Incompatible Deformations in Additively Fabricated Solids: Discrete and Continuous Approaches

The present paper is intended to show the close interrelationship between non-linear models of solids, produced with additive manufacturing, and models of solids with distributed defects. The common feature of these models is the incompatibility of local deformations. Meanwhile, in contrast with the conventional statement of the problems for solids with defects, the distribution for incompatible local deformations in additively created deformable body is not known a priori, and can be found from the solution of the specific evolutionary problem. The statement of the problem is related to the mechanical and physical peculiarities of the additive process. The specific character of incompatible deformations, evolved in additive manufactured solids, could be completely characterized within a differential-geometric approach by specific affine connection. This approach results in a global definition of the unstressed reference shape in non-Euclidean space. The paper is focused on such a formalism. One more common factor is the dataset which yields a full description of the response of a hyperelastic solid with distributed defects and a similar dataset for the additively manufactured one. In both cases, one can define a triple: elastic potential, gauged at stress-free state, and reference shape, and some specific field of incompatible relaxing distortion, related to the given stressed shape. Optionally, the last element of the triple may be replaced by some geometrical characteristics of the non-Euclidean reference shape, such as torsion, curvature, or, equivalently, as the density of defects. All the mentioned conformities are illustrated in the paper with a non-linear problem for a hyperelastic hollow ball.

A minimization problem for the sum of weighted convolutions’ difference and a novel approach to the inverse problem of ECG- and PPG-signals recovering

In this paper, we consider an unstudied problem of approximation of an observed pulse train by by a quasiperiodic signal generated by a pulse with a given pattern (reference) shape. The quasiperiodicity allows variation of time intervals between repetitions of the pattern pulse, as well as nonlinear expansions of the pattern in time. Such inverse problems are common in electrocardiogram (ECG) and photoplethysmogram (PPG) features extraction. The following two variants of the problem are considered. In the first variant, the number of the pulse repetitions is unknown, while in the second one, that number is given. The polynomial-time solvability of the both variants of the problem is constructively proved.

The Nonlinear evolutionary problem for self-stressed multilayered hyperelastic spherical bodies

The present paper studies the evolutionary problem for self-stressed multilayered spherical shells. Their stress-strain state is characterized by incompatible local finite deformations that arise due to the geometric incompatibility of the stress-free shapes of the individual layers with each other. In the considered problem, these shapes are thin-walled hollow balls that cannot be assembled into a single solid without gaps or overlaps. Such an assembly is possible only with the preliminary deformations of individual layers, which cause self-balanced stresses in them. For multilayered structures with a large number of layers, a smoothing procedure is proposed, as a result of which the piecewise continuous functions defining the preliminary deformation of the layers are replaced by continuous distributions. The reference stress-free shape of a body constructed in this way is defined within the framework of geometric continuum mechanics as a manifold with a non-Euclidean (material) connection. For the problem in question, this connection is determined by the metric tensor and its deviation from the Euclidean connection is characterized by the scalar curvature. Generalized representations for Cauchy and Piola stresses are also obtained by the methods of geometric continuum mechanics. Computations, provided for the discrete structure and body with a non-Euclidean reference shape defined by the approximation of deformation parameters, numerically illustrate the convergency of the solution for the discrete model to corresponded solution for the continuous problem if the number of layers is increasing while their total thickness is constant. In modelling it is assumed that the material of the layers is compressible, homogeneous, hyperelastic, and determined by the first-order Mooney - Rivlin elastic potential. Individual layerwise finite deformations are supposed to be centrally symmetric.

Modelling of the reference STARs procedures in the context of RPAS integration in non-segregated airspace

Purpose This work presents the part of the research in the integration of the remotely piloted aircraft systems (RPAS) in non-segregated airspace. The purpose of this study is to elaborate the reference shape of the Standard Instrument Arrivals (STARs) procedures of controlled airports. The STARs parameters are unique for the aerodromes and depend on navigational aids (NAVAIDs), manoeuvres and aircraft categories. Therefore, the elaboration of reference shapes was advisable in the context of RPAS integration research. Design/methodology/approach The models were based on the procedure design guidelines by International Civil Aviation Organization. The statistics of existing STARs were prepared using Aeronautical Information Publications to determine the representative procedural parameters. Construction of procedural shapes required to define the nominal flight path and tolerance areas. Findings In statistics, the standard deviation of distances was below the determined reference mean values, thus the models were convergent with existing procedures. Research limitations/implications The modelling was limited to initial, intermediate, final and missed approach segments. Arrival segment was not modelled. NAVAIDs include Instrument Landing System Category 1 (in final and missed approach) and very high-frequency omni-directional ranging or global navigation satellite systems (in initial and intermediate approach segments). Practical implications Prepared models may be used in research in the integration of the new types of aerial vehicles in existing air traffic management systems. Originality/value The reference STARs possess commonly used procedural manoeuvres (straight-in, turn, racetrack and base turn) and different NAVAIDs. The parameters of approach segments were determined as representative of the existing procedures. Moreover, the models are suitable to place at arbitrary origin and runway axis bearing.

Unsupervised Bayesian Nonparametric Approach with Incremental Similarity Tracking of Unlabeled Water Demand Time Series for Anomaly Detection

In this paper, a fusion of unsupervised clustering and incremental similarity tracking of hourly water demand series is proposed. Current research using unsupervised methodologies to detect anomalous water is limited and may possess several limitations such as a large amount of dataset, the need to select an optimal cluster number, or low detection accuracy. Our proposed approach aims to address the need for a large amount of dataset by detecting anomaly through (1) clustering points that are relatively similar at each time step, (2) clustering points at each time step by the similarity in how they vary from each time step, and (3) to compare the incoming points with a reference shape for online anomalous trend detection. Secondly, through the use of Bayesian nonparametric approach such as the Dirichlet Process Mixture Model, the need to choose an optimal cluster number is eliminated and provides a subtle solution for ‘reserving’ an empty cluster for the future anomaly. Among the 165 randomly generated anomalies, the proposed approach detected a total of 159 anomalies and other anomalous trends present in the data. As the data is unlabeled, identified anomalous trends cannot be verified. However, results show great potential in using minimally unlabeled water demand data for a preliminary anomaly detection.

Simulation of Laser-assisted Directed Energy Deposition of Aluminum Powder: Prediction of Geometry and Temperature Evolution

One of the main current challenges in the field of additive manufacturing and directed energy deposition of metals, is the need for simulation tools to prevent or reduce the need to adopt a trial-and-error approach to find the optimum processing conditions. A valuable help is offered by numerical simulation, although setting-up and validating a reliable model is challenging, due to many issues related to the laser source, the interaction with the feeding metal, the evolution of the material properties and the boundary conditions. Indeed, many attempts have been reported in the literature, although some issues are usually simplified or neglected. Therefore, this paper is aimed at building a comprehensive numerical model for the process of laser-assisted deposition. Namely: the geometry of the deposited metal is investigated in advance and the most effective reference shape is found to feed the simulation as a function of the governing factors for single- and multi-track, multi-layer deposition; then, a non-stationary thermal model is proposed and the underlying hypotheses to simulate the addition of metal are discussed step-by-step. Validation is eventually conducted, based on experimental evidence. Aluminum alloy 2024 is chosen as feeding metal and substrate.

Geometric Deep Learning for Shape Correspondence in Mass Customization

Many industries, such as human-centric product manufacturers, are calling for mass customization with personalized products. One key enabler of mass customization is 3D printing, which makes the flexible design and manufacturing possible. However, personalized designs bring obstacles for the shape matching and analysis, owing to the high complexity and large shape variations. Traditional shape matching methods are limited to shape alignment, which cannot determine the intrinsic in-variance of mass customized models. To extract the deformations widely seen in mass customization paradigm and address the issues of alignment methods in shape matching, we redefine the geometry matching problem as a correspondence problem, and solve for the correspondence of all vertices on a queried shape to a reference shape. A state-of-the-art geometric deep learning method is used to learn the correspondence of a set of collected models. Through learning the intrinsic deformations of the products, the underlying variations of the shapes are extracted. We demonstrate the application of the proposed approach in orthodontics industry, and the experimental results show the effectiveness of the proposed method and the defined problem is favorably suitable for shape analysis in mass customization.

Physics-Based Design by Optimization of Unconventional Supercavitating Hydrofoils

A computational framework to design a new family of unconventional super cavitating (SC) hydrofoils with optimized hydrodynamic performance is developed. A low-order boundary element method is used to solve for the steady potential flow over the hydrofoil predicting its hydrodynamic characteristics, including the vapor-cavity interface. Shape variations are obtained by an ad hoc parametrization scheme by composite B-spline curves whose control points represent the design variables to the hydrodynamic optimization problem. The accuracy of the Computational Fluid Dynamics (CFD) tools is also preventively validated on the experimental characteristics of a conventional SC hydrofoil. A computational test case is performed to maximize the efficiency of a SC hydrofoil accounting for both shape and angle of attack variations. The new hydrofoil leads to 40% improvement on the lift over drag ratio compared to the initial reference shape. This result is confirmed by high-fidelity unsteady multiphase viscous solver.