Boundary Representation Research Articles

Discretization Approaches to Model Metal Cutting with Lagrangian, Arbitrary Lagrangian Eulerian and Smooth Particle Hydrodynamics formulations

AbstractWith significant technological growth and computing power it is possible to simulate metal cutting processes with different discretization techniques. Classically the Lagrangian or Eulerian finite element formulations are used to model metal cutting process. Lagrangian approach is accurate with it's representation of the domain boundary, but requires a re‐meshing procedure to avoid element distortions. Eulerian approach provides a steady state solution of the chip‐workpiece separation, however its limitation lies in the treatment of convective terms during motion. The Arbitrary Lagrangian‐Eulerian method can be used to combine the advantages of both methods and avoid the disadvantages. In the Lagrangian framework, use of a meshless technique– Smooth Particle Hydrodynamics (SPH) has its advantage in large strain deformation problems without the need for re‐meshing algorithms. This work compares the LAG, ALE and SPH approaches by modelling a turning process.

Geometrically nonlinear analysis of solids using an isogeometric formulation in boundary representation

This paper presents a geometrically nonlinear formulation in boundary representation for the isogeometric analysis of solids. The proposed formulation employs the parameterization of the scaled boundary finite element method. Thus, the geometry of the boundary is sufficient to describe the entire domain. In contrast to the scaled boundary finite element method, NURBS basis functions approximate the solution on the boundary and also in the interior of the domain. In this way, the exact geometry of the boundary is preserved and geometrically nonlinear problems are treated without further measures. The formulation is derived for two-dimensional domains with arbitrary number of boundaries. Numerical benchmarks evaluate the accuracy and efficiency of the formulation. Furthermore, the influence of the discretization in the interior of the domain and the performance of complex geometries is studied. The proposed formulation compares well with other numerical methods and is suitable for geometries that are designed in boundary representation.

Scaled boundary finite element method for mid-frequency interior acoustics

In this talk, a semi-analytical framework, based on the scaled boundary finite element method (SBFEM), is proposed, to study interior acoustic problems in the mid-frequency range. The SBFEM shares the advantages of both the finite element method (FEM) and the boundary element method (BEM). Like the FEM, it does not require the fundamental solution (Green's function) and similar to the BEM only the boundary is discretized, thus reducing the spatial dimensionality by one. The solution within the domain is represented analytically, while on the boundary, it is represented by finite elements. Different choices of boundary representations, such as Lagrange and NURBS description will be discussed. The proposed framework is validated using closed-form solutions and direct comparisons are made with conventional FEM based on Lagrangian description; this will be demonstrated using two two-dimensional cavities available from the literature. The improved accuracy and reduced computational time can be attributed to the semi-analytical formulation combined with the boundary discretization.

Impaired behavioral and neural representation of scenes in Williams syndrome

Boundaries are crucial to our representation of the geometric shape of scenes, which can be used to reorient in space. Behavioral research has shown that children and adults share exquisite sensitivity to a defining feature of a boundary: its vertical extent. Imaging studies have shown that this boundary property is represented in the parahippocampal place area (PPA) among typically developed (TD) adults. Here, we show that sensitivity to the vertical extent of scene boundaries is impaired at both the behavioral and neural level in people with Williams syndrome (WS), a genetic deficit that results in severely impaired spatial functions. Behavioral reorientation was tested in three boundary conditions: a flat Mat, a 5 cm high Curb, and full Walls. Adults with WS could reorient in a rectangular space defined by Wall boundaries, but not Curb or Mat boundaries. In contrast, TD age-matched controls could reorient by all three boundary types and TD 4-year-olds could reorient by either Wall or Curb boundaries. Using fMRI, we find that the WS behavioral deficit is echoed in their neural representation of boundaries. While TD age-matched controls showed distinct neural responses to scenes depicting Mat, Curb, and Wall boundaries in the PPA, people with WS showed only a distinction between the Wall and Mat or Curb, but no distinction between the Mat and Curb. Taken together, these results reveal a close coupling between the representation of boundaries as they are used in behavioral reorientation and neural encoding, suggesting that damage to this key element of spatial representation may have a genetic foundation.

Direct numerical simulation of turbulent forced and mixed convection of LBE in a bundle of heated rods with [formula omitted

In this work, reference data obtained by means of Direct Numerical Simulations of fully-developed flow and heat transfer around a vertical rod bundle are presented. Finite-Volume computations are performed by an original discretization technique based on the representation of arbitrarily-shaped cylindrical boundaries on a non-uniform Cartesian grid. A periodic domain consisting of four subchannels of a triangular lattice of rods with a pitch-to-diameter ratio P/D=1.4 is considered as the reference geometry. A Prandtl number Pr = 0.031 is chosen to represent Liquid Lead-Bismuth Eutectic (LBE) as the working fluid. A single friction Reynolds number value is simulated, namely Reτ=550. Both forced and mixed convection regimes are investigated, buoyancy effects being introduced by imposing a Rayleigh number Ra = 5×105, corresponding to a Richardson number Ri = 0.22. Instantaneous snapshots and relevant statistics of the velocity and thermal fields are reported and discussed for the considered cases, focusing on the effect of aiding buoyancy on turbulent flow and heat transfer. Integral results are also compared against available literature data.

Segmenting Cellular Retinal Images by Optimizing Super-pixels, Multi-level Modularity, and Cell Boundary Representation.

We introduce an interactive method for retina layer segmentation in gray-level and RGB images based on super-pixels, multi-level optimization of modularity, and boundary erosion. Our method produces highly accurate segmentation results and can segment very large images. We have evaluated our method with two datasets of 2D confocal microscopy (CM) images of a mammalian retina.We have obtained average Jaccard index values of 0.948 and 0.942 respectively, confirming the high-quality segmentation performance of our method relative to a known ground truth segmentation. Average processing time was two seconds.

Exchange of parametric assembly models based on neutral assembly constraints

It is difficult to exchange parametric assembly models using conventional neutral formats such as the standard for the exchange of product model data or the initial graphics exchange specification. These formats only support the boundary representation information that leads to the inability to perform parametric re-evaluation, once a model is exchanged. In order to exchange parametric information along with the design intent, a design history-based macro-parametric approach was proposed. Our method is macro-parametrics approach, however, supported only the exchange of individual part models. As most of the products are manufactured in assemblies, where several components are connected with multiple constraints, it is necessary to exchange the assembly model data. To overcome the issue of post-exchange editability, a collection of neutral assembly commands was introduced to extend the capabilities of the macro-parametric approach. A set of neutral assembly constraints was defined and a system for exchanging the parametric assembly models was implemented. An assembly model consisting of coaxial and incidence constraints was successfully exchanged between two commercial computer-aided design systems: CATIA and NX. It was possible to re-evaluate the assembly model parametrically after the exchange. The method can be further extended to exchange the remaining constraint types in different commercial computer-aided design systems.

Layered manufacturing for medical imaging data

Layered manufacturing techniques have been successfully employed to construct scanned objects from three-dimensional medical image data sets. The printed physical models are useful tools for anatomical exploration, surgical planning, teaching, and related medical applications. Before fabricating scanned objects, we have to first build watertight geometrical representations of the target objects from medical image data sets. Many algorithms had been developed to fulfill this duty. However, some of these methods require extra efforts to resolve ambiguity problems and to fix broken surfaces. Other methods cannot generate legitimate models for layered manufacturing. To alleviate these problems, this article presents a modeling procedure to efficiently create geometrical representations of objects from computerized tomography scan and magnetic resonance imaging data sets. The proposed procedure extracts the iso-surface of the target object from the input data set at the first step. Then it converts the iso-surface into a three-dimensional image and filters this three-dimensional image using morphological operators to remove dangling parts and noises. At the next step, a distance field is computed in the three-dimensional image space to approximate the surface of the target object. Then the proposed procedure smooths the distance field to soothe sharp corners and edges of the target object. Finally, a boundary representation is built from the distance field to model the target object. Compared with conventional modeling techniques, the proposed method possesses the following advantages: (1) it reduces human efforts involved in the geometrical modeling process. (2) It can construct both solid and hollow models for the target object, and wall thickness of the hollow models is adjustable. (3) The resultant boundary representation guarantees to form a watertight solid geometry, which is printable using three-dimensional printers. (4) The proposed procedure allows users to tune the precision of the geometrical model to compromise with the available computational resources.

Dissociation between Postrhinal Cortex and Downstream Parahippocampal Regions in the Representation of Egocentric Boundaries

Navigation requires the integration of many sensory inputs to form a multi-modal cognitive map of the environment, which is believed to be implemented in the hippocampal region by spatially tuned cells [1-10]. These cells encode various aspects of the environment in a world-based (allocentric) reference frame. Although the cognitive map is represented in allocentric coordinates, the environment is sensed through diverse sensory organs, mostly situated inthe animal's head, and therefore represented insensory and parietal cortices in head-centered egocentric coordinates. Yet it is not clear how and where the brain transforms these head-centered egocentric representations to map-like allocentric representations computed in the hippocampal region. Theoretical modeling has predicted a role for both egocentric and head direction (HD) information in performing an egocentric-allocentric transformation [11-15]. Here, we recorded new data and also used data from a previous study [16]. Adapting a generalized linear model (GLM) classification [17]; we show that the postrhinal cortex (POR) contains a population of pure egocentric boundary cells (EBCs), in contrast with the conjunctive EBCs × HD cells, which we found downstream mostly in the parasubiculum (PaS) and in the medial entorhinal cortex (MEC). Our finding corroborates the idea of a brain network performing an egocentric to allocentric transformation by HD cells. This is a fundamental building block in the formation of the brain's internal cognitive map.

3D Topological Error Detection for Cadastral Parcels Based on Conformal Geometric Algebra

Topological models in Euclidean space are difficult for spatial analysis because of the lack of direct representation of geometric three-dimensional (3D) object information. A 3D cadastral data model in the form of boundary representation based on conformal geometric algebra (CGA) is proposed to realize the integrated representation of geometric and topological information based on previous research. On the basis of the 3D cadastral data model based on CGA and basic geometric operators, self-defined geometric algebraic operators are designed using the advantages of geometric algebra in spatial topological calculation. A computation framework for cadastral parcel topological error detection is put forward based on those self-defined geometric operators. A case study is designed to verify the feasibility of topological error detection methods proposed in this paper. This study is an expansion of research for a 3D cadastral data model based on CGA.

Parametric studies and manufacturability experiments on smooth self-supporting topologies

ABSTRACT This paper aims to explore the effects of optimisation parameters (the filter radius, mesh size, and target volume fraction) on the compliance and manufacturability of smooth self-supporting topologies for additive manufacturing (AM); and conduct manufacturability experiments of selected simulation results with the Selective Laser Melting (SLM) technology. In this study, smooth self-supporting topologies are obtained with a combined method of the Solid Isotropic Microstructure with Penalization method (SIMP) with the smooth boundary representation and Langelaar's AM filter. Numerical examples illustrate that a higher filter radius can lead to simpler smooth self-supporting topologies, but curved top corners that violate the critical overhang angle of 45° are inevitably generated. Additionally, the mesh size is found to be not as an important factor as the filter radius in affecting the manufacturability and performance. As a result of the self-supporting constraint, a small volume fraction can easily result in structural discontinuity. The experimental results demonstrate that the self-supporting topologies obtained are all printable in SLM.

Parallel analysis system for free-surface flow using MPS method with explicitly represented polygon wall boundary model

This study develops a parallel solver of free-surface flow based on a mesh-free particle method, the explicit MPS method, with polygon boundary representation. We adopt the explicitly represented polygon (ERP) wall boundary model, which expresses wall boundaries as arbitrarily shaped triangular polygons. A bucket-based domain decomposition algorithm for dynamic load balancing is expanded to the polygon-based computation of the ERP model. The validity and parallel efficiency of the developed solver are tested by analyzing a dam break problem, and the numerical results are compared with experimental results. Our developed solver can simplify the evaluation of the integrity of coastal structures since it can be easily connected to finite element analyses of the structures.

Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods

The boundary element method (BEM) is a powerful tool in computational acoustics, because the analysis is conducted only on structural surfaces, compared to the finite element method (FEM) which resorts to special techniques to truncate infinite domains. The isogeometric boundary element method (IGABEM) is a recent progress in the category of boundary element approaches, which is inspired by the concept of isogeometric analysis (IGA) and employs the spline functions of CAD as basis functions to discretize unknown physical fields. As a boundary representation approach, IGABEM is naturally compatible with CAD and thus can directly perform numerical analysis on CAD models, avoiding the cumbersome meshing procedure in conventional FEM/BEM and eliminating the difficulty of volume parameterization in isogeometric finite element methods. The advantage of tight integration of CAD and numerical analysis in IGABEM renders it particularly attractive in the application of structural shape optimization because (1) the geometry and the analysis can be interacted, (2) remeshing with shape morphing can be avoided, and (3) an optimized solution returns a CAD geometry directly without postprocessing steps. In the present paper, we apply the IGABEM to structural shape optimization of three dimensional exterior acoustic problems, fully exploiting the strength of IGABEM in addressing infinite domain problems and integrating CAD and numerical analysis. We employ the Burton–Miller formulation to overcome fictitious frequency problems, in which hyper-singular integrals are evaluated explicitly. The gradient-based optimizer is adopted and shape sensitivity analysis is conducted with implicit differentiation methods. The design variables are set to be the positions of control points which directly determine the shape of structures. Finally, numerical examples are provided to verify the algorithm.

Nonstationary Shape Estimation in Electrical Impedance Tomography Using a Parametric Level Set-Based Extended Kalman Filter Approach

This paper presents a parametric level set-based reconstruction method for nonstationary applications using electrical impedance tomography (EIT). Due to relatively low signal-to-noise ratios in EIT measurement systems and the diffusive nature of EIT, the reconstructed images often suffer from low spatial resolution. In addressing these challenges, we propose a computationally efficient shape-estimation approach where the conductivity distribution to be reconstructed is assumed to be piecewise constant, and the region boundaries are assumed to be nonstationary in the sense that the characteristics of region boundaries change during measurement time. The EIT inverse problem is formulated as a state estimation problem in which the system is modeled with a state equation and an observation equation. Given the temporal evolution model of the boundaries and observation model, the objective is to estimate a sequence of states for the nonstationary region boundaries. The implementation of the approach is based on the finite-element method and a parametric representation of the region boundaries using level set functions. The performance of the proposed approach is evaluated with the simulated examples of thorax imaging, using noisy synthetic data and experimental data from a laboratory setting. In addition, robustness studies of the approach with respect to the modeling errors caused by inaccurately known boundary shape, non-homogeneous background and varying conductivity values of the targets are carried out and it is found that the proposed approach tolerates such kind of modeling errors, leading to good reconstructions in nonstationary situations.

High-order discontinuous Galerkin methods for coastal hydrodynamics applications

This paper applies high-order discontinuous Galerkin finite element solutions of the shallow water equations to realistic coastal hydrodynamics problems. The goal is to obtain results on par with the accuracy of current low-order models, while significantly surpassing their performance. Accomplishing this requires developing mesh discretizations with boundary and parameter field representations that are consistent with the high-order accuracy of the numerical methods. These developments allow coarse-mesh, high-order, solutions to provide comparable accuracy to today’s state-of-the-art high-resolution, low-order coastal models at reduced computational expense.

Positive matrices in the Hardy space with prescribed boundary representations via the Kaczmarz algorithm

For a singular probability measure μ on the circle, we show the existence of positive matrices on the unit disc which admit a boundary representation on the unit circle with respect to μ. These positive matrices are constructed in several different ways using the Kaczmarz algorithm. Some of these positive matrices correspond to the projection of the Szegő kernel on the disc to certain subspaces of the Hardy space corresponding to the normalized Cauchy transform of μ. Other positive matrices are obtained which correspond to subspaces of the Hardy space after a renormalization, and so are not projections of the Szegő kernel. We show that these positive matrices are a generalization of a spectrum or Fourier frame for μ, and the existence of such a positive matrix does not require μ to be spectral.

An ABAQUS toolbox for soil-structure interaction analysis

It is well established that the soil-structure interaction (SSI) effects can bear important consequences under strong earthquakes, and their accurate quantification can become a critical issue in designing earthquake-resistant structures. In general, SSI analyses are carried out by means of either direct or substructure methods. In either option, the numerical models feature truncated and/or reduced-order computational domains. For truncation, boundary representations that perfectly absorb the outgoing waves and enable the consistent prescription of input motions are crucial. At the present time, the aforementioned capabilities are not broadly available to researchers and practicing engineers. To this end, we implement the so-called Domain Reduction Method (DRM) and Perfectly-Matched-Layers (PMLs) in ABAQUS, by computing and prescribing the effective nodal forces, and through a user-defined element (UEL) subroutine, respectively. We then verify the accuracy and stability of these implementations for both homogeneous and heterogeneous soil domains, vertical and inclined incident SV waves, and two- and three-dimensional problems. Finally, we present two useful application examples of using the implemented features—namely, the extraction of impedance functions, the response analysis of buried structures subjected to inclined plane waves. The implemented codes for both DRM and PML will be disseminated for broader use.

Neuronal representation of environmental boundaries in egocentric coordinates

Movement through space is a fundamental behavior for all animals. Cognitive maps of environments are encoded in the hippocampal formation in an allocentric reference frame, but motor movements that comprise physical navigation are represented within an egocentric reference frame. Allocentric navigational plans must be converted to an egocentric reference frame prior to implementation as overt behavior. Here we describe an egocentric spatial representation of environmental boundaries in the dorsomedial striatum.

Integration of BIM and GIS: IFC geometry transformation to shapefile using enhanced open-source approach

Efficient data exchange is the foundation of effective integration of Building Information Modeling (BIM) and Geographic Information System (GIS). However, it has not been fully achieved. This study aims to enhance the previously developed Open-Source Approach (OSA), which is for geometry transformation of Industry Foundation Classes (IFC) into the shapefile format. OSA will be strengthened to be enhanced OSA (E-OSA) by developing an enhanced Automatic Multipatch Generation (E-AMG) algorithm that is capable of transforming various types of 3D representation, such as clipping and mapped representation, to boundary representation (Brep). The proposed method was tested and validated using a house model and two building models provided by Karlsruhe Institute of Technology (KIT) as well as a bridge model. The results show that E-AMG has the capacity to successfully transform these models from IFC to shapefile without building element loss. A comparison between Data Interoperability Extension for ArcGIS (DIA), Feature Manipulation Engine (FME) and the proposed E-OSA shows that the proposed method is more reliable than others while dealing with complex models. However, this method currently needs human intervention when handling multiple-clipping geometry. This issue should be addressed in the future to improve the effectiveness of E-OSA.

Research of Visual Conversion Technology for Reactor Core Monte Carlo Model Based on CSG

In order to improve the efficiency of 3D visualization analysis of the core Monte Carlo fine transport calculation model (MC calculation model), on the basis of fully investigating the current development status of the MC calculation model 3D visualization tools, and by analyzing the characteristics of different types of geometric models and the description methods of constructive solid geometry (CSG) models, this paper proposed an automatic 3D visualization converting method for the core fine MC calculation model, and conducted a deep study on the key technologies such as the conversion from CSG model to boundary representation (BREP) model, the mesh discretization of BREP model and the optimization of conversion efficiency for CSG model. The test results show that the proposed method can meet the engineering requirements in terms of function and efficiency.