Conical Meshes Research Articles

An asymptotic preserving scheme for the $$M_1$$ model on polygonal and conical meshes

An asymptotic preserving scheme for the $$M_1$$ model on polygonal and conical meshes

MODELING OF 3D-PRINTING PROCESSES FOR COMPOSITE TOOLING AND TRANSFER MOLDING OF GRID STRUCTURES

The paper discusses the method of obtaining a digital passport of the material and the development of a digital twin of the product at various stages of its manufacture. The object of research is a conical mesh structure. The subject of research is the processes occurring in the product at the manufacturing stages. The following main stages of creating a mesh structure were considered in the work: 3D printing of a workpiece tooling, laying out a carbon unidirectional material, heating and impregnation of the preform with a binder, polymerization of the binder, and warpage of the product geometry. An algorithm for determining the properties of materials and their calibration using modern software and hardware and universal equipment was described. Modeling of the tooling 3D printing process was carried out in the Ansys software package. Step-by-step technological modeling of the transfer molding process was carried out using the ESI PAM-COMPOSITE software package. The result of the simulation is the optimal technological manufacturing parameters and the geometry of the shaping tooling with anticipation of warping.

Asymptotic preserving schemes on conical unstructured 2D meshes

AbstractIn this article, we consider the hyperbolic heat equation. This system is linear hyperbolic with stiff source terms and satisfies a diffusion limit. Some finite volume numerical schemes have been proposed which reproduce this diffusion limit. Here, we extend such schemes, originally defined on polygonal meshes, to conical meshes (using rational quadratic Bezier curves). We obtain really new schemes that do not reduce to the polygonal version when the conical edges tend to straight lines. Moreover, these schemes can handle curved unstructured meshes so that geometric error on initial data representation is reduced and geometry of the domain is improved. Extra flux coming from conical edge (through his midedge point) has a deep impact on the stabilization when compared with the original polygonal scheme. Cross‐stencil phenomenon of polygonal scheme has disappeared, and issue of positivity for the diffusion problem (although unresolved on distorted mesh and/or with varying cross‐section) has been in some sense improved.

КОНСТРУКТИВНО-ТЕХНОЛОГІЧНІ ОСОБЛИВОСТІ ХВОСТО-ВИХ БАЛОК СІТЧАСТОГО ТИПУ З ПОЛІМЕРНИХ КОМПО-ЗИЦІЙНИХ МАТЕРІАЛІВ ВЕРТОЛЬОТІВ ТРАНСПОРТНОЇ КАТЕГОРІЇ

The analysis of the design and technological features of the tail boom (ТB) of a helicopter made of polymer composite materials (PCM) is carried out.Three structural and technological concepts are distinguished - semi-monocoque (reinforced metal structure), monocoque (three-layer structure) and mesh-type structure. The high weight and economic efficiency of mesh structures is shown, which allows them to be used in aerospace engineering. The physicomechanical characteristics of the network structures are estimated and their uniqueness is shown. The use of mesh structures can reduce the weight of the product by a factor of two or more.The stress-strain state (SSS) of the proposed tail boom design is determined. The analysis of methods for calculating the characteristics of the total SSS of conical mesh shells is carried out. The design of the tail boom is presented, the design diagram of the tail boom of the transport category rotorcraft is developed. A finite element model was created using the Siemens NX 7.5 system. The calculation of the stress-strain state (SSS) of the HC of the helicopter was carried out on the basis of the developed structural scheme using the Advanced Simulation module of the Siemens NX 7.5 system. The main zones of probable fatigue failure of tail booms are determined. Finite Element Analysis (FEA) provides a theoretical basis for design decisions.Shown is the effect of the type of technological process selected for the production of the tail boom on the strength of the HB structure. The stability of the characteristics of the PCM tail boom largely depends on the extent to which its design is suitable for the use of mechanized and automated production processes.A method for the manufacture of a helicopter tail boom from PCM by the automated winding method is proposed. A variant of computer modeling of the tail boom of a mesh structure made of PCM is shown.The automated winding technology can be recommended for implementation in the design of the composite tail boom of the Mi-2 and Mi-8 helicopters.

Shape Recognition Using V4 Dominant Conical Meshes

This research work introduces a new concept of shape recognition where we obtain a geometric form from some given parameters related to architecture geometry. They include cell face slope, edge length initial value of the vertical alignment and boundary vertices of the horizontal alignment. Here we construct a conical mesh with horizontal planar latitudes from initial horizontal and vertical alignments. For this purpose, analytic geometry, interpolation, data structures using Visual C++ Programming, computational geometry and CAD features are used

Curve-pleated structures

In this paper we study pleated structures generated by folding paper along curved creases. We discuss their properties and the special case of principal pleated structures. A discrete version of pleated structures is particularly interesting because of the rich geometric properties of the principal case, where we are able to establish a series of analogies between the smooth and discrete situations, as well as several equivalent characterizations of the principal property. These include being a conical mesh, and being flat-foldable. This structure-preserving discretization is the basis of computation and design. We propose a new method for designing pleated structures and reconstructing reference shapes as pleated structures: we first gain an overview of possible crease patterns by establishing a connection to pseudogeodesics, and then initialize and optimize a quad mesh so as to become a discrete pleated structure. We conclude by showing applications in design and reconstruction, including cases with combinatorial singularities. Our work is relevant to fabrication in so far as the offset properties of principal pleated structures allow us to construct curved sculptures of finite thickness.

Surfaces with planar curvature lines: Discretization, generation and application to the rationalization of curved architectural envelopes

Abstract Motivated by architectural applications, we propose a method to generate circular and conical meshes with planar curvature lines in both directions. The method is based on the discretization of the Gauss map of surfaces with planar curvatures lines. It allows generation of meshes in real-time via two planar guide curves. The resulting meshes can be used as a geometric base to build gridshells with flat panels, torsion free-nodes, node offset and planar arches. A particular technological application is for gridshells built with curved members: those can be built with planar piecewise-circular beams, and identical nodes if beams have circular cross-section.

Femoral hernia: reappraisal of low repair with the conical mesh plug.

Femoral hernias, rare among groin hernias, have been dealt with using various well-established techniques in emergency and elective settings. Lockwood's description and its various modifications have been used for decades. We here describe again a simple and elegant technique for femoral hernia repair using a conical mesh plug performed in a series of 31 patients. A prospective study of femoral hernia repair in 31 patients via a low inguinal approach using an improvised conical mesh plug is presented. Patients were followed up for any recurrence as the primary end point. The incidence of morbidity including chronic groin pain was recorded. Thirty-two hernias in 31 patients were managed in 2years. The majority of patients were female (94%) with a median age of 60 (16-70) years. Primary femoral hernias were preponderant with the majority on the left (81%). In an average follow-up period of 18months, there were no recurrences, minimal morbidity (3%) and no incidence of chronic inguinodynia. The low inguinal repair with a conical mesh plug is easily reproducible, elegant and probably the best method for femoral hernia repair.

Modulated heat transfer tube with short conical-mesh inserts: A linking from microflow to macroflow

This paper creates new method that uses microflows through mesh pores to modulate flow and temperature fields. Modulated heat transfer tube (MHTT) was constructed by suspending consecutive conical-mesh inserts in a tube. Because there are too many 3D mesh pores (10–100μm size) for a conical mesh insert, numerical simulations in laminar flow regime were performed by an 3D to 2D conversion of mesh pores applying equal equivalent diameter criterion and total flow area criterion of mesh pores. The multiscale grid generation linked micron scale of mesh pores and macroscale of the tube. Covering the present data ranges, MHTT had Nusselt numbers which are 1.4–4.1 times of that in a bare tube, PEC (performance evaluation criterion) was up to 2.2, demonstrating excellent heat transfer enhancement at low flow rate pumping cost. The perfect MHTT performance comes from the distinct flow field: an attached hydraulic boundary layer having large velocity and its gradient near the tube wall, a weak circulating flow region upstream of the mesh insert and a weakly positive flow region downstream of the mesh insert. A thin thermal boundary layer on the tube wall was reached to enhance heat transfer. The periodic unit length S and diameter of the conical mesh insert δ were optimized. The varied slopes of Nu versus Re were found and explained while increasing Re. There are best matches of PPI (pores per inch) and Re (Reynolds number). Low PPI mesh insert was suggested at low Re, high PPI mesh insert deformed streamlines to deviate from the perfect flow and temperature fields. Meanwhile, high PPI mesh insert had better performance at high Re. Low PPI mesh insert had good performance, which can be further improved by raising PPI. Because metallic mesh screen is commercialized and cheap, MHTT has wide potential engineering applications.

Extension of centered hydrodynamical schemes to unstructured deforming conical meshes : the case of circles

In a prior work (CEMRACS10), a curvilinear bi-dimensional nite volume extension of Lagrangian centered schemes GLACE (GLACE) on unstructured cells, whose edges are parame- terized by rational quadratic B ezier curves was proposed and we showed numerical results for this scheme. Now, we extend the EUCCLHYD scheme (EUCCLHYD) to these cells. To simulate ows with evolving large deformations, we write a formalism allowing the time evolution of the conic pa- rameter. As an example, this allows an edge changing from an ellipse segment to a hyperbolic one. In this framework, we consider the case of a mesh whose edges are circle segments with non xed centers. We show that this formalism extends also the previous work (GLACE CIRCLE) (which is equivalent to (CEMRACS10) when conic edges are all circles). This is a necessary rst step toward general conical deformation. R esum e.

Extension of ALE methodology to unstructured conical meshes

We propose a bi-dimensional finite volume extension of a continuous ALE method on unstructured cells whose edges are parameterized by rational quadratic Bezier curves. For each edge, the control point possess a weight that permits to represent any conic (see for example [LIGACH]) and thanks to [WAGUSEDE,WAGU], we are able to compute the exact area of our cells. We then give an extension of scheme for remapping step based on volume fluxing [MARSHA] and self-intersection flux [ALE2DHAL]. For the rezoning phase, we propose a three step process based on moving nodes, followed by control point and weight re-adjustment. Finally, for the hydrodynamic step, we present the GLACE scheme [GLACE] extension (at first-order) on conic cell using the same formalism. We only propose some preliminary first-order simulations for each steps: Remap, Pure Lagrangian and finally ALE (rezoning and remapping).

Infinitesimally flexible meshes and discrete minimal surfaces

We explore the geometry of isothermic meshes, conical meshes, and asymptotic meshes around the Christoffel dual construction of a discrete minimal surface. We present a discrete Legendre transform which realizes discrete minimal surfaces as conical meshes. Conical meshes turn out to be infinitesimally flexible if and only if their spherical image is isothermic, which implies that discrete minimal surfaces constructed in this way are infinitesimally flexible, and therefore possess reciprocal-parallel meshes. These are discrete minimal surfaces in their own right. In our study of relative kinematics of infinitesimally flexible meshes, we encounter characterizations of flexibility and isothermicity which are of incidence-geometric nature and are related to the classical Desargues configuration. The Lelieuvre formula for asymptotic meshes leads to another characterization of isothermic meshes in the sphere which is based on triangle areas.

The focal geometry of circular and conical meshes

Circular meshes are quadrilateral meshes all of whose faces possess a circumcircle, whereas conical meshes are planar quadrilateral meshes where the faces which meet in a vertex are tangent to a right circular cone. Both are amenable to geometric modeling – recently surface approximation and subdivision-like refinement processes have been studied. In this paper we extend the original defining property of conical meshes, namely the existence of face/face offset meshes at constant distance, to circular meshes. We study the close relation between circular and conical meshes, their vertex/vertex and face/face offsets, as well as their discrete normals and focal meshes. In particular we show how to construct a two-parameter family of circular (resp., conical) meshes from a given conical (resp., circular) mesh. We further discuss meshes which have both properties and their relation to discrete surfaces of negative Gaussian curvature. The offset properties of special quadrilateral meshes and the three-dimensional support structures derived from them are highly relevant for computational architectural design of freeform structures. Another aspect important for design is that both circular and conical meshes provide a discretization of the principal curvature lines of a smooth surface, so the mesh polylines represent principal features of the surface described by the mesh.

Geometric modeling with conical meshes and developable surfaces

In architectural freeform design, the relation between shape and fabrication poses new challenges and requires more sophistication from the underlying geometry. The new concept of conical meshes satisfies central requirements for this application: They are quadrilateral meshes with planar faces, and therefore particularly suitable for the design of freeform glass structures. Moreover, they possess a natural offsetting operation and provide a support structure orthogonal to the mesh. Being a discrete analogue of the network of principal curvature lines, they represent fundamental shape characteristics. We show how to optimize a quad mesh such that its faces become planar, or the mesh becomes even conical. Combining this perturbation with subdivision yields a powerful new modeling tool for all types of quad meshes with planar faces, making subdivision attractive for architecture design and providing an elegant way of modeling developable surfaces.

A New Tool-Path Generation Method Using a Cylindrical End Mill for 5-Axis Machining of a Spatial Cam with a Conical Meshing Element

The geometry of a spatial cam is normally generated using a form-milling cutter and a special multi-axis machine and software. The general purpose CAD/CAM software can generate the cutter location file of this class of product only by the sculpturing method. Because of the limited choice of cutting tool when using the generating method, this paper presents a new toolpath generating method which combines the advantages of the generating and sculpturing methods for machining a spatial cam. In the machining process, the cutter location is derived for rough and finish machining using a cylindrical end mill. The guidelines for choosing cutter diameter for the machining process are discussed. To avoid interference, the principal curvatures and the principal induced normal curvatures are analysed. The mathematical errors including chordal deviation and scallop height are used as the basis for generating appropriate tool-paths. Cutting simulation of a solid model was performed to verify the proposed tool-path generation method.

Evaluation of a partial flow-through culture technique for pearl oyster (Pinctada margaritifera L.) larvae

This study evaluated a partial flow-through culture system for larvae of the blacklip pearl oyster (Pinctada margaritifera, L.). Water flowed through the 500-l larval rearing tanks for 12 h day−1 and provided a 100% water exchange during this period. Larvae were prevented from leaving the culture tanks by a conical mesh screen placed over a central stand-pipe. Tanks were completely drained every 7 days to prevent build-up of debris on the tank bottom. First `eyed' larvae were seen on day 23 and, by day 28, approximately 5% of the larvae initially stocked had reached the `eyed' stage and were removed into settlement tanks. Larval growth and survival compared favourably with previous studies in which P. margaritifera larvae were cultured using conventional static culture methods. However, when compared to static culture systems, the partial flow-through system described in this study requires less labour and, as such, is likely to be more appropriate for hatchery culture in developing Pacific nations.

Computer aided photoelastic stress analysis of a variable-pitch lead screw

Three-dimensional stress-freezing photoelasticity is applied to analyse the stress in a variable-pitch lead screw at contact with two conical meshing elements. A PC-based image-processing system and the relevant digital techniques are used to collect the photoelastic data, and the cubic technique is used to evaluate the effective stress at the contact region. The model-making and computer aided data collection procedures are described. Contour plots of the effective stress at the contact regions are presented. It was found that the highest effective stress values on the two contact thread surfaces are approximately the same, although the exerting forces are quite different.

Surface Geometry of Variable Pitch Cylindrical Cams with Conical Meshing Elements

This paper presents mathematical expressions for the surface geometry of variable pitch cylindrical cams with four conical meshing elements based on the theory of conjugate surfaces. The unit normal of the element is derived, with given surface geometry of the meshing element, by differential geometry. The contact lines of the conjugate surface are defined according to the equation of meshing and the specified input-output relation. By the coordinate transformation of contact lines, we have the complete profile of the variable pitch cylindrical cam. The results of this work are instrumental in computer-aided manufacturing of variable pitch cylindrical cams for industrial applications.

Curvature analysis of variable pitch cylindrical cams with conical meshing elements

Based on the theory of gearing, we determine the geometry and the contact line of variable pitch cylindrical cams. Then, according to curvature theory, we obtain the principal curvatures and their directions at any contact point. Furthermore, we derive the orientation of the contacting line, the reduced normal curvature along any tangential direction, and the angle between the normal of contact line and the relative velocity. The results of this work are needed for contact stress analysis and wear/lubrication analysis for variable pitch cylindrical cams with conical meshing elements.

Axially symmetric propagation of small-amplitude ion-acoustic waves

In this paper a generalization of the Korteweg–de Vries equation, which may be applicable to the axially symmetric propagation of ion-acoustic waves from a conical mesh, is sought. In an appropriate limit the equation for propagation of axially symmetric waves in a cylindrical geometry is also obtained.