The plane problem solution of impact deformation in a preliminary unstressed incompressible elastic medium

Решается задача одномерной плоской деформации нелинейноупругого несжимаемого полупространства под действием ударной нагрузки на его границе. До момента ударного воздействия полупространство находится в свободном состоянии. Именно это условие позволяет осуществить движение разрыва в краевых условиях на границе полупространства в виде единственной плоскополяризованной ударной волны, на которой сохраняется неизменным направление предварительного сдвига. Перечисленные свойства переднего фронта ударного воздействия следуют из совместного анализа характеристических направлений задачи и видов ударных волн для одномерной плоской задачи в несжимаемой среде с произвольными предварительными деформациями. Приводятся два варианта приближенного решения задачи на основе метода сращиваемых асимптотических разложений и на основе метода лучевых рядов. The problem of one-dimensional plane deformation of a nonlinear elastic incompressible half-space under the impact load action on its boundary is solved. The half-space is in a free state until the moment of impact action. This condition leads to the discontinuity in the boundary conditions at the half-space boundary moves as the only plane-polarized shock wave, on which the direction of the preliminary shear remains unchanged. The pointed out properties of the leading edge of the shock action follow from the joint analysis of the characteristic directions of the problem and the shock waves types for a one-dimensional plane problem in an incompressible medium with arbitrary preliminary deformations. Two versions of the problem approximate solution based on the method of matched asymptotic expansions and on the basis of the ray series method are presented.

EVALUATION OF THE FASHION DRAWING (ILLUSTRATION) LESSON TEACHING PROGRAM UNDER THE LIGHT OF LECTURERS’ AND STUDENTS’ OPINIONS

While clothing is produced and consumed rapidly, it strives to create appropriate forms and to create appropriate identities by giving correct messages; therefore, it is one of the most important fields requiring art and design education. The fashion design student, who forms the infrastructure with basic art education and figure drawing, not only transfers the imagination to the two-dimensional plane with the fashion drawing lesson but also transfers it to the two-dimensional plane; at the same time, he takes art and design education, which is aesthetic education, and feeds his visual vision and mind. In this research, the Fashion Drawing Lesson has been examined in detail in terms of determining the place, position, importance, processing and content of the Fashion Drawing Lesson in the official fashion design curriculum and a comprehensive literature search has been conducted; then the matter has been tried to be examined thanks to a link has been established between education, fashion, art and design disciplines. The course syllabus in Turkey and some of fashion design course programs in the world were examined; the experts providing fashion formal education and the students who received fashion formal education were interviewed face-to-face to obtain information first-hand. First of all, the study started by determining the fashion design undergraduate programs in the OSYM (Assessment Selection and Placement Center) placement guide and examining the course hours, course times and course contents of the fashion formal courses in these programs. The researcher visited the designated universities for the purpose of on-site observation and interview, and conducted semi-structured interview questions and face-to-face interviews with experts and students and recorded them. The transcribed interviews were analyzed using content analysis method and the findings were interpreted within the framework of the research questions. The findings were interpreted and discussed, and after the results were written, suggestions about the study were included. As a result, it has been determined that the admission of students to the fashion design program should be made with the combination of central examination system and talent exam suitable for fashion design education. It was seen that the time granted for the program was not sufficient in mean of implementation of the fashion drawing lessons properly in the fashion design education programs. Keywords: Fashion drawing, fashion illustration, design education, fashion design education, art education

On topological properties of weakly m-convex sets

The topological properties of classes of generally convex sets in multidimensional real Euclidean space $\mathbb{R}^n$, $n\ge 2$, known as $m$-convex and weakly $m$-convex, $1\le m<n$, are studied in the present work. A set of the space $\mathbb{R}^n$ is called \textbf{\emph{$m$-convex}} if for any point of the complement of the set to the whole space there is an $m$-dimensional plane passing through this point and not intersecting the set. An open set of the space is called \textbf{\emph{weakly $m$-convex}}, if for any point of the boundary of the set there exists an $m$-dimensional plane passing through this point and not intersecting the given set. A closed set of the space is called \textbf{\emph{weakly $m$-convex}} if it is approximated from the outside by a family of open weakly $m$-convex sets. These notions were proposed by Professor Yuri Zelinskii. It is known the topological classification of (weakly) $(n-1)$-convex sets in the space $\mathbb{R}^n$ with smooth boundary. Each such a set is convex, or consists of no more than two unbounded connected components, or is given by the Cartesian product $E^1\times \mathbb{R}^{n-1}$, where $E^1$ is a subset of $\mathbb{R}$. Any open $m$-convex set is obviously weakly $m$-convex. The opposite statement is wrong in general. It is established that there exist open sets in $\mathbb{R}^n$ that are weakly $(n-1)$-convex but not $(n-1)$-convex, and that such sets consist of not less than three connected components. The main results of the work are two theorems. The first of them establishes the fact that for compact weakly $(n-1)$-convex and not $(n-1)$-convex sets in the space $\mathbb{R}^n$, the same lower bound for the number of their connected components is true as in the case of open sets. In particular, the examples of open and closed weakly $(n-1)$-convex and not $(n-1)$-convex sets with three and more connected components are constructed for this purpose. And it is also proved that any compact weakly $m$-convex and not $m$-convex set of the space $\mathbb{R}^n$, $n\ge 2$, $1\le m<n$, can be approximated from the outside by a family of open weakly $m$-convex and not $m$-convex sets with the same number of connected components as the closed set has. The second theorem establishes the existence of weakly $m$-convex and not $m$-convex domains, $1\le m<n-1$, $n\ge 3$, in the spaces $\mathbb{R}^n$. First, examples of weakly $1$-convex and not $1$-convex domains $E^p\subset\mathbb{R}^p$ for any $p\ge3$, are constructed. Then, it is proved that the domain $E^p\times\mathbb{R}^{m-1}\subset\mathbb{R}^n$, $n\ge 3$, $1\le m<n-1$, is weakly $m$-convex and not $m$-convex.

Research on geometric error modelling and decoupling of machine tool based on NURBS projection curve

As a geometric measuring instrument of machine tool, double ball bar (DBB) instrument can effectively identify the geometric error of machine tool. In the existing literature, DBB mostly uses the two-dimensional circle as the identification trajectory to identify the geometric error continuously, and the most efficient way of single recognition is still in two-dimensional plane. Aiming at the low efficiency of DBB spatial geometric error recognition, the recognition range of DBB is extended from two-dimensional plane to spatial hemisphere. A method of space recognition and decoupling based on NURBS projection curve is proposed in this paper. The error decoupling of feed axis and rotation axis is realized in an experiment. The identification method has the characteristics of high efficiency, no secondary assembly and avoiding interference. It can decouple all the five axes in hemispherical space at one time and get the effective solution.

THE ALGORITHM OF GOOD PLACEMENT ON THE SHELF BY CONSIDERING THE WEIGHT AND VOLUME OF THE GOODS TO THE CENTRE OF MASS

This study aims to develop an algorithm for placing goods on warehouse shelves. The process of placing goods in a warehouse is generally placed or arranged in a rack. Placement of goods must be correct to achieve space efficiency and high shelf utilization while maintaining balance on the storage shelf. The placement of items that have various volumes and weights must consider their placement position on the storage rack. Placing goods carelessly and only consider the shelf utilization rate will cause an imbalance. Shelf imbalance will accelerate the damage to storage racks, as well as the risk of collapsing shelves. Best placement of goods, in order to achieve shelf utilization and maintain shelf balance, must consider the weight and volume of goods placed against the total center mass of the rack. The procedure for placing goods on the shelf by considering the total center of mass was developed from research on warehouse layout. The procedure for placing goods in warehouse layout research is carried out on a two-dimensional plane (x-axis and y-axis). Whereas in this study, the placement of goods was carried out by considering the location of the goods in a three-dimensional plane (x, y and z axes). The placement algorithm is designed to place goods with various size (volume and weight) on multi-layer racks (with assumption each layer has same load capacity). This research produces two placing algorithms. The first algorithm focuses on the weight and volume of goods, so the pallets containing with largest volume and weight goods are arranged first and placed on the lowest layer. The second algorithm focuses on the weight of the goods, the pallets containing the heaviest goods will be arranged first on the lowest layer. Both algorithms are simulated using numerical data. The algorithm that focuses on weight (the second algorithm) has a better mass center than the algorithm that focuses on the weight and volume of goods (the first algorithm).