Дослідження розтягу перфорованих пластин методом скінченних елементів

The problem of axial stretching of a plate with a double-periodic system of round holes arranged in a checkerboard pattern is considered. The specified problem is reduced to elasticity second problem for one period of plate, which was solved by the finite element method. As a result, the reduced elastic characteristics of the equivalent homogeneous orthotropic plate are found. The analysis of their behavior depending on dimensionless geometrical parameters is carried out. The area of variation of the geometric parameters was divided into two subareas. The behavior of the equivalent elastic characteristics in these areas is significantly different. It turned out that the double-periodic perforated plate shows significantly anisotropic behavior. The limit values of the Poisson's ratios can reach unity and, on the other hand, may be less than the original value. Dependences of the stress concentration coefficient on dimensionless geometrical parameters are obtained too. Performed comparative analysis of the obtained results with the results known from the literature, confirmed their adequacy. Pages of the article in the issue: 55 - 58 Language of the article: UkrainianРозглянута задача про осьовий розтяг пластини, послабленої двояко-періодичною системою круглих отворів, розташованих в шаховому порядку. Вихідну задачу зведено до другої задачі теорії пружності для одного періоду, яка розв’язувалася методом скінченних елементів. У результаті її розв’язку знайдені приведені пружні характеристики еквівалентної однорідної ортотропної платівки. Проведено аналіз їх поведінки в залежності від безрозмірних геометричних параметрів. Область зміни геометричних параметрів виявилася розбитою на дві підобласті. Поведінка приведених пружних характеристик в цих областях суттєво відрізняється. Виконаний порівняльний аналіз отриманих результатів з відомими з літератури результатами, підтвердив їх адекватність

Metrical properties of the set of bent functions in view of duality

In the paper, we give a review of metrical properties of the entire set of bent functions and its significant subclasses of self-dual and anti-self-dual bent functions. We present results for iterative construction of bent functions in n + 2 variables based on the concatenation of four bent functions and consider related open problem proposed by one of the authors. Criterion of self-duality of such functions is discussed. It is explored that the pair of sets of bent functions and affine functions as well as a pair of sets of self-dual and anti-self-dual bent functions in n > 4 variables is a pair of mutually maximally distant sets that implies metrical duality. Groups of automorphisms of the sets of bent functions and (anti-)self-dual bent functions are discussed. The solution to the problem of preserving bentness and the Hamming distance between bent function and its dual within automorphisms of the set of all Boolean functions in n variables is considered

Mathematical methods in solutions of the problems from the Third International Students' Olympiad in Cryptography

The mathematical problems and their solutions of the Third International Students' Olympiad in Cryptography NSUCRYPTO'2016 are presented. We consider mathematical problems related to the construction of algebraic immune vectorial Boolean functions and big Fermat numbers, problems about secrete sharing schemes and pseudorandom binary sequences, biometric cryptosystems and the blockchain technology, etc. Two open problems in mathematical cryptography are also discussed and a solution for one of them proposed by a participant during the Olympiad is described. It was the first time in the Olympiad history

Approximate approach of research and assessment of crack resistance of cylindrical housings

In this work, we propose a procedure that allows us to quickly, without involving finite-element packages at the execution stage, evaluate the state of postulated cracks in cylindrical structural elements with internal anticorrosion cladding under pressure and unsteady temperature loading. The procedure contains three components. The first component of the procedure is based on the analytical solution of the unsteady thermal conductivity problem. The second component of the procedure is also analytical relations specifying circumferential and longitudinal stresses in a two-layer cylinder as a function of internal pressure and temperature distribution along the depth of the wall. In the third stage of the procedure, the coefficients of stress intensity along the crack front are determined by the method of influence functions using the known distribution of stresses. To implement this part of the procedure, the influence functions must first be calculated by the finite element method. In this work the example of calculating the functions of influence for longitudinal semi-elliptical cracks of 1/8 wall thickness depth and with the ratio of the principal half-diameters 0.3 and 0.7 is presented. As an example of the implementation of the procedure, comparative calculations were carried out and the elastic-plastic calculation of a cylindrical shell containing longitudinal cracks was given. Stress intensity coefficients along the part of the front located in the base metal were calculated. The results of analytical calculations were conservative until plastic deformations developed in the cladding. At significant plastic strains, the values of the stress intensity coefficients calculated by the proposed procedure, on the contrary, are significantly inferior. This demonstrates once again the fact that calculations in the framework of linear fracture mechanics are not always conservative in relation to calculations in the elastic-plastic formulation. The paper gives an explanation of the reason for the obtained effect