Design of manned lunar rover wheels and improvement in soil mechanics formulas for elastic wheels in consideration of deformation

Most of the current lunar rover vehicle wheels are inconvenient for changing broken wheels and have poor shock absorbing in driving, so they cannot be used to carry people on the moon. To meet the demands for manned lunar transportation, a new wheel possessing a woven metal wire mesh tire and using hub-rim combination slide mechanism is designed in this article. The characteristics of the new wheel is analyzed by comparing with the same-size conventional rover wheels after demonstrating the validity of FEM simulation. The new wheel possesses lighter structure and superior shock absorbing. It also provides stronger traction because the deformation of the designed wheel increases the contact area between the tire and lunar terrain. In order to establish an on-line soil parameter estimation algorithm for low cohesion soil, the stress distribution along a driven deformable wheel on off-road terrain is simplified. The basic mechanics equations of the interaction between the wheel and the lunar soil can be used for analytical analysis. Simulation results show that the soil estimation algorithm can accurately and efficiently identify key soil parameters for loose sand.     

Differential characteristic set algorithm for the complete symmetry classification of partial differential equations

In this paper, we present a differential polynomial characteristic set algorithm for the complete symmetry classification of partial differential equations （PDEs） with some parameters. It can make the solution to the complete symmetry classification problem for PDEs become direct and systematic. As an illustrative example, the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary function parameter are presented. This is a new application of the differential form characteristic set algorithm, i.e., Wu＇s method, in differential equations.     

The conjugate gradient method and block iterative method for penalty finite element of three dimensional navier-stokes equation

A conjugate gradient and block iterative algorithm for element solution of penalty variational form of Navier-Stokes equations are presented. Because the algorithm of solving single variable minimizing problem is simplified, the computing time is greatly saved. In this paper numerical examples are also provided.     

Two-layer debris mixture flows on arbitrary terrain with mass exchange at the base and the interface

Granular-fluid gravity driven flow down arbitrary topographic terrain is modelled as a two-layer system of a solid-fluid mixture layer overlain by a slurry, consisting of a particle-laden fluid. The lower layer is dynamically treated as a two-phase flow with two constituent mass and momentum balance laws. By contrast, the slurry is described by mass and momentum balances for the mixture as a whole and a diffusive mass balance for the suspended particle phase. At the base, the mixture interacts with the stagnant base by solid-fluid deposition or erosion. At the mixture-slurry interface, solid and fluid mass exchanges are equally taken into account, but the free surface is treated as material and tractionless. The dynamical equations are formulated in three-dimensional form as general balance laws of mass and momentum in each layer. Intrinsic expressions of the jump conditions of mass and momentum are given for the basal and interface surfaces. The field equations are put into dimensionless form and presented relative to topography adjusted coordinates. These equations are further simplified and approximated by a depth-averaging procedure using an order parameter ${\varepsilon = H/L}$ , where H and L are typical thickness and length scales of the gravity current. Detailed proposals are worked out for the parameterizations of the solid and fluid mass flows across the basal surface and layer interface.     

An Uzawa-type algorithm for the coupled Stokes equations

An Uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element method. The velocity solved by the presented algorithm is weakly divergence-free, which is different from the one solved by the common Uzawa method. Besides, an optimal relaxation parameter of the presented algorithm is provided.     

圆锥壳自由振动传递函数解

本文在线性弹性理论基础上，给出了一种求解圆锥薄壳自由振动的渐进传递函数解法，壳体的三个位移分量，外力和边界条件首先沿环向展开的Ｆｏｕｒｉｅｒ级数，然后关于时间变量进行Ｌａｐｌａｃｅ变换，这样就将壳体的控制方程化为一系列含复参数ｓ的变系数常微分方程组，通过定义状态变量。得到了壳体动力学问题的状态空间控制微分方程，引入一小参数，并利用摄动技术就可以得到微分方程的渐进传递函数解，将各于锥段的解进行综合，     

On axisymmetric flow of Sisko fluid over a radially stretching sheet

This study presents an analysis of the axisymmetric flow of a non-Newtonian fluid over a radially stretching sheet. The momentum equations for two-dimensional flow are first modeled for Sisko fluid constitutive model, which is a combination of power-law and Newtonian fluids. The general momentum equations are then simplified by invoking the boundary layer analysis. Then a non-linear ordinary differential equation governing the axisymmetric boundary layer flow of Sisko fluid over a radially stretching sheet is obtained by introducing new suitable similarity transformations. The resulting non-linear ordinary differential equation is solved analytically via the homotopy analysis method (HAM). Closed form exact solution is then also obtained for the cases n=0 and 1. Analytical results are presented for the velocity profiles for some values of governing parameters such as power-law index, material parameter and stretching parameter. In addition, the local skin friction coefficient for several sets of the values of physical parameter is tabulated and analyzed. It is shown that the results presented in this study for the axisymmetric flow over a radially non-linear stretching sheet of Sisko fluid are quite general so that the corresponding results for the Newtonian fluid and the power-law fluid can be obtained as two limiting cases.     

Substructure computational algorithm for exact analytic method

In[1],the exact analytic method for the solution of differential equation with variablecoefficients was suggested and an analytic expression of solution was given by initialparameter algorithm.But to some problems such as the bending,free vibration andbuckling of nonhomogeneous long cylinders,it is difficult to obtain their solutions by theinitial parameter algorithm on computer.In this paper,the substructure computationalalgorithm for the exact analytic method is presented through the bending of non-homogeneous long cylindrical shell.This substructure algorithm can be applied to solve theproblems which can not be calculated by the initial parameter algorithm on computer.Finally,the problems can be reduced to solving a low order system of algebraic equationslike the initial parameter algorithm.Numerical examples are given and compared with theinitial para-algorithm at the end of the paper,which confirms the correcthess of thesubstructure computational algorithm.     

A segregated implicit solution algorithm for 2D and 3D laminar incompressible flows

A segregated algorithm for the solution of laminar incompressible, two- and three-dimensional flow problems is presented. This algorithm employs the successive solution of the momentum and continuity equations by means of a decoupled implicit solution method. The inversion of the coefficient matrix which is common for all momentum equations is carried out through an approximate factorization in upper and lower triangular matrices. The divergence-free velocity constraint is satisfied by formulating and solving a pressure correction equation. For the latter a combined application of a preconditioning technique and a Krylov subspace method is employed and proved more effecient than the approximate factorization method. The method exhibits a monotonic convergence, it is not costly in CPU time per iteration and provides accurate solutions which are independent of the underrelaxation parameter used in the momentum equations. Results are presented in two- and three-dimensional flow problems.     

计算动力学中的伪弧长方法研究

动力学问题通常采用微分方程来描绘,但由于工程实际问题的复杂性,微分方程模型常伴随着解的不连续性、刚性或激波间断奇异性特点,传统方法很难求解,奇异性问题是计算动力学难点,同时也是国内外学者研究的热点.伪弧长数值算法是针对计算动力学中的奇异性问题所提出的,其基本思想为通过在解曲线上引入伪弧长参数,并增加一个约束方程,在伪弧长参数作用下,使得原始离散单元发生扭曲形变,从而达到消除或减弱奇异性的目的.本文首先介绍伪弧长方法求解定常对流-扩散方程的奇异性问题,并提出针对双曲守恒定律的局部伪弧长算法,其思想在于首先通过间断解的梯度变换来确定强间断所处位置,进而通过局部网格点重构以及数值修正来达到强间断处奇异性消除与降低的目的.针对高维问题,提出全局伪弧长方法,通过对整个计算区域内的网格点进行重构,使得所有网格点向奇异间断点处移动,从而降低间断点的影响域,达到降低奇异性的目的.重点讨论了三维全局伪弧长算法问题的计算难点,即三维空间网格扭曲大变形导致的数值算法不收敛,并提出在算法设计过程中采用分块重构与整体计算相结合的策略,实现了三维空间中的伪弧长数值算法,最后通过数值实验来验证伪弧长算法对于奇异性问题的有效性.     

带约束平面多刚体系统动力学方程的隐式算法

在多体系统动力学正则方程的基础上建立了平面多体系统正则方程的隐式数值算法。利用平面运动的特性，对正则方程进行了简化，导出了该方程的Ｊａｃｏｂｉ矩阵的一般表达式，给出了Ｒｕｎｇｅ－Ｋｕｔａ多体系统动力学方程隐式数值计算方法。算例表明，该方法是一种计算速度和精度均理想的数值方法。     

Free vibration analysis of curved nanotube structures

In reality, nanotubes may not be straight structures. In this work, we study free vibration analysis of curved nanotubes based on a proposed nonlocal shell model. The free vibration of curved single-walled nanotubes (SWNTs), double-walled nanotubes (DWNTs) and multi-walled nanotubes (MWNTs) is analyzed. The governing equations of a curved nanotube are developed using the proposed nonlocal shell model based on elasticity theory of Eringen. Governing differential equations of motion are simplified to the ordinary differential equations using Fourier series expansion. And solutions are obtained by applying Galerkin method. Results obtained by the present model are verified by those presented in the literature. The numerical results demonstrate the effects of the curved nanotube length, thickness, bend angle and nonlocal parameter on the natural fundamental frequency.     

A method for on-line soil parameters modification to planetary rover simulation

In planetary exploratory rover simulation, the contact model between wheel and terrain inevitably has some differences in contrast with the real one, which can make rover depart the planned track. To eliminate the dynamic errors caused by it, this paper presents a method for on-line soil parameters modification. This paper classifies data errors between virtual rover and real rover as model errors and asynchronous errors. Before modification, data identification is utilized to eliminate asynchronous errors and get a group of effective data with least additional errors. Based on the simplified terramechanics model, the origins of model errors are analyzed in detail from static status and kinetic status; meanwhile, some soil parameters are decoupled from the complicated model, and it makes on-line soil parameters modification feasible. An effective coefficient is also proposed to maintain the stability and convergence of modification. Lastly, through simulations on ROSTDyn (ROver Simulation based on Terramechanics and Dynamics), it is demonstrated that the soil parameters modification method is effective and useful for rover simulation to eliminate dynamic errors of predictive model.     

Effects of heat and mass transfer peristaltic flow of?Williamson fluid in a vertical annulus

In the present investigation, we have studied the effects of mixed convection heat and mass transfer on peristaltic flow of Williamson fluid model in a vertical annulus. The governing equations of Williamson fluid model are simplified using the assumptions of long wavelength and low Reynold’s number. An approximated analytical and numerical solutions are found for the velocity field using (i) Perturbation method (ii) Shooting method. The comparisons of analytical and numerical solutions have been presented. The expressions for pressure rise, velocity against various physical parameter are discussed through graphs.     

Micropolar hypo-elasticity

In this paper, the concept of hypo-elasticity is generalized to the micropolar continuum theory, and the general forms of the constitutive equations of the micropolar hypo-elastic materials are presented. A new co-rotational objective rate whose spin is the micropolar gyration tensor is introduced which describes the deformation of the material in view of an observer attached to the micro-structure. As special case, simplified versions of the proposed constitutive equations are given in which the same fourth-order elasticity tensors are used as in the micropolar linear elasticity. A 2-D finite element formulation for large elastic deformation of micropolar hypo-elastic media based on the simplified constitutive equations in conjunction with Jaumann and gyration rates is presented. As an example, buckling of a shallow arc is examined, and it is shown that an increase in the micropolar material parameters results in an increase in the buckling load of the arc. Also, it is shown that micropolar effects become important for deformations taking place at small scales.     

基于MARG传感器的自主姿态测量新算法

针对基于三轴陀螺、三轴加速度计以及三轴磁强计组成的传感器组合(MARG传感器)的姿态测量算法存在的不足和限制,以自主姿态测量为前提,提出了一种新的基于四元数的优化递推估计算法。这一算法能够在线估计补偿陀螺漂移误差,不再需要对系统方程进行线性化处理。与基于EKF的方法相比,在同等计算复杂度下,该算法具有更高的精度和更好的稳定性。算法本身内蕴了对四元数单位长度的限制,不再需要任何归一化处理。仿真结果显示出了该算法具有令人满意的效果,利用水上漂浮试验初步验证了该算法的稳定性。     

Averaging over Fast Gravity Waves for Geophysical Flows with Unbalanced Initial Data

Various facets of recent mathematical theories for averaging over fast gravity waves on advective time scales for geophysical flows with unbalanced initial data are presented here including nonlinear Rossby adjustment and simplified reduced dynamics. This work is presented within the context of simplified geophysical models involving the rotating shallow-water equations and the rotating stably stratified Boussinesq equations. Novel mechanisms for enhanced gravity wave dissipation through the catalytic interaction with potential vortical modes are also developed here within the context of the rotating shallow-water equations. Received 2 May 1997 and accepted 20 August 1997     

流固耦合介质轴对称动力问题解法的改进

用直接求解常微分方程组解文［１］所得的控制方程，减少了传递矩阵计算工作量，避免了子阵求逆，使问题的求解得到了简化     

Radiative and Thermal Dispersion Effects on Non-Darcy Natural Convection with Lateral Mass Flux for Non-Newtonian Fluid from a Vertical Flat Plate in a Saturated Porous Medium

The problem of natural convective heat transfer for a non-Newtonian fluid from an impermeable vertical plate embedded in a fluid-saturated porous medium has been analyzed. Non-Darcian, radiative and thermal dispersion effects have been considered in the present analysis. The governing boundary layer equations and boundary conditions are cast into a dimensionless form and simplified by using a similarity transformation. The resulting system of equations is solved by using a double shooting Runge–Kutta method. The effect of viscosity index n, the conduction–radiation parameter R, the non-Darcy parameter Gr*, the thermal dispersion parameter Ds and the suction/injection parameter f_w on the fluid velocities, temperatures and the local Nusselt number are discussed.     

Incremental deformation analysis of shell and corrugated diaphragm based on arbitrary configuration

With respect to an arbitrary configuration of a deformed structure, two sets of incremental equations are proposed for the deformation analysis of revolution shells and diaphragms loaded by both lateral pressures and the initial stresses produced in manufacturing. These general equations can be reduced to the simplified Koiter's Reissner-Meissner-Reissner (RMR) equations and the simplified Reissner's equations, when the initial stresses are set to zero. They can also be deduced to the total Lagrange form or the updated Lagrange form, respectively, as the structure is specified as the un-deformed or the former-deformed configurations. These incremental equations can be easily transformed into finite difference forms and solved by common numerical solvers of ordinary differential equations. Some numerical examples are presented to show the applications of the incremental equations to the deep shell of revolution and the corrugated diaphragms used in microelectronical mechanical system (MEMS). The results are in good agreement with those from finite element method (FEM).