Table of Content

01 September 2014, Volume 35 Issue 9

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Articles

Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

Hai-jun PENG;Qiang GAO;Hong-wu ZHANG;Zhi-gang WU;Wan-xie ZHONG

2014, 35(9):  1079-1098.  doi:10.1007/s10483-014-1858-6

Abstract ( 856 )   HTML   PDF (638KB) ( 410 )  

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A parametric variational principle and the corresponding numerical algorithm are proposed to solve a linear-quadratic (LQ) optimal control problem with control inequality constraints. Based on the parametric variational principle, this control problem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is effective for LQ optimal control problems with control inequality constraints.

Bifurcation analysis of fan casing under rotating air flow excitation

Deng-zhe WEN;Yu-shu CHEN

2014, 35(9):  1099-1114.  doi:10.1007/s10483-014-1853-6

Abstract ( 619 )   HTML   PDF (1538KB) ( 210 )  

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A fan casing model of cantilever circular thin shell is constructed based on the geometric characteristics of the thin-walled structure of aero-engine fan casing. According to Donnelly's shell theory and Hamilton's principle, the dynamic equations are established. The dynamic behaviors are investigated by a multiple-scale method. The effects of casing geometric parameters and motion parameters on the natural frequency of the system are studied. The transition sets and bifurcation diagrams of the system are obtained through a singularity analysis of the bifurcation equation, showing that various modes of the system such as the bifurcation and hysteresis will appear in different parameter regions. In accordance with the multiple relationship of the fan speed and stator vibration frequency, the fan speed interval with the casing vibration sudden jump is calculated. The dynamic reasons of casing cracks are investigated. The possibility of casing cracking hysteresis interval is analyzed. The results show that cracking is more likely to appear in the hysteresis interval. The research of this paper provides a theoretical basis for fan casing design and system parameter optimization.

 

Variational principles for buckling and vibration of MWCNTs modeled by strain gradient theory

Xiao-jian XU;Zi-chen DENG

2014, 35(9):  1115-1128.  doi:10.1007/s10483-014-1855-6

Abstract ( 594 )   HTML   PDF (484KB) ( 355 )  

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Implicit scheme for integrating constitutive model of unsaturated soils with coupling hydraulic and mechanical behavior

Tian-tian MA;Chang-fu WEI;Pan CHEN;Hou-zhen WEI

2014, 35(9):  1129-1154.  doi:10.1007/s10483-014-1859-6

Abstract ( 639 )   HTML   PDF (1064KB) ( 219 )  

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A constitutive model of unsaturated soils with coupling capillary hysteresis and skeleton deformation is developed and implemented in a fully coupled transient hydro-mechanical finite-element model (computer code U-DYSAC2). The obtained results are compared with experimental results, showing that the proposed constitutive model can simulate the main mechanical and hydraulic behavior of unsaturated soils in a unified framework. The non-linearity of the soil-water characteristic relation is treated in a similar way of elastoplasticity. Two constitutive relations are integrated by an implicit return-mapping scheme similar to that developed for saturated soils. A consistent tangential modulus is derived to preserve the asymptotic rate of the quadratic convergence of Newton's iteration. Combined with the integration of the constitutive model, a complete finite-element formulation of coupling hydro-mechanical problems for unsaturated soils is presented. A number of practical problems with different given initial and boundary conditions are analyzed to illustrate the performance and capabilities of the finite-element model.

Similarity solutions for non-Newtonian power-law fluid flow

D. M. WEI;S. AL-ASHHAB

2014, 35(9):  1155-1166.  doi:10.1007/s10483-014-1854-6

Abstract ( 743 )   HTML   PDF (227KB) ( 256 )  

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The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelöf theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curvature of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 < n 1, the solution has a positive curvature, while for n > 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

Width effects on hydrodynamics of pendulum wave energy converter

Dong-jiao WANG;Shou-qiang QIU;Jia-wei YE

2014, 35(9):  1167-1176.  doi:10.1007/s10483-014-1857-6

Abstract ( 539 )   HTML   PDF (414KB) ( 325 )  

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Based on two- and three-dimensional potential flow theories, the width effects on the hydrodynamics of a bottom-hinged trapezoidal pendulum wave energy converter are discussed. The two-dimensional eigenfunction expansion method is used to obtain the diffraction and radiation solutions when the converter width tends to be infinity. The trapezoidal section of the converter is approximated by a rectangular section for simplification. The nonlinear viscous damping effects are accounted for by including a drag term in the two- and three-dimensional methods. It is found that the threedimensional results are in good agreement with the two-dimensional results when the converter width becomes larger, especially when the converter width is infinity, which shows that both of the methods are reasonable. Meantime, it is also found that the peak value of the conversion efficiency decreases as the converter width increases in short wave periods while increases when the converter width increases in long wave periods.

Study of velocity effects on parachute inflation performance based on fluid-structure interaction method

Han CHENG;Xin-hua ZHANG;Li YU;Meng CHEN

2014, 35(9):  1177-1188.  doi:10.1007/s10483-014-1852-6

Abstract ( 534 )   HTML   PDF (727KB) ( 345 )  

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The inflation of a five-ring cone parachute with the airflow velocity of 18 m/s is studied based on the simplified arbitrary Lagrange Euler (SALE)/fluid-structure interaction (FSI) method. The numerical results of the canopy shape, stability, opening load, and drag area are obtained, and they are well consistent with the experimental data gained from wind tunnel tests. The method is then used to simulate the opening process under different velocities. It is found that the first load shock affected by the velocity often occurs at the end of the initial inflation stage. For the first time, the phenomena that the inflation distance proportion coefficient increases and the dynamic load coefficient decreases, respectively, with the increase in the velocity are revealed. The above proposed method is competent to solve the large deformation problem without empirical coefficients, and can collect more space-time details of fluid-structure-motion information when it is compared with the traditional method.

Efficient high-order immersed interface methods for heat equations with interfaces

Jian-kang LIU;Zhou-shun ZHENG

2014, 35(9):  1189-1202.  doi:10.1007/s10483-014-1851-6

Abstract ( 502 )   HTML   PDF (293KB) ( 395 )  

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An efficient high-order immersed interface method (IIM) is proposed to solve two-dimensional (2D) heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact (HOC) difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit (ADI) scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.

High-order Lagrangian cell-centered conservative scheme on unstructured meshes

Quan-wen GE

2014, 35(9):  1203-1222.  doi:10.1007/s10483-014-1856-6

Abstract ( 529 )   HTML   PDF (705KB) ( 264 )  

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A high-order Lagrangian cell-centered conservative gas dynamics scheme is presented on unstructured meshes. A high-order piecewise pressure of the cell is introduced. With the high-order piecewise pressure of the cell, the high-order spatial discretization fluxes are constructed. The time discretization of the spatial fluxes is performed by means of the Taylor expansions of the spatial discretization fluxes. The vertex velocities are evaluated in a consistent manner due to an original solver located at the nodes by means of momentum conservation. Many numerical tests are presented to demonstrate the robustness and the accuracy of the scheme.