РЕШЕНИЕ ПРОБЛЕМЫ ФОРМООБРАЗОВАНИЯ ОБТЯЖКОЙ ДЕТАЛЕЙ ОБШИВОК САМОЛЕТА ЧЕРЕЗ ВНУТРЕННЮЮ ГЕОМЕТРИЮ ПОВЕРХНОСТИ

Axis estimation and grouping of rotationally symmetric object segments

A method for revealing the localised work hardened region (plastic deformation zone) in Mg–9Al–1Zn alloy (AZ91) has been developed using a new etching technique. With this technique, etching with the solution (9 g picric acid, 30 mL acetic acid, 150 mL ethyl alcohol and 20 mL H2O) was executed on the samples after plastic deformation and then heating to 300°C for 3 h. Because of the high strain energy in the plastic deformation zone, the microstructural characteristic in the deformation zone changed substantially after the heating process, where severe precipitation of Mg17Al12 phase occurred in the Mg rich α phase. With the change of microstructural characteristics, the deformation region can be revealed. The plastic zone was revealed by the different degrees of etching response in the deformation and undeformed regions; the plastic zone was slightly etched, whereas the other region was deeply etched. From the different surface height level, the deformation zone was found to be observable even at low magnification.

Experimental observation and numerical modeling of formation of local plastic zones in hardened surface layers due to contact overloading

Slowness surface for bulk wave propagation in anisotropic media can be divided into concave, saddle and convex regions by the parabolic lines. When a parabolic line crosses a symmetry plane, it leaves either an inflection point or a parabolic point. Surface normal at these points is associated with cuspidal point and swallowtail point, respectively, on the wave surface and in phonon focusing patterns. By examining the degeneracies in the Stroh eigenvalue equation, we have calculated the cuspidal points in cubic crystals analytically. In this work, the parabolic point and its surface normal are discussed. The main idea is to establish a connection between the parabolic point and the extraordinary transonic state that is related to a degeneracy with a multiplicity of four in the Stroh eigenvalue equation. Such a connection yields a series of simple expressions, which determine the locations of parabolic points and the corresponding swallowtail points. The result is demonstrated using phonon focusing patterns of cubic crystals, and the method also provides a tool for general discussion of the slowness surface geometry.

Low-temperature impact toughness and deformation mechanism of CT20 titanium alloy

With the rapid growth of free form architectures, the demand for architectural geometry technologies increases dramatically in recent years. Architectural geometry contains knowledge highly relevant to computer graphics and geometry especially discrete differential geometry. In addition, architectural geometry provides new context for some well-established concepts and brings new challenges and new objectives. In this dissertation, we tackle four challenges in architectural geometry. These four proposed solutions cover various processes including architecture maintenance, architecture construction, architecture texture mapping and architecture decoration. In Chapter 4, we present a data model synchronization method that preserves semantic information across editing operations relying only on geometry, UV mappings, and materials. This enables easy integration of existing and future 3D editing techniques with rich data models. The method links the original data model to the edited geometry using point set registration, recovering the existing information based on spatial and UV search methods, and automatically labels the newly created geometry. The implementation synchronized changes in the 3D geometry with a CityGML data model. In Chapter 5, we present a simple yet effective method for constructing 3D self-supporting surfaces with planar quadrilateral (PQ) elements. Starting with a self-supporting surface in triangle mesh, we first compute the principal curvatures and directions of each triangular face using a new approach, yielding more accurate results than existing methods. Then, we smooth the principal direction field to reduce the number of singularities and partition all faces into two groups in terms of principal curvature difference. For each face with small curvature difference, we compute a stretch matrix that turns the principal directions into a pair of conjugate directions. Finally, applying a mixed-integer programming solver to the mixed principal and conjugate direction field, we obtain a planar quadrilateral mesh. Experimental results show that our method is computationally efficient and can yield high-quality PQ meshes that well approximate the geometry of the input surfaces and maintain their self-supporting properties. In Chapter 6, we present a simple and robust algorithm to compute quad layout. We first propose an interpolation strategy to find tracing directions for singularities: given a singularity with index k (which is a multiple of 1/4), there are exactly 4-4k searching directions produced. We then trace integral curves with a rounding strategy to encourage them to go through mesh vertices, which can effectively reduce the number of short segments. Finally, we partition the triangle mesh along the integral curves to extract the quadrilateral patches. Our method does not require any numerical solver and is easy to implement and computationally efficient. Computational results show that our results have consistently fewer quad patches than those of the existing methods. For models with rich geometric details, our method can save up to 50\% patches in the quad layout. In Chapter 7, we present research in contrast-enhanced high-relief modeling. We present a simple and effective method to generate contrast-enhanced high-reliefs. Our key idea is a depth compression function with only two variables for 3D models. In this function, normals and mean curvatures are utilized to enhance the contrast of the resulting high-reliefs. To calculate the two variables in depth compression function, we construct an optimization framework with two objectives, volume minimization and contrast maximization. The variables are obtained when the two terms reach a balance point. Our method narrows down the solution space to only two variables and is easy to implement and produces good-quality high-reliefs. We show results on a range of real 3D models including real-world and synthetic models. In summary, we present four algorithms in architectural geometry. These solutions cover many applications including semantic information update, free form surface construction, surface parameterization and architecture surface decoration. We demonstrate the effectiveness of the proposed methods through extensive evaluation and comparison with the state-of-the-art methods.

Methodical aspects of estimating plastic deformation zones following contrasting types of loading (static and explosive) are addressed using holographic interferometry. The paper presents sample cases of identification and determination of the shape and dimensions of plastic deformation zones near the geometric stress concentrator at the uniaxial tension of plane samples of constructional materials, as well as the so-called effective plastic trace left after the directed local explosive effect on a steel plate. In the latter case we use the method of determining the site of deformation of the objects with the diffuse reflection. A plastic zone is identified by interferograms and/or according to the distribution of the orders of the interference bands.

Test studies of gas flow in rock and coal surrounding a mined coal seam

This study investigates the geometry and singular behavior of swept surfaces generated by the move of Bishop frame along a spatial curve in Euclidean 3-space. The surface is defined as the envelope of a family of unit spheres whose centers trace an axial trajectory, with the contact points forming great circles within a prescribed plane. A parametric representation is established to highlight the dependence of the surface on both the axial and profile curves. Key geometric features including the coefficients of the first fundamental form, unit normal vectors, and curvature characteristics are analyzed, revealing that the profile curves act as planar geodesics and curvature lines. We further examine singularities, offset surfaces, and parabolic curves, deriving conditions for smoothness, geodesicity, and convexity. Special attention is given to the criteria under which the surface becomes developable, particularly when it reduces to a cylinder, cone, or tangent surface. Several illustrative examples, including those arising from mate curves of slant helices and circular trajectories, demonstrate the resulting geometric phenomena.

We study experimentally the slow growth of a single crack in a glassy film of polycarbonate submitted to uniaxial and constant imposed load. Flame-shaped macroscopic zones of plastic deformation appear at the tips of the crack and the formation of these plastic zones involves a necking instability. In order to understand the crack growth dynamics, we study first the growth dynamics of the plastic zones alone, i.e. without crack, at constant imposed load. We find that the growth velocity of the neck can be very well described by the same Eyring's factor as the one describing the creep flow of polycarbonate. In addition, we discover that a surface oscillation with a very large wavelength-to-amplitude ratio occurs during the neck propagation, and that both wavelength and amplitude are proportional to the film thickness. Finally, we succeed in modelling analytically the dependence of the instantaneous crack velocity on experimental variables using Dugdale-Barenblatt static description of crack tip plastic zones associated to Eyring's law and an empirical dependence on the crack length that may come from a residual elastic field.

The relations between parabolic and planar points of a Lambertian surface M and critical points of the corresponding image irradiance E are studied. It is proved that critical points of E, with the exception of nondegenerate global maxima, occur at points on M with zero Gaussian curvature and that critical points of E that are stable with respect to changes of the position of the light source occur at planar points of M. Furthermore, it is shown that at global maxima of E there exists a simple relation between the principal curvatures of M and L, the graph of E. The relations between planar (parabolic) points of L and planar (parabolic) points of M are also analyzed. Finally, some relationships between isophotes of E and lines of curvature of M are investigated.

The variation-difference method is a convenient numerical method for shells of complex forms. It is enough when only cinematic boundary conditions are satisfied because the method is based on the principle of Lagrange. Another advantage of the variation-difference method is the better opportunity to create computer programs based on it. For shell analysis in orthogonal coordinate system as well as for shell analysis in principal curvatures the system of equations describing stress-strain state can be simplified. In this paper the difference between analysis in orthogonal coordinate system and analysis in principal curvatures of the surface is considered. The main distinction of the analysis of shells in orthogonal curvilinear coordinate system is the necessity of determination of components which include curvature of torsion of coordinate lines. The addition of these components in the equations of the theory of shells for the coordinate system in principal curvatures gives possibility to analyze shells in common orthogonal coordinate system. In this article shell analysis in orthogonal coordinate system is applied to shells based on normal cyclic surfaces.

Depth-sensing indentation, on the sub-micron scale— nanoindentation, is now routinely used as a means of measurement of the mechanical properties of thin films and small volumes of materials. Significant effort has been applied to an understanding of the load displacement response in order to obtain meaningful data for elastic modulus and hardness with respect to corrections for instrument and materials related issues [1]. The most common indenter used in nanoindentation experiments is the three-sided pyramidal Berkovich indenter with which it is usually desired to obtain a fullydeveloped plastic zone in the specimen material corresponding to indenter displacements of less than a micron. The formation of the plastic zone is physically associated with the generation of heat within the specimen material, and as a consequence, a temperature rise. Such a temperature rise results in the thermal expansion of the specimen material in the vicinity of the indenter, and this may in turn be registered in the displacement readings taken during the indentation—thus having an undesirable effect on the subsequent analysis of the load-displacement data. Such an effect has hitherto not been considered in the analysis of depthsensing nanoindentation test data. The purpose of the present work is to present a first-order treatment of the phenomenon, and to stimulate further study of the related material issues. Although most analyses of nanoindentation test data assume a quasi-static process, typical indentations are usually accomplished over a matter of a few seconds, and for the purpose of the present discussion, we shall assume that the process is adiabatic. The net work of indentation will be assumed to be accounted for by heat within the plastic zone, and any dissipative effects due to friction at the interface between the indenter and specimen will be ignored. The work of indentation Up can be easily calculated by numerically calculating the net area under the loaddisplacement curve. The volume Vp of material affected by plastic deformation can be calculated from the dimensions of the plastic zone, which in turn are more easily determined by finite element analysis. The mass of material thus affected is calculated from the density ρ and volume V of the plastic zone. The resulting average temperature rise T is thus given by:

Compared to usual cold rolling conditions the length of contact between work roll and strip is very short in case of temper rolling. As a consequence, work roll flattening becomes critical even for small contact pressures, and the simplifying assumption of a “circular arc” contour of the deformed work roll cannot be justified anymore. A new temper rolling model is presented applying a non circular arc theory using a semi‐analytical procedure for the calculation of the elastic work roll deformations based on numerical superposition of influence functions. In addition to the radial displacements of the work roll, also the circumferential displacements, generated mainly by the shear stresses acting on the work roll surface, are taken into account. The circumferential displacements heavily affect the relative speed (slip speed) between the surfaces of work roll and strip, this speed being a crucial input parameter for any friction law. Hence, the evolution of the shear stresses in the roll gap is re‐affected by these circumferential displacements. Their influence is increasing with decreasing temper degrees and cannot be neglected in such cases. The formation of a neutral zone instead of a neutral point is a natural consequence of this approach. The model for the strip is based on Karman’s theory. In addition to the elastic compression‐, elastic recovery‐ and plastic zone, also elastic regions are allowed to arise between plastic zones (Internal Elastic Zones). The consequence is that the case of contained plastic flow will appear automatically without additional simplifying assumptions. Simulation results from the new model are presented and discussed. Their comparison with results from FE‐simulations shows very good agreement. The model was calibrated against practical data from an existing temper rolling mill. For this purpose extensive temper rolling tests were performed.

Localized plastic deformation in amorphous films on a ductile substrate