Calculation Of Curvature Research Articles

Generating virtual process maps of SLM using powder-scale SPH simulations

In selective laser melting (SLM), three-dimensional parts are build up from a metal powder bed by layer-wise melting with a laser. While SLM offers a high flexibility in geometrical design and material texture, the interplay of dozens of parameters is difficult to analyze experimentally. The current research focuses on numerical simulation to increase confidence in manufactured parts and to reduce the time to market. Using a smoothed particle hydrodynamics (SPH) implementation on GPU, the 3D melt pool dynamics in a single laser track can be simulated within less than 2 h with a reasonable spatial resolution of 3 $$\upmu $$m. This is an extreme speedup compared to concurrent CFD methods that have recently been applied to the same problem. Using a SPH implementation on GPU, the 3D melt pool dynamics in a single laser track can be simulated within less than an hour with a reasonable spatial resolution of 3 $$\upmu $$m. This is an extreme speedup compared to concurrent CFD methods that have recently been applied to the same problem. The computational efficiency allows to conduct parameter studies, which before were prohibitively expensive, to generate a virtual process. To make the simulations possible a curvature calculation technique was applied, which is novel in the field of SPH. Additionally the advantage of a direct description of the internal energy is outlined by comparing the approach with the commonly applied apparent heat approach. Designers may profit from the fast simulations in two different scenarios: firstly, through a direct numerical simulation of certain parameter combinations and scenarios and, secondly, by informing advanced surrogate models or part-scale models to predict the behavior of the entire part being produced. When adapting the heat source model, the SPH framework may also be used to describe the related electron beam melting process.

High Order Anchoring and Reinitialization of Level Set Function for Simulating Interface Motion

A second order interface anchoring method has been developed and used with fast sweeping algorithm for reinitialization of a level set function. The algebraic anchoring formulation ensures that the location of the actual interface is preserved, leading to better mass conservation property. It also provides high order accurate algebraic constraint for solving the Eikonal equation on a finite difference grid. Geometric properties of the interface such as surface normal and curvature are subsequently computed from the reinitialized distance function. Various analytical functions for modeling distortion in level set field are considered and accuracy of reinitialization is evaluated using first and second order anchoring schemes. It is also shown that accurate computation of interface curvature requires a high order anchor in addition to a high order fast sweeping method. Mass conservation property of reinitialization is also analyzed by considering test problems from literature including the classic Rider–Kothe single vortex problem. The formulation is suitable for efficient parallelization for both distributed memory and on-node shared memory parallel systems. Scalability and performance of the reinitialization scheme on multiple architectures are demonstrated.

Dislocation density distribution at slip band-grain boundary intersections

We study the mechanisms of slip transfer at a grain boundary, in titanium, using Differential Aperture X-ray Laue Micro-diffraction (DAXM). This 3D characterisation tool enables measurement of the full (9-component) Nye lattice curvature tensor and calculation of the density of geometrically necessary dislocations (GNDs). We observe dislocation pile-ups at a grain boundary, as the neighbour grain prohibits easy passage for dislocation transmission. This incompatibility results in local micro-plasticity within the slipping grain, near to where the slip planes intersect the grain boundary, and we observe bands of GNDs lying near the grain boundary. We observe that the distribution of GNDs can be significantly influenced by the formation of grain boundary ledges that serve as secondary dislocation sources. This observation highlights the non-continuum nature of polycrystal deformation and helps us understand the higher order complexity of grain boundary characteristics.

Computing interface curvature from volume fractions: A machine learning approach

The volume of fluid (VOF) method is widely used to simulate the flow of immiscible fluids. It uses a discrete and sharp volume fractions field to represent the fluid-fluid interface on a Eulerian grid. The most challenging part of the VOF method is the accurate computation of the local interface curvature which is essential for evaluation of the surface tension force at the interface. In this paper, a machine learning approach is used to develop a model which predicts the local interface curvature from neighbouring volume fractions. A novel data generation methodology is devised which generates well-balanced randomized data sets comprising of spherical interface patches of different configurations/orientations. A two-layer feed-forward neural network with different network parameters is trained on these data sets and the developed models are tested for different shapes i.e. ellipsoid, 3D wave and Gaussian. The best model is selected on the basis of specific criteria and subsequently compared with conventional curvature computation methods (convolution and height function) to check the nature and grid convergence of the model. The model is also coupled with a multiphase flow solver to evaluate its performance using standard test cases: i) stationary bubble, ii) oscillating bubble and iii) rising bubble under gravity. Our results demonstrate that machine learning is a feasible approach for fairly accurate curvature computation. It easily outperforms the convolution method and even matches the accuracy of the height function method for some test cases.

Quantifying Tongue Tip Shape in Apical and Laminal /s/: Contributions of Palate Shape.

Purpose Anterior tongue shape during /s/ production is often described as "tip-up" or apical, versus "tip-down" or laminal. Typically, this is determined by observing the shape of the anterior midline tongue. The purpose of this study was to identify methods of curvature calculation that quantify the observed shape differences and to examine whether the shape differences were affected by palate shape. Previous work shows that palate height has some effect (Grimm et al., 2017). Method Four curvature-based measures were applied to a series of points selected along the tongue surface in midsagittal cine magnetic resonance images during speech. The measures were minimal curvature, averaged largest curvature (ALC), normalized ALC, and interpolated normalized ALC. These measures were compared to visual judgments of apical and laminal /s/. Anterior palate shape was measured from dental casts. Results The apical /s/ contained a flat or concave region in the anterior tongue, while the laminal /s/ had a convex shape along the entire tongue. Thus, the laminal shape was less complex than the apical. The last 2 metrics, based on averages of multiple normalized curvatures, captured this complexity difference. Subjects with a more steeply sloped anterior palate tended to use laminal /s/. Conclusions The tongue shape for the 2 /s/ types was best defined by complexity of the shape, rather than local anterior shape. Statistical quantities that measured curvature in multiple locations, and normalized across subjects, were best at distinguishing the 2 /s/ shapes. Interpolating additional points between the manually selected ones did not improve the method. Supplemental Material https://doi.org/10.23641/asha.9733709.

A Novel Framework for Early Detection of Hypertension using Magnetic Resonance Angiography

Hypertension is a leading mortality cause of 410,000 patients in USA. Cerebrovascular structural changes that occur as a result of chronically elevated cerebral perfusion pressure are hypothesized to precede the onset of systemic hypertension. A novel framework is presented in this manuscript to detect and quantify cerebrovascular changes (i.e. blood vessel diameters and tortuosity changes) using magnetic resonance angiography (MRA) data. The proposed framework consists of: 1) A novel adaptive segmentation algorithm to delineate large as well as small blood vessels locally using 3-D spatial information and appearance features of the cerebrovascular system; 2) Estimating the cumulative distribution function (CDF) of the 3-D distance map of the cerebrovascular system to quantify alterations in cerebral blood vessels’ diameters; 3) Calculation of mean and Gaussian curvatures to quantify cerebrovascular tortuosity; and 4) Statistical and correlation analyses to identify the relationship between mean arterial pressure (MAP) and cerebral blood vessels’ diameters and tortuosity alterations. The proposed framework was validated using MAP and MRA data collected from 15 patients over a 700-days period. The novel adaptive segmentation algorithm recorded a 92.23% Dice similarity coefficient (DSC), a 94.82% sensitivity, a 99.00% specificity, and a 10.00% absolute vessels volume difference (AVVD) in delineating cerebral blood vessels from surrounding tissues compared to the ground truth. Experiments demonstrated that MAP is inversely related to cerebral blood vessel diameters (p-value < 0.05) globally (over the whole brain) and locally (at circle of Willis and below). A statistically significant direct correlation (p-value < 0.05) was found between MAP and tortuosity (medians of Gaussian and mean curvatures, and average of mean curvature) globally and locally (at circle of Willis and below). Quantification of the cerebrovascular diameter and tortuosity changes may enable clinicians to predict elevated blood pressure before its onset and optimize medical treatment plans of pre-hypertension and hypertension.

WEB-BASE 3D SOFTWARE UNTUK PERENCANAAN DAN PELAKSANAAN TRAJECTORY PEMBORAN BERARAH

In drilling activities there are several types of trajectories, one of which is directional drilling. In a directed drilling operation, the engineer must carry out a design of the well trajectory and then do a calculation then the results are used as a reference for the calculation of the well trajectory after the drilling operation. In this study a system was built in the application to help engineers perform calculations on Plan Trajectory data and Survey Trajectory data so that further evaluation can be made of deviations that occur by implementing the Minimum Of Curvature calculation method.While the system development method used is the Waterfall method which will be divided into three stages in building a system, namely problem analysis, gathering system requirements and system design. The method of data collection is done by collecting secondary data sources. The application is built with the support of PHP, Javascript and PHPMyAdmin programming languages for database management.From the results of the analysis, design and testing carried out successfully built 3D Application Planning and Implementation of Drilling Trajectory Leading to the "X" Well With the Minimum Of Curvature Method which is quite accurate at 62.26% in reducing the possibility of formula writing errors from the previous system usage which results in the risk of errors calculations and can help make it easier for engineers to analyze and make drilling operations more effective and efficient.

Treatments of the singularity in the level set method for unstructured meshes

Straightforward computation of normal vectors and curvature of interface is a main advantage of the level set method. However, the level set method may have discontinuities (kinks) in its derivatives that may lead to erroneous estimation of the normal vector and curvature during topological changes. In this study, we extended two existing methods of singularity treatment for the level set method on structured mesh, i.e., the Salac and Lu method (SLM) and local level set extraction method (LOLEX), to those with unstructured mesh in the framework of finite element formulation. An iterative treatment for the dependent nodes that belong to two elements cut by different interfaces was newly proposed for the LOLEX approach on unstructured mesh. Three static simulations showed that the present SLM or LOLEX for unstructured mesh accurately computed the normal vector and the curvature in the regions with singularity. Two dynamic cases were further simulated to investigate the effect of singularity-treatment on the mass conservation as well as the merging mechanism of droplets. While SLM and LOLEX provided results consistent with existing experimental results, it was confirmed that LOLEX provided a better mass conservation and more accurate curvature fields than SLM after coalescence.

Curvature-based sparse rule base generation for fuzzy rule interpolation

Fuzzy logic has been successfully widely utilised in many real-world applications. The most common application of fuzzy logic is the rule-based fuzzy inference system, which is composed of mainly two parts including an inference engine and a fuzzy rule base. Conventional fuzzy inference systems always require a rule base that fully covers the entire problem domain (i.e., a dense rule base). Fuzzy rule interpolation (FRI) makes inference possible with sparse rule bases which may not cover some parts of the problem domain (i.e., a sparse rule base). In addition to extending the applicability of fuzzy inference systems, fuzzy interpolation can also be used to reduce system complexity for over-complex fuzzy inference systems. There are typically two methods to generate fuzzy rule bases, i.e., the knowledge driven and data-driven approaches. Almost all of these approaches only target dense rule bases for conventional fuzzy inference systems. The knowledge-driven methods may be negatively affected by the limited availability of expert knowledge and expert knowledge may be subjective, whilst redundancy often exists in fuzzy rule-based models that are acquired from numerical data. Note that various rule base reduction approaches have been proposed, but they are all based on certain similarity measures and are likely to cause performance deterioration along with the size reduction. This project, for the first time, innovatively applies curvature values to distinguish important features and instances in a dataset, to support the construction of a neat and concise sparse rule base for fuzzy rule interpolation. In addition to working in a three-dimensional problem space, the work also extends the natural three-dimensional curvature calculation to problems with high dimensions, which greatly broadens the applicability of the proposed approach. As a result, the proposed approach alleviates the ‘curse of dimensionality’ and helps to reduce the computational cost for fuzzy inference systems. The proposed approach has been validated and evaluated by three real-world applications. The experimental results demonstrate that the proposed approach is able to generate sparse rule bases with less rules but resulting in better performance, which confirms the power of the proposed system. In addition to fuzzy rule interpolation, the proposed curvature-based approach can also be readily used as a general feature selection tool to work with other machine learning approaches, such as classifiers.

A comparison of methods for the calculation of interface curvature in two-dimensional cellular automata solidification models

Four methods for the calculation of interface curvature in cellular automata models for solidification are evaluated. Three of the methods are based on the level-set interpretation of the solid fraction field and calculate the required spatial derivatives by finite differences or by a Taylor approximation in different neighborhoods. The fourth method is the height function method, an interface reconstruction method based on the row- or columnwise summation of solid fractions.Two benchmark problems are investigated, representative for two types of cellular automata models for solidification where interface cells exist in either Moore or von Neumann neighborhoods of solid cells. For the case of interface cells in the Moore neighborhood of solid cells, the height function method yields the most accurate results, while all level-set based methods exhibit significant numerical scatter. For the case of interface cells existing in the von Neumann neighborhood of solid cells, all methods yield a higher level of numerical scatter. The best curvature calculations for this case are achieved by the height function method and by the level set method with a Taylor approximation in an extended neighborhood.

Comparison between the diffuse interface and volume of fluid methods for simulating two-phase flows

A wide variety of interface capturing methods have been introduced for simulating two-phase flows throughout the years. However, there is a noticeable dearth of literature focusing on objective comparisons between these methods, especially when they are coupled to the momentum equation and applied in physically relevant regimes. In this article, we compare two techniques for simulating two-phase flows that possess attractive qualities, but belong to the two distinct classes of diffuse interface (DI) and volume of fluid (VOF) methods. Both of these methods allow for mass-conserving schemes that can naturally capture large interfacial topology changes omnipresent in realistic two phase flows. The DI solver used in this work is based on a conservative and bounded phase field method, developed recently. Similar to level set methods, this diffuse interface method takes advantage of the smoothness of the phase field in computing curvature and surface tension forces. Geometric VOF methods track the fractional tagged volume in a cell. The specific geometric VOF scheme used here is a discretely conservative and bounded implementation that uses geometric algorithms for unsplit advection and interface reconstruction, while employing height functions for normal and curvature calculation. We present a quantitative comparison of these methods on Cartesian meshes in terms of their accuracy, convergence rate, and computational cost using canonical two-dimensional (2D) two-phase test cases: an equilibrium static drop, an oscillating drop, damped surface wave and the Rayleigh–Taylor instability. We further compare these methods in their ability to resolve thin films by simulating the impact of a water drop on a deep water pool. Using results of these studies, we suggest qualitative guidelines for selection of schemes for two-phase flow calculations.

Discrete Curvature Representations for Noise Robust Image Corner Detection.

Image corner detection is very important in the fields of image analysis and computer vision. Curvature calculation techniques are used in many contour-based corner detectors. We identify that existing calculation of curvature is sensitive to local variation and noise in the discrete domain and does not perform well when corners are closely located. In this paper, discrete curvature representations of single and double corner models are investigated and obtained. A number of model properties have been discovered, which help us detect corners on contours. It is shown that the proposed method has a high corner resolution (the ability to accurately detect neighboring corners), and a corresponding corner resolution constant is also derived. Meanwhile, this method is less sensitive to any local variations and noise on the contour; and false corner detection is less likely to occur. The proposed detector is compared with seven state-of-the-art detectors. Three test images with ground truths are used to assess the detection capability and localization accuracy of these methods in cases with noise-free and different noise levels; 24 images with various scenes without ground truths are used to evaluate their repeatability under affine transformation, JPEG compression, and noise degradations. The experimental results show that our proposed detector attains a better overall performance.

Study of Geometrically Necessary Dislocations of a Partially Recrystallized Aluminum Alloy Using 2D EBSD.

During recrystallization, the growth of fresh grains initiated within a deformed microstructure causes dramatic changes in the dislocation structure and density of a heavily deformed matrix. In this paper, the microstructure of a cold rolled and partially recrystallized Al-Mg alloy (AA5052) was studied via electron backscattered diffraction (EBSD) analysis. The structure and density of the geometrically necessary dislocations (GNDs) were predicted using a combination of continuum mechanics and dislocation theory. Accordingly, the Nye dislocation tensor, which determines the GND structure, was estimated by calculation of the lattice curvature. To do so, five components of the Nye dislocation tensor were directly calculated from the local orientation of surface points of the specimen, which was determined by two-dimensional EBSD. The remaining components of GNDs were determined by minimizing a normalized Hamiltonian equation based on dislocation energy. The results show the elimination of low angle boundaries, lattice curvature, and GNDs in recrystallized regions and the formation of low angle boundaries with orientation discontinuities in deformed grains, which may be due to static recovery.

Design of Magnetic Field LUT Model for Femto-Satellites

Aiming at the high computational complexity and large storage of IGRF geomagnetic field model in Attitude Determination and Control System (ADCS), the uniform sampling model and K-Curvature weighted model have been established. First of all, storage format and track deduction method of uniform look-out-table (LUT) model is proposed. Then, this paper uses U-Discrete curvature calculation method to solve the discrete curvature of magnetic field data. Finally, the uniform sampling method and K-Curvature Weighted model in fitting the original curve has been compared. In general, this paper presents K curvature weighted non-uniform LUT model with only 80 points needed, and it only needs 0.96 kB. It proves great advantages in terms of computing speed and storage space compared with the existing technology.

Damage assessment of shear wall components for RC frame–shear wall buildings using story curvature as engineering demand parameter

Reinforced concrete (RC) frame–shear wall structures are extensively used in urban areas. As a major part of the lateral load resisting system, the shear wall is a key component for the seismic performance assessment of such structures. In this study, a method for the seismic damage assessment of shear wall components is proposed by using the story curvature as the engineering demand parameter (EDP). The method involves (1) a shear wall story curvature calculation method and (2) a shear wall damage limit determination method that uses the story curvatures as the EDP. The story curvature adopted in this study denotes the maximum shear wall curvature within each story level. Based on the piecewise linear assumption of the curvature distribution, the story curvature calculation method requires story drifts and shear wall key design parameters as inputs. Meanwhile, based on the plane cross-sectional assumption and sectional analysis, the damage limits can be determined by considering the influences of the shear wall key design parameters, such as the axial load ratio, shear wall component length, and material information, thereby yielding more accurate estimation. Finally, the proposed method is validated by comparing it with the numerical results of several wall panels and an RC frame–shear wall structure. It is further validated by comparing it with the experiment results obtained from six shear wall tests and a full-scale shaking table test of a seven-story shear wall structure.

A Semianalytical Model for the Determination of Bistability and Curvature of Metallic Cylindrical Shells

Bistable metal shells with a fully closed unfolded geometry are of great interest as lightweight construction parts which could be transported without housing and unfolded at the construction place. In order to achieve the effect of bistability in metallic shells, residual stresses with a specific distribution along the shell thickness are necessary. These residual stresses can be introduced in bending processes. The tools with specific bending radii are used to influence the curvature of the shell in the different stable states and thus determine whether a completely closed profile can be achieved. In addition to the forming process, the shell thickness and the shell material have an effect on the achievable geometries and stability. In order to manufacture bistable metallic cylindrical shells from different materials and shell thicknesses, it is necessary to be able to determine a promising process sequence and corresponding bending radii in advance. For this reason, this article presents a semianalytical model for the calculation of bistability and final curvatures. This model is applied to an incremental die-bending process using two bending operations with bending radii of 6 to 12 mm and a 0.2 mm thick steel shell of grade 1.1274 (AISI 1095). The calculation results show that bistability cannot be reached for all combinations of the two bending radii. Moreover, the model indicates that a bistable and fully closed shell is only achieved for a bending radii combination of R1 = 6 mm and R2 = 6 mm. With the aim of model verification, experiments with a closed-die incremental bending tool were performed. Calculated and experimental results show good correlation regarding bistability and curvature. In addition, X-ray diffraction measurement of the residual stresses shows a good qualitative agreement regarding the calculated and experimental results.

Testing imaging confocal microscopy, laser scanning confocal microscopy, and focus variation microscopy for microscale measurement of edge cross-sections and calculation of edge curvature on stone tools: Preliminary results

The application of micro- and nanotechnology, adopted from engineering and materials sciences, is proving valuable in studying stone tool surfaces. Measurement systems for surface characterization have been coupled with parameters that allow for the mathematical characterization of stone tool surfaces. For this project, a Sensofar S neox imaging confocal microscope (ICM)/focus variation microscope (FVM) and an Olympus LEXT OLS4100 laser scanning confocal microscope (LSCM) are used to mathematically document the edge cross-sections on five chipped stone tools made from basalt, chert, obsidian, and quartz. Based on the surface documentation of edge cross-sections, a new algorithm for the calculation of edge curvature at multiple scales is tested. Results indicate the confocal systems experience difficulty documenting edge cross-sections. However, focus variation microscopy can mathematically document edge cross-sections on stone tools made from basalt and chert, thus permitting the calculation of edge curvature over multiple scales of measurement. Microscale documentation of edge cross-sections and calculation of edge curvature will be helpful in understanding the relationships between tool edges, edge sharpness, edge attrition, and microwear. Comparisons between these three measurement systems (ICM, LSCM, FVM) provide information necessary for further method development in edge cross-section measurement and the potential to generate more robust edge analysis protocols.

A discrete method of sphere-pipe intersecting curve for robot welding by offline programming

Abstract The sphere-pipe intersecting curve is a kind of spatial complex curve, which is controlled by robot in the sphere-pipe welding. In this paper, a discrete method for robot welding by offline programming is put forward. To move the robot with the specified curve trajectory, it need to be discretized to generate the robot motion instructions. As the core innovation of this paper, a discrete method of sphere-pipe intersecting curve is given according to the chord error limit and principle of equal arc length, which guarantees the accuracy of robot welding. To achieve this goal, this paper has done the following related works. First, the geometrical model of the sphere-pipe intersection is established, which can cover most of the intersection modes. Second, this paper gives the parameter equations in two different coordinate systems because the expression is very complex. This operation will simplify the subsequent calculations. Although the curve expression is simplified, it is very complicated to find the maximum based on the definition of curvature. After experimental analysis, this paper presents a simple and effective algorithm for the calculation of maximum curvature. Finally, this paper takes the Puma560 robot for simulation, and the simulation results are used to verify the feasibility and effectiveness of our method.

Theoretical Analysis of Five‐Point Bending and Springback for Preforming Process of ERW Pipe FFX Forming

Flexible forming excellent (FFX) forming of electric resistance welding (ERW) pipe is an advanced roll forming method. In order to understand FFX forming mechanism and set reasonable roll parameters, five‐point bending process and springback process for preforming section of ERW pipe FFX forming are analyzed. Under various assumptions, the bending process of sheet metal is divided into full elastic bending stage and elastic‐plastic bending stage by analyzing the forming law and simplifying the contact state model of roll bending process. Based on the theory of plane bending theory, the five‐point bending springback model is established. Mathematical expressions of bending curvature and rotation angle of arbitrary particle on plate under arbitrary state are derived. The curvature calculation formulas of each particle on plate after springback are obtained, and then the calculation formulas of bending angle and rebound angle after springback are obtained. The theoretical analysis results are verified by the wide plate five‐point bending experiment. The theoretical value of springback angle agrees well with the experimental results. The maximum deviation of springback angle is 0.42 degrees. The results show that the five‐point bending model is reasonable. It provides theoretical support for the preforming model of flexible roll forming.

Study on Calculation Method of Long Term Deformation of RAC Beam based on Creep Adjustment Coefficient

The creep shrinkage of concrete is an important factor in the long-term deformation of concrete structures. It is also a key link for solving long-term deformation calculation accuracy and complex calculation forms. In this paper, a 1200-day long-term deformation test was conducted on beams with 0%, 50%, and 100% substitution ratios of recycled coarse aggregate. Meanwhile, based on the principle of virtual work, the creep coefficient of recycled concrete is introduced into the calculation of additional curvature of the beam section, and the formula for calculating the long-term deformation of recycled concrete is established. According to the size of recycled coarse aggregate, through the calculation of creep and shrinkage of concrete, the regeneration adjustment coefficient of concrete creep and shrinkage, the calculation results into three typical model of ordinary concrete creep and shrinkage, creep and shrinkage of concrete and regeneration model of deformation calculation of long period, the calculated and experimental results agree well; based on this, the deflection increase coefficient is proposed, which simplifies the long-term calculation formula. It not only can meet the calculation accuracy requirements, but also can be easily adapted to engineering promotion.