浅谈重积分的定限

首先说明,本文着重探讨重积分的定限方法,为书写简便计,所论的重积分及其累次积分假设都存在。重积分定限通常有两种方法:几何观察法与代数法。本文只讨论前者。所谓几何观察定限法,就是根据重积分积分区域的几何图形,按照所要化成的累次积分的次序,从图形上直观地确定各层积分上、下限的方法,由于直观简便,因此它是数学分析课程中所讲述的主要方法。

Limit equilibrium stability analysis of slopes under external loads

Two calculation modes for the effect of external load on slope stability, i.e., mode I in which the external load is thought to act on slope surface, and mode II in which the external load is thought to act on slip surface along the force action line, were considered. Meanwhile, four basic distribution patterns of external load were used, of which complex external loads could be composed. In analysis process, several limit equilibrium methods, such as Swedish method, simplified Bishop method, simplified Janbu method, Spencer method, Morgenstern-Price(M-P) method, Sarma method, and unbalanced thrust method, were also adopted to contrast their differences in slope stability under the external load. According to parametric analysis, some conclusions can be obtained as follows:(1) The external load, with the large magnitude, small inclination angle, and acting position close to the slope toe,has more positive effect on slope stability;(2) The results calculated using modes I and II of external load are similar, indicating that the calculation mode of external load has little influence on slope stability;(3) If different patterns of external loads are equivalent to each other, their slope stability under these external loads are the same, and if not, the external load leads to the better slope stability,as action position of the resultant force for external load is closer to the lower sliding point of slip surface.

Study on the FEM design of reinforced earth retaining wall with geogrid

At present,limit equilibrium method is often adopted in the design of reinforced earth retaining wall. Geotechnical engineers home and abroad have done a lot of work to improve the traditional calculation methods in recent years,while there are lots of defects. This paper first identifies the location of failure surface and safety factor through the finite element program of PLAXIS and then analyses the influencing factors of the stability of reinforced earth retaining wall with geogrid. The authors adopt strength reduction FEM (finite element method)in the design and stability analysis of reinforced earth retaining wall and have achieved some satisfying results. Without any assumptions,the new design method can automatically judge the failure mode of reinforced earth retaining wall,consider the influence of axial tensile stiffness of the reinforcement stripe on the stability of retaining wall,identify reasonable distance and length of the reinforcement stripe,and choose suitable parameters of reinforcement stripe,including strength,stiffness and pseudo-friction coefficient which makes the design optimal. It is proved through the calculation examples that this method is more reasonable,reliable and economical in the design of reinforced earth retaining wall.

Settling Time Design and Parameter Tuning Methods for Finite-Time P-PI Control

High precision position control and high speed control of the robot manipulators are fundamental and important control problems. The effectiveness of finite-time P-PI control was confirmed by end-effector position control of robot manipulators. However, parameter tuning method has not been proposed to finite-time P-PI control. In this paper, we propose a settling time design method and a parameter tuning method for the finite-time P-PI control. The effectiveness of the proposed parameter tuning method is confirmed by experiments of end-effcctor position control of a robot manipulator.

Verified Solution for a Statically Determinate Truss Structure with Uncertain Node Locations

We consider a statically determinate structural truss problem where all of the physical model parameters are uncertain： not just the material values and applied loads, but also the positions of the nodes are assumed to be inexact but bounded and are represented by intervals. Such uncertainty may typically arise from imprecision during the process of manufacturing or construction, or round-off errors. In this case the application of the finite element method results in a system of linear equations with numerous interval parameters which cannot be solved conventionally. Applying a suitable variable substitution, an iteration method for the solution of a parametric system of linear equations is firstly employed to obtain initial bounds on the node displacements. Thereafter, an interval tightening （pruning） technique is applied, firstly on the element forces and secondly on the node displacements, in order to obtain tight guaranteed enclosures for the interval solutions for the forces and displacements.

Analysis of Unbalances Forces Using Methods of Identification and Finite Elements

The study of damage in rotating machineries is of fundamental interest in the fields of machine and structure design. A rotating system, supported by bearings and under some dynamic conditions, can generate a variety of problems that are encountered in many different types of rotating machines. One of these problems is the unbalance due to non-homogeneous mass distribution along the shaft. One of the techniques which are widespread today is the identification of parameters and excitation forces that may well followed by monitoring the evolution and change of possible variations of these parameters. Although several methods for the identification of unbalance excitation force are available in the literature, none of them can be considered unrestricted to be applied for all rotating systems. In this study, two methodologies to identify unknown excitations, such as unbalance, have been proposed. This project refers to the analysis of unbalanced forces from displacement parameters and speed by using methods of identification by Fourier series and Legendre polynomials together with the finite element method, state observers in reasons of the problem of absence of signs of rotational displacement, bandpass filter were used to noise suppression of the data collected from the experimental part, Quasi-Newton method to minimize a function in which the bearing stiffness and its damping are unknowns, and also the experimental verification of the methodology, using for this system owned by a rotary mechanical vibrations of the Department of Mechanical Engineering of Faculty of Engineering, campus of llha Solteira.

Effect of Rotational Speed on the Stability of Two Rotating Side-by-side Circular Cylinders at Low Reynolds Number

Flow around two rotating side-by-side circular cylinders of equal diameter D is numerically studied at the Rey- nolds number 40〈 Re 〈200 and various rotation rate 8i. The incoming flow is assumed to be two-dimensional laminar flow. The governing equations are the incompressible Navier-Stokes equations and solved by the finite volume method （FVM）. The ratio of the center-to-center spacing to the cylinder diameter is T/D=2. The objective of the present work is to investigate the effect of rotational speed and Reynolds number on the stability of the flow. The simulation results are compared with the experimental data and a good agreement is achieved. The stability of the flow is analyzed by using the energy gradient theory, which produces the energy gradient function K to identify the region where the flow is the most prone to be destabilized and the degree of the destabilization. Numerical results reveal that K is the most significant at the separated shear layers of the cylinder pair. With Re in- creases, the length of the wake is shorter and the vortex shedding generally exhibits a symmetrical distribution for θi〈θcrit. It is also shown that the unsteady vortex shedding can be suppressed by rotating the cylinders in the counter-rotating mode.

Hybrid method of limit equilibrium and finite element internal force for analysis of arch dam stability against sliding

A hybrid method of limit equilibrium and finite element internal force for analysis of arch dam stability against sliding is presented.The finite element internal force method(FEIFM) is used to provide more accurate thrust forces acting on the faces of a slip body,and the limit equilibrium method(LEM) is employed to evaluate the factor of safety of the slip body.The method presented can deal with a slip body with large amount of geometrically complex slip faces.In addition,compared with the traditional LEM,it can meet the balance condition of the forces in the slip faces.An example shows that the factor of safety obtained by the method presented agrees well with the theoretical solution.A practical example is also presented to demonstrate the application of the method in the stability analysis of an arch dam project.The results from the examples show that the method is promising in analysis of arch dam stability against sliding.

Stability analysis and a priori error estimate of explicit Runge-Kutta discontinuous Galerkin methods for correlated random walk with density-dependent turning rates

In this paper,we analyze the explicit Runge-Kutta discontinuous Galerkin(RKDG)methods for the semilinear hyperbolic system of a correlated random walk model describing movement of animals and cells in biology.The RKDG methods use a third order explicit total-variation-diminishing Runge-Kutta(TVDRK3)time discretization and upwinding numerical fluxes.By using the energy method,under a standard CourantFriedrichs-Lewy(CFL)condition,we obtain L2stability for general solutions and a priori error estimates when the solutions are smooth enough.The theoretical results are proved for piecewise polynomials with any degree k 1.Finally,since the solutions to this system are non-negative,we discuss a positivity-preserving limiter to preserve positivity without compromising accuracy.Numerical results are provided to demonstrate these RKDG methods.

A Novel Approach to Predict the Stability Limits of Combustion Chambers with Large Eddy Simulation

Lean premixed combustion,which allows for reducing the production of thermal NOx,is prone to combustion instabilities.There is an extensive research to develop a reduced physical model,which allows-without time-consuming measurements-to calculate the resonance characteristics of a combustion system consisting of Helmholtz resonator type components (burner plenum,combustion chamber).For the formulation of this model numerical investigations by means of compressible Large Eddy Simulation (LES) were carried out.In these investigations the flow in the combustion chamber is isotherm,non-reacting and excited with a sinusoidal mass flow rate.Firstly a combustion chamber as a single resonator subsequently a coupled system of a burner plenum and a combustion chamber were investigated.In this paper the results of additional investigations of the single resonator are presented.The flow in the combustion chamber was investigated without excitation at the inlet.It was detected,that the mass flow rate at the outlet cross section is pulsating once the flow in the chamber is turbulent.The fast Fourier transform of the signal showed that the dominant mode is at the resonance frequency of the combustion chamber.This result sheds light on a very important source of self-excited combustion instabilities.Furthermore the LES can provide not only the damping ratio for the analytical model but the eigenfrequency of the resonator also.