КАРКАСНА МОДЕЛЬ РОЗТЯГУВАННЯ КУЛІРНОГО ТРИКОТАЖУ ВЗДОВЖ ПЕТЕЛЬНИХ РЯДІВ

Purpose. The purpose of this study is to develop a mathematical description of the transformation of the frame model of weft-knits under the action of tensile forces in the courswise direction for further three-dimensional modeling of the knited structure.Methodology. Methods of theoretical analysis and synthesis, basics of knitting theory, methods of geometric modeling and parameterization were used in the research process.Findings. Considering the knitwear stretching during the use of the clothing is one of the determining factors of the quality of design decisions. When stretching the weft-knitted fabrics in the coursewise direction, the configuration of its individual stitches’ changes, as well as the thread’s cross-section due to the force interaction between the adjacent structure elements. To simulate the physical and mechanical behavior of knitwear under the stretching, it is suggested using a complex model of knitwear deformation, that includes the suggested frame model of uniaxial coursewise stretching of knitted fabrics. An algorithm for constructing a frame model of stretching a sample of knitted fabric in the coursewise direction is described in the paper. The algorithm is based on the structure parameters, including the wale spacing and course spacing in a dry relaxed state, the relative elongation of the sample at the time of modeling, number of wales and courses in the sample, the coefficient of courses narrowing. Scientific novelty. The paper investigates the features of the transformation of the knitting structure during stretching in the coursewise direction and offers algorithmic and mathematical support for the automated generation of the mesh frame in the context of three-dimensional modeling, which provides for the possibility of considering the dynamics of deformation of knitted fabric undergoing tensile deformations.Practical value. Frame model of the weft-knits deformation and algorithm of mesh-frame construction suggested in the paper, form the basis for determination of coordinates of characteristic points of the structural elements of the knit in a state of uniaxial tension for construction of a three-dimensional model of thread a deformed knitted fabric.

Construction of Credibility Model for Evaluating the Effectiveness of Ecological Civilization Education

The concept of green development as a rational grasp of the relationship between man and nature is not only an important embodiment of the line of thought of seeking truth from facts and advancing with the times but also a concrete application of Marxist materialistic dialectics combined with the current situation of China’s development. Ecological consciousness is a value orientation that reflects the harmonious development of man and nature as a worldview and methodology to explore and reflect on the ecological and environmental problems of the current society. College students are an important force in promoting China’s development in the future, and cultivating their good ecological consciousness with the concept of green development as a guide for action is of great significance at both the theoretical level and the practical level. Based on the review of online reviews, this study proposes that the content of positive reviews can be classified into praiseworthy reviews. In order to verify the objectivity of the content dimensions of the three types of positive comments, this study selected 1,800 positive comments as the research sample using stratified random sampling and conducted a content analysis of the comment samples one by one using the NET method. The content analysis results showed that praiseworthy comments appeared in almost all of the samples, constructive comments appeared in 23% of the samples, and prosocial comments appeared in only 14% of the sample. The results of the content analysis show that it is necessary to identify the dimensions of positive online comments because the single-dimensional constructs cannot effectively present the multidimensional information content contained in positive comments. By studying the geometric modeling method in soft tissue modeling technology, we propose covering the surface model on the outer surface of the physical model and using the tetrahedral mesh as the support skeleton of the physical model. Through the purification of the initial items and secondary testing, a scale with good reliability and validity for measuring the three constructs of praiseworthy, constructive, and prosocial comments was finally obtained.

Integrated Intelligent CAD System for Interactive Design, Analysis and Prototyping of Compression and Torsion Springs

This paper presents the development and implementation of integrated intelligent CAD (computer aided design) system for design, analysis and prototyping of the compression and torsion springs. The article shows a structure of the developed system named Springs IICAD (integrated intelligent computer aided design). The system bounds synthesis and analysis design phases by means of the utilization of parametric 3D (three-dimensional) modeling, FEM (finite element method) analysis and prototyping. The development of the module for spring calculation and system integration was performed in the C# (C Sharp) programming language. Three-dimensional geometric modeling and structural analysis were performed in the CATIA (computer aided three-dimensional interactive application) software, while prototyping is performed with the Ultimaker 3.0 3D printer with support of Cura software. The developed Springs IICAD system interlinks computation module with the basic parametric models in such a way that spring calculation, shaping, FEM analysis and prototype preparation are performed instantly.

Review of Subdivision Schemes and their Applications

Background: Subdivision surfaces modeling method and related technology research gradually become a hot spot in the field of computer-aided design(CAD) and computer graphics (CG). In the early stage, research on subdivision curves and surfaces mainly focused on the relationship between the points, thereby failing to satisfy the requirements of all geometric modeling. Considering many geometric constraints is necessary to construct subdivision curves and surfaces for achieving high-quality geometric modeling. Objective: This paper aims to summarize various subdivision schemes of subdivision curves and surfaces, particularly in geometric constraints, such as points and normals. The findings help scholars to grasp the current research status of subdivision curves and surfaces better and to explore their applications in geometric modeling. Methods: This paper reviews the theory and applications of subdivision schemes from four aspects. We first discuss the background and key concept of subdivision schemes. We then summarize the classification of classical subdivision schemes. Next, we show the subdivision surfaces fitting and summarize new subdivision schemes under geometric constraints. Applications of subdivision surfaces are also discussed. Finally, this paper gives a brief summary and future application prospects. Results: Many research papers and patents of subdivision schemes are classified in this review paper. Remarkable developments and improvements have been achieved in analytical computations and practical applications. Conclusion: Our review shows that subdivision curves and surfaces are widely used in geometric modeling. However, some topics need to be further studied. New subdivision schemes need to be presented to meet the requirements of new practical applications.

Graph-Based Classification and Urban Modeling of Laser Scanning and Imagery: Toward 3D Smart Web Services

Recently, remotely sensed data obtained via laser technology has gained great importance due to its wide use in several fields, especially in 3D urban modeling. In fact, 3D city models in urban environments are efficiently employed in many fields, such as military operations, emergency management, building and height mapping, cadastral data upgrading, monitoring of changes as well as virtual reality. These applications are essentially composed of models of structures, urban elements, ground surface and vegetation. This paper presents a workflow for modeling the structure of buildings by using laser-scanned data (LiDAR) and multi-spectral images in order to develop a 3D web service for a smart city concept. Optical vertical photography is generally utilized to extract building class, while LiDAR data is used as a source of information to create the structure of the 3D building. The building reconstruction process presented in this study can be divided into four main stages: building LiDAR points extraction, piecewise horizontal roof clustering, boundaries extraction and 3D geometric modeling. Finally, an architecture for a 3D smart service based on the CityGML interchange format is proposed.

RESEARCH OF THE CUTTING MECHANISM AT ELECTRICAL DISCHARGE GRINDING

The paper presents the results of a study of the cutting mechanism during electrical discharge grinding of hard alloys. The cutting mechanism during electrical discharge grinding was studied using mathematical modeling. By means of geometric modeling, a method of grinding cup wear was developed. The functional dependence of the diamonds use factor in the Kw wheel on the technological parameters of processing, wear and tool characteristics were determined. Analysis of the results of the study shows that an increase in efficiency at electrical discharge grinding can be achieved by reducing the wear of S, and by corresponding variation in the concentration of diamonds and technological modes of processing.

Approximation of Generalized Ovals and Lemniscates towards Geometric Modeling

This paper considers an approach towards the building of new classes of symmetric closed curves with two or more focal points, which can be obtained by generalizing classical definitions of the ellipse, Cassini, and Cayley ovals. A universal numerical method for creating such curves in mathematical packages is introduced. Specific aspects of the provided numerical data in computer-aided design systems with B-splines for three-dimensional modeling are considered. The applicability of the method is demonstrated, as well as the possibility to provide high smoothness of the curvature profile at the specified accuracy of modeling.

КАРКАСНА МОДЕЛЬ ОДНООСНОГО РОЗТЯГУВАННЯ КУЛІРНОГО ТРИКОТАЖУ ВЗДОВЖ ПЕТЕЛЬНИХ СТОВПЧИКІВ

The purpose of this study is to develop a frame model for stretching the weft-knits in the wale direction, suitable for further integration into the algorithm for building a three-dimensional knitwear model in a stretched state and modeling of interactive deformation dynamics. Methodology. Methods of theoretical analysis, basics of knitting theory, topological model of knitwear, methods of geometric modeling and parameterization were used in the research process. Findings. Modeling the physical and mechanical behavior of knitwear in a computer environment is one of the promising ways to increase the level of conformity of knitted products with the requirements of comfort and functionality. However, the complexity of the internal structure, the anisotropy of properties and the instability of the parameters of the loop structure determine the need to find non-trivial ways to solve the problem of mathematical description of the three-dimensional model of the thread, knitted in the knitwear, considering the stretching deformations. During the study, a frame model of a uniaxial stretching of knitwear in the wale direction was developed. The basis of the frame model is the idea of a knitted structure, represented as a logically organized set of elements, each of which is interlaces with other elements in accordance with the topology of knit. The frame of the jersey fragment is described as a set of bars and hinges. The hinges are located at the interlacing points of the loop heads and loop feet, and each rod in the model is an imaginary element representing a complex of force factors that prevent the change of distance between the hinges connected to the given rod. In the process of stretching, the geometrical characteristics of the elements change, while the logical connections remain unchanged. The wireframe model allows to define coordinates of interlacement points in the coordinate system of the sample, relative position of coordinate systems of each elementary fragment, which correspond to given loops, coordinates of characteristic points of a loop for transition to a three-dimensional model of a knitted structure. Scientific novelty. For the first time, a frame model of deformation of the knit, suitable for three-dimensional modeling of its structure, considering deformation of the thrust, was developed. Practical value. The developed model can be used as mathematical support of systems of automated designing of knits.

Analysis of a Preliminary Design Approach for Conformal Lattice Structures

An important issue when designing conformal lattice structures is the geometric modeling and prediction of mechanical properties. This paper presents suitable methods for obtaining optimized conformal lattice structures and validating them without the need for high computational power and time, enabling the designer to have quick feedback in the first design phases. A wireframe modeling method based on non-uniform rational basis spline (NURBS) free-form deformation (FFD) that allows conforming a regular lattice structure inside a design space is presented. Next, a previously proposed size optimization method is adopted for optimizing the cross-sections of lattice structures. Finally, two different commercial finite element software are involved for the validation of the results, based on Euler–Bernoulli and Timoshenko beam theories. The findings highlight the adaptability of the NURBS-FFD modeling approach and the reliability of the size optimization method, especially in stretching-dominated cell topologies and load conditions. At the same time, the limitation of the structural beam analysis when dealing with thick beams is noted. Moreover, the behavior of different kinds of lattices was investigated.

Mechanical-Geometrical Modeling Of The Hyperelastic Materials At Uniaxial Stretching

Hyperelastic materials, such as rubber, occupy an important place in the design and operation of various technological equipment and machines. The article analyzed the deformation behavior of hyperelastic materials using a mechanical-geometric model. The method of mechanical-geometric modeling is a new method for obtaining constitutive relations and strain energy density functions for nonlinear elastic solids. It is based on physically and geometrically consistent prerequisites. The resulting models can describe broad classes of nonlinear elastic materials (both isotropic and anisotropic) depending on the mechanical and geometric properties “embedded” in them at the first stages of design. This paper discusses two basic types of models based on different initial geometry. The mechanical parameters of the models are constants, and the models themselves are considered in a statement corresponding to isotropic hyperelastic materials. The article presents the most common diagrams of deformation of artificial and natural rubbers, as well as steel. Hyperelastic materials, depending on the task, can be described in the nonlinear theory of elasticity as ideal incompressible, or as weakly compressible. Parameters of expressions of strain energy density functions of mechanical-geometric models obtained for cases of incompressible and weakly compressible continuous solids were identified. Stretch diagrams and diagrams of the transverse deformation function of the obtained mechanical-geometric models for the two cases mentioned above are plotted. The extension diagram for the model with parameters corresponding to the classic structural material of the steel type is also shown. Comments are given on the possibility of further paths of developing the method of mechanical-geometric modeling to obtain results not only in the field of nonlinear theory of elasticity, but also viscoelasticity.