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Steady-state responses of axially accelerating viscoelastic beams: Approximate analysis and numerical confirmation

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Science china(Physics,mechanics & Astronomy) 2008年第11期51卷 1707-1721页

作者： CHEN LiQun1,2 & DING Hu2 1 department of mechanics, shanghai university, shanghai 2.0444, china 2 shanghai Institute of Applied Mathematics and mechanics, shanghai 200070, china department of mechanics Shanghai University Shanghai 200444 China shanghai Institute of Applied Mathematics and mechanics Shanghai 200070 China

Nonlinear parametric vibration of axially accelerating viscoelastic beams is inves-tigated via an approximate analytical method with numerical confirmations. Based on nonlinear models of a finite-small-stretching slender beam moving at a speed with a periodic fluctuation, a solvability condition is established via the method of multiple scales for subharmonic resonance. Therefore, the amplitudes of steady-state periodic responses and their existence conditions are derived. The amplitudes of stable steady-state responses increase with the amplitude of the axial speed fluctuation, and decrease with the viscosity coefficient and the nonlinear coefficient. The minimum of the detuning parameter which causes the existence of a stable steady-state periodic response decreases with the amplitude of the axial speed fluctuation, and increases with the viscosity coefficient. Nu-merical solutions are sought via the finite difference scheme for a nonlinear par-tial-differential equation and a nonlinear integro-partial-differential equation. The calculation results qualitatively confirm the effects of the related parameters pre-dicted by the approximate analysis on the amplitude and the existence condition of the stable steady-state periodic responses. Quantitative comparisons demonstrate that the approximate analysis results have rather high precision.

关键词： nonlinearity parametric vibration axially accelerating beam method of multiple scales numerical confir-mation

Some variational principles in electroelastic media under finite deformation

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Science china(Physics,mechanics & Astronomy) 2008年第9期51卷 1390-1402页

作者： KUANG ZhenBang department of Engineering mechanics,shanghai Jiaotong university,shanghai 200240,china department of Engineering mechanics Shanghai Jiaotong University Shanghai 200240 China

It is proposed that the universal thermodynamic energy variational principle is in-cluded in the first law of thermodynamics. Some variational principles in the elec-troelastic media under finite deformation are derived from this universal thermo-dynamic variational principle. It is suggested that in the general electroelastic analysis the environment should be considered together with the discussed elec-troelastic medium. For the variational principle of nonlinear electroelastic media the variation of the electric potential is coupled with the virtual displacement,and the variation of the initial volume should be considered. The Maxwell stress in the initial configuration is naturally derived from this variational principle and it is unique in the second order precision.

关键词： first law of thermodynamics variational principle the electroelastic media the governing equation

The complex variable reproducing kernel particle method for elasto-plasticity problems

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Science china(Physics,mechanics & Astronomy) 2010年第5期53卷 954-965页

作者： CHEN Li1 & CHENG YuMin2 1 department of Engineering mechanics,Chang’an university,Xi’an 710064,china 2 shanghai Institute of Applied Mathematics and mechanics,shanghai university,shanghai 200072,china 1. department of Engineering mechanics Chang’an University Xi’an 710064 China2. Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

On the basis of reproducing kernel particle method(RKPM),using complex variable theory,the complex variable reproducing kernel particle method(CVRKPM) is discussed in this *** advantage of the CVRKPM is that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is *** the CVRKPM is applied to solve two-dimensional elasto-plasticity *** Galerkin weak form is employed to obtain the discretized system equation,the penalty method is used to apply the essential boundary *** then,the CVRKPM for two-dimensional elasto-plasticity problems is formed,the corresponding formulae are obtained,and the Newton-Raphson method is used in the numerical *** numerical examples are given to show that this method in this paper is effective for elasto-plasticity analysis.

关键词： meshless method reproducing kernel particle method(RKPM) complex variable reproducing kernel particle method(CVRKPM) correction function elasto-plasticity

Boundary element-free method for elastodynamics

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Science china(Physics,mechanics & Astronomy) 2005年第6期48卷 641-657页

作者： CHENG Yumin1 & PENG Miaojuan2 1. shanghai Institute of Applied Mathematics and mechanics, shanghai university, shanghai 200072, china 2. department of Civil Engineering, shanghai university, shanghai 200072, china 1. shanghai Institute of Applied Mathematics and mechanics Shanghai University 200072 Shanghai China 2. department of Civil Engineering Shanghai University 200072 Shanghai China

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.

关键词： moving least-square approximation, improved moving least-square approximation, elastodynamics, boundary integral equation, meshless method, boundary element-free method, Fourier eigen transform.

Optimal motion planning of an underactuated spacecraft using wavelet approximate method

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Progress in Natural Science:Materials International 2006年第8期16卷 868-873页

作者： GE Xinsheng, CHEN Liqun and LIU Yanzhu (Beijing Institute of Machinery, Beijing 100085, china department of mechanics, shanghai university, shanghai 200072, china department of Engineering mechanics, shanghai Jiaotong university, shanghai 200030, china) [a]Beijing Institute of Machiner Beijing China [b]department of mechanics Shanghai University Shanghai China [c]department of Engineering mechanics Shanghai Jiaotong University Shanghai China

An optimal motion planning scheme using wavelet approximation is proposed for an underactuated spacecraft. The motion planning of an underactuated spacecraft can be formulated as an optimal control of a drift-free system. A cost functional is used to incorporate the control energy and the final state errors. The motion planning is to determine control inputs to minimize the cost functional. Using the method of wavelet, one can transform an infinite-dimensional optimal control problem to a finite-dimensional one and use Gauss-Newton algorithm to solve it for a feasible trajectory which satisfies nonholonomic constraints. The proposed scheme has been applied to a rigid spacecraft with two momentum wheels. The numerical simulation results indicate that optimal control with wavelet approximation is an effective approach to steering an underactuated spacecraft system from the initial configuration to the final configuration.

关键词： underactuated spacecraft motion planning optimal control nonholonomic constraint wavelet analysis.

WATER ENTRY OF A WEDGE BASED ON SPH MODEL WITH AN IMPROVED BOUNDARY TREATMENT

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Journal of Hydrodynamics 2009年第6期21卷 750-757页

作者： GONG Kai LIU Hua WANG Ben-long department of Engineering mechanics Shanghai Jiao Tong University Shanghai 200240 China State Key Laboratory of Ocean Engineering Shanghai Jiao Tong University Shanghai 200240 China

The hydrodynamic problem of a two-dimensional wedge entering water is studied based on Smoothed Particle Hydrodynamics （SPH） model. A non-reflection boundary treatment for SPH method is proposed to reduce the reflection of sound waves. The boundary pressure is obtained using an improved coupling boundary treatment approach, which is validated by comparing the simulation results with experimental and analytical results in literature. A series of cases with different initial entering velocities are simulated. The maximum force on the wedge and the corresponding time required to reach it for the different cases of initial entering velocities of the wedge are obained and fitted into formulas against the initial entering velocity of the wedge. The maximum drag coefficients of the wedge for the different cases with Froude number greater than 2 are all near the value of 0.91.

关键词： water entry Smoothed Particle Hydrodynamics (SPH) non-reflection boundary

CALCULATION OF ADDED MASS OF A VEHICLE RUNNING WITH CAVITY

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Journal of Hydrodynamics 2010年第3期22卷 312-318页

作者： LI Jie LU Chuan-jing HUANG Xuan department of Engineering mechanics Shanghai Jiao Tong University Shanghai 200240 China department of Engineering mechanics Shanghai Jiao Tong University Shanghai 200240 China State Key Laboratory of Ocean Engineering Shanghai Jiao Tong University Shanghai 200030 China

A numerical method is developed to obtain the added mass coefficients of a vehicle running with cavity in numerical simulation for the multiphase flow of the vehicle which is imposed an added vibration and analyzing its hydrodynamic loads. The method is verified through the cases of non-cavitating sphere and ellipsoid. The changing rule of the added mass of a sphere during water exit is gained. Then the influence of cavitation on the added mass of a cylinder is studied. The results show that λ 11, λ22, λ26, λ66 all decrease as the cavitation number reduces and the length of the attached cavity increases. There is almost a linear relationship between the cavity length and λ22 .The base cavity has great influence on λ11 its contribution decreases more than 60%, when the cavitation number changes from 0.6 to 0.2.

关键词： added mass cavity carrying forced vibration method

A New Approach to Nonlinear Partial Differential Equations

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Communications in Nonlinear Science and Numerical Simulation 1997年第4期2卷 230-235页

作者： Jihuan HE (shanghai university,shanghai Institute of Applied Mathematics and mechanics,shanghai 2 0 0 0 72 ,china) shanghai university Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

In this paper,a novel method called variational iteration method is proposed to solve nonlinear partial differential equations without linearization or small *** this method,a correction functional is constructed by a general Lagrange multiplier,which can be identified via variational *** analytical solution can be obtained from its trial- function with possible unknown constants,which can be identified by imposing the boundary conditions,by successively iteration.

关键词： Nonlinear Problems Partial Differential Equations Variational Iteration Method Variational Theory

Virtual multi-dimensional internal bonds model and its application in simulation of rock mass

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Science china(Technological Sciences) 2008年第2期51卷 192-201页

作者： ZHANG ZhenNan1,2 & GE XiuRun3,4 1 department of Civil Engineering,shanghai university,shanghai 200072,china 2 shanghai Institute of Applied Mathematics and mechanics,shanghai university,shanghai 200072, china 3 Institute of Geotechnical Engineering,shanghai Jiao Tong university,shanghai 200030,china 4 Institute of Rock and Soil mechanics,Chinese Academy of Sciences,Wuhan 430071,china 1. department of Civil Engineering Shanghai University Shanghai 200072 China 2. shanghai Institute of Applied Mathematics and mechanics Shanghai University Shanghai 200072 China 3. Institute of Geotechnical Engineering Shanghai Jiao Tong University Shanghai 200030 China 4. Institute of Rock and Soil mechanics Chinese Academy of Sciences Wuhan 430071 China

VMIB (virtual multi-dimensional internal bonds) is a multiscale mechanical model developed from the VIB (virtual internal bond) theory. In VIB theory,the solid mate-rial is considered to consist of random-distributed material particles in microscale. These particles are connected with normal bonds. The macro constitutive relation is derived from the cohesive law between particles. However,in VMIB,the micro particles are connected with both normal and shear bonds. The macro constitutive relation is derived in terms of bond stiffness coefficients. It has been theoretically certified that there exists a corresponding relationship between the two bond stiffness coefficients and the two macro material constants,i.e. the Young’s modulus and Poisson ratio. This corresponding relationship suggests that it should be necessary and sufficient to simultaneously account for the normal and shear interactions between particles. Due to the fact that the fracture criterion is directly incorporated into the constitutive relation,both VIB and VMIB present many advantages in simulating fractures of materials. In the damage model of rock mass,a damage tensor is usually defined to describe the distribution of cracks. The damage value in one direction determines the relative stiffness of rock mass in this direction. In VMIB solid,the relative distribution density of micro bonds in one direction determines the relative macro stiffness of the material in this direction. The effects of the damage value and the relative distribution density of bonds are consistent. To simulate the failure behavior of rock mass with VMIB,the presented paper sets up a quantitative relationship between the damage tensor and the rela-tive distribution density of bonds. Comparison of the theoretical and the experi-mental results shows that VMIB model can represent the effect of distributed cracks on rock mass with this relationship. The presented work provides a founda-tion for further simulating fracture behavior

关键词： VMIB (virtual multi-dimensional internal bonds) rock mass VIB (virtual internal bonds) multi-cracked body numerical simulation