, respectively, which are identical to those of other literatures. When Reynolds number is fixed, the friction coefficient increases with the aspect ratio, and when the aspect ratio is fixed, friction coefficient decreases with Reynolds number increase.

An Efficient Numerical Integration Method for the Capillary Hysteresis Internal Variable Model

LI Wen-tao, WEI Chang-fu, MA Tian-tian

2013, 34(8): 863-870. doi: 10.3879/j.issn.1000-0887.2013.08.010

Abstract(1735) PDF(1078)

Abstract:
Derived from thermo dynamic principle, the capillary hysteresis internal variable model is capable of describing the capillary hysteretic phenomena in unsaturated soils. The mathematical characteristics of this model were studied, followed by a numerical experimentation with classical Euler method, fourth-order Runge-Kutta method and fourth-order Adams-Bashforth method. The results show that Euler method has lower accuracy and larger accumulated error, whereas Adams-Bashforth method holds the upper most accuracy and the better efficiency compared with the same order Runge-Kutta method and is suitable for the solution and calibration of the internal variable model. Moreover, Adams-Bashforth method is implemented into the finite element programme, leading to more accurate results in simulation of two-phase flow.

Comparisons of Several Non-Probabilistic Models for Structural Reliability

WANG Rui-xing, WANG Xiao-jun, WANG Lei, QIU Zhi-ping

2013, 34(8): 871-880. doi: 10.3879/j.issn.1000-0887.2013.08.011

Abstract(1863) PDF(1212)

Abstract:
Non-probabilistic models for structural reliability, which are based on interval analysis, are much less demanding in data when compared with probabilistic reliability models and fuzzy reliability models. Therefore, study of non-probabilistic models for structural reliability becomes more and more significant in practical projects. Theory of non-probabilistic models for structural reliability was well developed and improved in recent years. The existing four main non-probabilistic models for structural reliability were reviewed. With regard to the linear performance function, comparison and summary were made in aspects of measurement principle, physical significance of indicators, scope of application and result accuracy. As for the nonlinear performance function, the four models’ feasibility was discussed. Hence, a more comprehensive and thorough understanding of non-probabilistic models for structural reliability is achieved a theoretical base for choice of non-probabilistic models in practical projects provided.