On one boundary problem for nonlinear stationary controlled system

The object of study is nonlinear stationary controlled system of ordinary differential equations with constant disturbance in the right part. The problem of constructing the synthesising control function providing the transfer of this system from the initial state to the origin is considered. The sufficiently simple for numerical implementation algorithm of solution of the above-mentioned problem is obtained. It is shown that for local null controllability of the considered system, it is sufficient that the conditions of the Kalman's type were satisfied. In addition, the estimates restricting the choice of initial conditions and external disturbances under which the transfer is guaranteed are obtained. The main idea of the method of construction of the desired control function consists in reducing the original problem to stabilisation of a special kind linear non-stationary system and solving the Cauchy problem for an auxiliary system of ordinary differential equations closed by stabilising control. The simplicity of the realisation of this algorithm is determined by the construction of the auxiliary system and its stabilisation that could be obtained by analytical methods. The effectiveness of the method is illustrated by solving the problem of crane control and its numerical simulation.     

An overlapping domain decomposition dual reciprocity method

We present a domain decomposition boundary integral equation method for two-dimensional partial differential equations. The overlapping Schwarz method is employed to improve the dual reciprocity boundary element method. The resulting algorithm turns out to be more accurate than a non-overlapping approach previously proposed. Some numerical results showing the improved accuracy and efficiency of the methods are given.     

Stabilization of uncertain boundary control systems

We consider a class of linear infinite-dimensional systems subject to boundary uncertainties, which are linear and time-invariant. Using a deterministic approach to the design of stabilizing feedback controls, uniform exponential stability of the zero state is achieved. Lyapunov techniques are combined with Datko or Ichikawa theory. Three illustrative examples are presented.     

A note on the satisfaction of the boundary conditions for Chebyshev collocation methods in rectangular domains

The way boundary conditions are imposed when applying Chebyshev collocation methods to Poisson and biharmonic-type problems in rectangular domains is investigated. It is shown that careful selection of the number of collocation points leads to a linear system ofn linearly independent equations inn unknowns.     

Breakdown of oil films and formation of residual films

The breakdown processes of oil films under quasi-static loading have been investigated by using a newly developed steel-oil-mercury system. The relationship between the thickness and breakdown ratio of a hexadecane film is represented by a single master curve independently of the indentation speed, indentation load, and temperature. The master curve shows that the breakdown process of hexadecane includes two stages; one is the decrement of the thickness without breakdown and the other is the decrement of the thickness with a drastic progress of breakdown. By solving a small amount of fatty acid in hexadecane, the thickness increases and the breakdown ratio decreases noticeably; a multilayer residual film supporting normal load is formed between two metal surfaces. Experiments at different temperatures reveal a negative relationship between the temperature and thickness of residual film, which indicates that the residual film is organized by physical interaction rather than chemical interaction. At least under a lower concentration, the residual film appears to consist of not only fatty acid molecules but also hexadecane molecules.     

Three dimensional boundary element analysis of internal cracks under sliding contact load with a spherical indenter

Using boundary element based three dimensional modelling for linear fracture mechanics, we present an analysis of cracking in a homogeneous medium subject to contact load. The proposed iterative solution procedure allows a simultaneous treatment of a reasonable number of partially closed cracks. It is shown that the most probable direction of propagation of a vertical internal crack is strongly dependent on its size compared to the contact radius and its location with respect to the axis of maximum normal load.     

Displacement Discontinuity Method for Fracture Mechanics Analysis of Reissner Plates: Static and Dynamic

This paper is concerned with the displacement discontinuity method applied to the shear deformable plates (Reissner’s and Mindlin’s theories) with cracks subjected to static and dynamic loads. Fundamental solutions of dislocation are derived using the Fourier transform method and the Laplace transformation technique. Boundary integral equations are presented in terms of rotations/displacement on the crack surfaces. The Chebyshev polynomials of the second kind are used to evaluate the integral equations with hypersingular kernels on the crack boundaries and determine the stress intensity factors at the crack tips. Comparisons are made with other numerical solutions to demonstrate the proposed method is accurate both for static and dynamic problems.     

A scheme to randomly generate surface dust points for the 3D complex variable boundary element method (CVBEM)

A scheme to randomly generate dust points on the surface of a three-dimensional (3D) object is proposed. This scheme will potentially eliminate the bias of a density of points which are approximately equally spaced on the surface, as well as eliminate possible weighting requirements for areas of higher density. This method has the potential to reduce computational effort, as fewer points might be required to define the surface area. The global trial function vector can be assigned to these dust points and then entered into the complex variable boundary element method (CVBEM) commercial code. This scheme can be applied to each piece of a system that is comprised of a connected multiple geometry. A noticeable benefit of this approach is that the same problem can be studied several times, using a new random distribution of surface points each time. The smallest error can then be determined and that run selected. The Mathematica code used to generate the scheme is attached as an appendix.     

Adaptive boundary control for unstable parabolic PDEs—Part II: Estimation-based designs

The certainty equivalence approach to adaptive control is commonly used with two types of identifiers: passivity-based identifiers and swapping identifiers. The “passive” (also known as “observer-based”) approach is the prevalent identification technique in existing results on adaptive control for PDEs but has so far not been used in boundary control problems. The swapping approach, prevalent in finite-dimensional adaptive control is employed here for the first time in adaptive control of PDEs. For a class of unstable parabolic PDEs we prove a separation principle result for both the passive and swapping identifiers combined with the backstepping boundary controllers. The result is applicable in any dimension. For physical reasons we restrict our attention to dimensions no higher than three. The results of the paper are illustrated by simulations.     

用边界元法提取VLSI版图电阻

介绍了ＶＬＳＩ版图验证中电阻提取的基本原理和主要方法，给出了一种新颖的基于边界元法的电阻提取算法。该算法采用变节点单元，较好地解决了实际问题中经常出现的角点问题。通过应用该算法对几个实例进行提取，证明使用本文的算法不仅在精度上而且在占用ＣＰＵ时间上都取得了令人满意的效果