A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in linear elasticity. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed method.

Application of finite element method and photo-elasticity to an lap welded connection

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A Relation between the Weyl Group W(e8) and Eight-Line Arrangements on a Real Projective Plane

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.

On the sense preserving mappings in the Helm topology in the plane

∗Research supported by the grant No. GAUK 186/96 of Charles University.

On Projective Plane of Order 13 with a Frobenius Group of Order 39 as a Collineation Group

One of the most outstanding problems in combinatorial mathematics and geometry is the problem of existence of finite projective planes whose order is not a prime power.

On Representations of Algebraic Polynomials by Superpositions of Plane Waves

* The author was supported by NSF Grant No. DMS 9706883.

On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

∗ Partially supported by Grant MM-428/94 of MESC.

On a 3D-Hypersingular Equation of a Problem for a Crack

MSC 2010: 45DB05, 45E05, 78A45

Self-Avoiding Walks in the Plane

Румен Руменов Данговски, Калина Христова Петрова - Разглеждаме броя на несамопресичащите се разходки с фиксирана дължина върху целочислената решетка. Завършваме анализа върху случая за лента, с дължина едно. Чрез комбинаторни аргументи получаваме точна формула за броя на разходките върху лента, ограничена отляво и отдясно. Формулата я изследваме и асимптотично.

Predegree Polynomials of Plane Configurations in Projective Space

2000 Mathematics Subject Classification: 14N10, 14C17.

Study of the calibration method of pressure-velocity probes and its application in a field of progressive plane waves

This dissertation presents a calibration procedure for a pressure velocity probe. The dissertation is divided into four main chapters. The first chapter is divided into six main sections. In the firsts two, the wave equation in fluids and the velocity of sound in gases are calculated, the third section contains a general solution of the wave equation in the case of plane acoustic waves. Section four and five report the definition of the acoustic impedance and admittance, and the practical units the sound level is measured with, i.e. the decibel scale. Finally, the last section of the chapter is about the theory linked to the frequency analysis of a sound wave and includes the analysis of sound in bands and the discrete Fourier analysis, with the definition of some important functions. The second chapter describes different reference field calibration procedures that are used to calibrate the P-V probes, between them the progressive plane wave method, which is that has been used in this work. Finally, the last section of the chapter contains a description of the working principles of the two transducers that have been used, with a focus on the velocity one. The third chapter of the dissertation is devoted to the explanation of the calibration set up and the instruments used for the data acquisition and analysis. Since software routines were extremely important, this chapter includes a dedicated section on them and the proprietary routines most used are thoroughly explained. Finally, there is the description of the work that has been done, which is identified with three different phases, where the data acquired and the results obtained are presented. All the graphs and data reported were obtained through the Matlab® routine. As for the last chapter, it briefly presents all the work that has been done as well as an excursus on a new probe and on the way the procedure implemented in this dissertation could be applied in the case of a general field.

Predicting residual stiffness of cracked composite laminates subjected to multi-axial in-plane loading

Peer reviewed

Predicting residual stiffness of cracked composite laminates subjected to multi-axial in-plane loading

Peer reviewed