Voronoi Diagram Method Research Articles

Numerical Simulation of Failure Process of Concrete Under Compression Based on Mesoscopic Discrete Element Model

A two-dimensional mesoscopic numerical method to simulate the failure process of concrete under compression was developed based on the discrete element method by modifying the rigid body-spring model proposed by Nagai et al. In the calculation model, aggregates or aggregate elements inside the concrete were simplified as rigid bodies with regular polygon profiles, which were surrounded by mortar polygons or mortar elements. All of the adjacent elements were connected by springs. According to the random distribution of aggregates, the mesh was generated by using Voronoi diagram method. Plastic behavior after the elastic limit for a spring was considered to set up the constitutive model of the spring, and Mohr-Coulomb criterion was adopted to judge the failure of a spring. Simulation examples show that the proposed method can be used to predict the mechanical behavior of concrete under compression descriptively and quantitatively both for small deformation problems and for larger deformation problems.

Simulation of polycrystalline aluminum tensile test with crystal plasticity finite element method

The crystal plasticity was implemented in the finite element method(FEM) software ABAQUS through the user subroutine UMAT. By means of discretizing the space at the grain level with the Voronoi diagram method, a polycrystal model was built and used in the FEM analysis. The initial orientation of each grain was generated based on the orientation distribution function(ODF). The developed model was successfully applied in simulation of polycrystalline aluminium samples deformed by the tensile tests. The theoretical strain—stress relation was in good agreement with the experimental result. The simulation results show that the grain size has significant effect on the deformation behavior. The initial plastic deformation usually occurs at grain boundaries, and multiple slip often results in an enhanced local hardening at grain boundaries.

A Geographical Study of School Attendance Areas Using Multiplicatively Weighted Voronoi Diagrams

Unlike developed countries, no enforced attendance areas exist in Iran to guide school selection or allow students to make the most convenient commutes to the nearest schools. Without defined school attendance areas, parents seeking better and more reputable schools often have no choice but to send children to schools outside the local area. In the case of the Northern Iranian city of Rasht, this parental-based system of schools selection has resulted in commutes that are longer than necessary for the female students of junior high school who journey on foot or on the city's public and private transport. Long commutes by vehicle and on foot are a heavy burden on students and parents in terms of travel expenses, stress and the possibility of physical harm. This paper presents the realities of the parental-based system of school selection through the case study of Rasht City using questionnaires. The criteria in the selection of school by parents were clarified through the use of questionnaire surveys. In order to reduce the time and distance of commutes to school, the research proposed to eliminate parental choice and to create school attendance areas that allocate students to the closest possible public female junior high (PFJH) schools of Rasht City. It concluded that through the introduction of school attendance areas based on the multiplicatively weighted Voronoi diagram method, it would be possible to not only eliminate most hazardous vehicle travel but also make walking commute shorter and more convenient.

Development of High-Performance FEM Modeling System Based on Fuzzy Knowledge Processing

This paper describes an automatic finite element (FE) mesh generation for three-dimensional structures consisting of tree-form surfaces. This mesh generation process consists of three subprocesses: (a) definition of geometric model, (b) generation of nodes, and (c) generation of elements. One of commercial solid modelers is employed for three-dimensional solid structures. Node is generated if its distance from existing node points is similar to the node spacing function at the point. The node spacing function is well controlled by the fuzzy knowledge processing. The Voronoi diagram method is introduced as a basic tool for element generation. Automatic generation of FE meshes for three-dimensional solid structures holds great benefits for analyses. Practical performances of the present system are demonstrated through several mesh generations for three-dimensional complex geometry.

COLLISION DETECTION OPTIMIZATION IN A MULTI-PARTICLE SYSTEM

Collision detection optimization in an event-driven simulation of a multi-particle system is one of the crucial tasks, determining the efficiency of the simulation. We present the event-driven simulation algorithm that employs dynamic computational geometry data structures as a tool for collision detection optimization (CDO). The first successful application of the dynamic generalized Voronoi diagram method for collision detection optimization in a system of moving particles is discussed. A comprehensive comparision of four kinetic data structures in d-dimensional space, performed in a framework of an event-driven simulation of a granular-type materials system, is supported by the experimental results.

On a Nearest-Neighbor Problem Under Minkowski and Power Metrics for Large Data Sets

The paper presents the sequential and the parallel algorithm for solving the nearest-neighbor problem in the plane, based on the generalized Voronoi diagram construction. The applications of the problem are found in the areas of networking, communications, distributed systems, computer modeling and information retrieval. The input for the problem is the set of circular sites S with varying radii, the query point p and the metric (Minkowski or power) according to which the site, neighboring the query point, is to be reported. The sequential algorithm takes O(n) time to build the data structure and O(log n) time for each query. The parallel algorithm requires O(log n log) preprocessing time and O(log) query time on EREW PRAM architecture with n/log n processors. The IDG/NNM software was developed for an experimental study of the problem. The experimental results demonstrate that the Voronoi diagram method outperforms the k − d tree method for all tested input configurations. The tests were conducted on large data sets, comprising thousands of generators.

Voronoi-based region approximation for geographical information retrieval with gazetteers

Gazeteers and geographical thesauri can be regarded as parsimonious spatial models that associate geographical location with place names and encode some semantic relations between the names. They are of particular value in processing information retrieval requests in which the user employs place names to specify geographical context. Typically the geometric locational data in a gazetteer are confined to a simple footprint in the form of a centroid or a minimum bounding rectangle, both of which can be used to link to a map but are of limited value in determining spatial relationships. Here we describe a Voronoi diagram method for generating approximate regional extents from sets of centroids that are respectively inside and external to a region. The resulting approximations provide measures of areal extent and can be used to assist in answering geographical queries by evaluating spatial relationships such as distance, direction and common boundary length. Preliminary experimental evaluations of the method have been performed in the context of a semantic modelling system that combines the centroid data with hierarchical and adjacency relations between the associated place names.

A unifying approach for a class of problems in the computational geometry of polygons

A generalized problem is defined in terms of functions on sets and illustrated in terms of the computational geometry of simple planar polygons. Although its apparent time complexity is O(n2), the problem is shown to be solvable for several cases of interest (maximum and minimum distance, intersection detection and rerporting) in O(n logn), O(n) or O(logn) time, depending on the nature of a specialized “selection” function. (Some of the cases can also be solved by the Voronoi diagram method; but time complexity increases with that approach.) A new use of monotonicity and a new concept of “locality” in set mappings contribute significantly to the derivation of the results.