Inverse three-dimensional problems of radiation transport theory close to two-dimensional plane and cylindrical problems

1989 ◽  
Vol 29 (5) ◽  
pp. 158-167
Author(s):  
V.I. Gryn
Keyword(s):  
Transport Theory ◽  
Radiation Transport ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Plane

Methods to Accelerate Ray Tracing in the Monte Carlo Method for Surface-to-Surface Radiation Transport

2006 ◽  
Vol 128 (9) ◽  
pp. 945-952 ◽  
Author(s):  
Sandip Mazumder
Keyword(s):  
Monte Carlo ◽  
Ray Tracing ◽  
Radiation Transport ◽  
Three Dimensional ◽  
Intersection Point ◽  
Surface Radiation ◽  
Computational Domain ◽  
Two Dimensional ◽  
Spatial Partitioning ◽  
The Monte Carlo Method

Two different algorithms to accelerate ray tracing in surface-to-surface radiation Monte Carlo calculations are investigated. The first algorithm is the well-known binary spatial partitioning (BSP) algorithm, which recursively bisects the computational domain into a set of hierarchically linked boxes that are then made use of to narrow down the number of ray-surface intersection calculations. The second algorithm is the volume-by-volume advancement (VVA) algorithm. This algorithm is new and employs the volumetric mesh to advance the ray through the computational domain until a legitimate intersection point is found. The algorithms are tested for two classical problems, namely an open box, and a box in a box, in both two-dimensional (2D) and three-dimensional (3D) geometries with various mesh sizes. Both algorithms are found to result in orders of magnitude gains in computational efficiency over direct calculations that do not employ any acceleration strategy. For three-dimensional geometries, the VVA algorithm is found to be clearly superior to BSP, particularly for cases with obstructions within the computational domain. For two-dimensional geometries, the VVA algorithm is found to be superior to the BSP algorithm only when obstructions are present and are densely packed.

Modeling of a Beam and a Rotor with an Edge Crack Using Dissimilar Elements

2003 ◽  
Vol 9 (10) ◽  
pp. 1159-1187 ◽  
Author(s):  
A. Nandi ◽  
S. Neogy
Keyword(s):  
Finite Elements ◽  
Stress Field ◽  
Edge Crack ◽  
Three Dimensional ◽  
Transition Element ◽  
Two Dimensional ◽  
Cracked Beam ◽  
One Dimensional ◽  
Beam Elements ◽  
Dimensional Plane

Vibration-based diagnostic methods are used for the detection of the presence of cracks in beams and other structures. To simulate such a beam with an edge crack, it is necessary to model the beam using finite elements. Cracked beam finite elements, being one-dimensional, cannot model the stress field near the crack tip, which is not one-dimensional. The change in neutral axis is also not modeled properly by cracked beam elements. Modeling of such beams using two-dimensional plane elements is a better approximation. The best alternative would be to use three-dimensional solid finite elements. At a sufficient distance away from the crack, the stress field again becomes more or less one-dimensional. Therefore, two-dimensional plane elements or three-dimensional solid elements can be used near the crack and one-dimensional beam elements can be used away from the crack. This considerably reduces the required computational effort. In the present work, such a coupling of dissimilar elements is proposed and the required transition element is formulated. A guideline is proposed for selecting the proper dimensions of the transition element so that accurate results are obtained. Elastic deformation, natural frequency and dynamic response of beams are computed using dissimilar elements. The finite element analysis of cracked rotating shafts is complicated because of the fact that elastic deformations are superposed on the rigid-body motion (rotation about an axis). A combination of three-dimensional solid elements and beam elements in a rotating reference is proposed here to model such rotors.

Stereographic Visual Displays and the Three-Dimensional Communication of Findings in Marketing Research

1997 ◽  
Vol 34 (4) ◽  
pp. 526-536 ◽  
Author(s):  
Morris B. Holbrook
Keyword(s):  
Three Dimensional ◽  
Marketing Research ◽  
Two Dimensional ◽  
Visual Displays ◽  
Structural Patterns ◽  
Dimensional Plane ◽  
Present Complex ◽  
Key Concepts

In their attempts to communicate with managers and other interested readers, marketing researchers frequently present complex findings in various sorts of visual displays. These diagrams, charts, maps, pictures, and other figures help elucidate the nature of the relationships and structural patterns involved. However, their ability to communicate is partially limited by their typical restriction to the two-dimensional plane of the printed page. As an aid to overcoming such problems, stereographic techniques permit the construction of three-dimensional representations whose vividness and depth provide greater clarity and enhance interpretability to strengthen the reader's grasp of key concepts. The author illustrates the stereographic approach to three-dimensional communication using general examples closely analogous to relevant applications in marketing research.

Numerical Simulation for Mechanical Behavior of Carbon Black Filler Particle Reinforced Rubber Matrix Composites

2011 ◽  
Vol 137 ◽  
pp. 1-6
Author(s):  
Qing Li ◽  
Xiao Xiang Yang
Keyword(s):  
Carbon Black ◽  
Mechanical Behavior ◽  
Plane Stress ◽  
Volume Fraction ◽  
Filler Particle ◽  
Three Dimensional ◽  
Rubber Matrix ◽  
Two Dimensional ◽  
Rubber Composites ◽  
Dimensional Plane

In this paper, the micromechanical finite element method based on Representative Volume Element has been applied to study and analyze the macro mechanical properties of the carbon black filled rubber composites by using two-dimensional plane stress simulations and three-dimensional axisymmetric simulations under uniaxial compression respectively. The dependence of the macroscopic stress-strain behavior and the effective elastic modulus of the composites, on particle shape, particle area/volume fraction and particle stiffness has been investigated and discussed. Additionally, the simulation results of the two-dimensional plane stress model and the three-dimensional axisymmetric model are evaluated and compared with the experimental data, which shows that the two-dimensional plane stress simulations generate poor predictions on the mechanical behavior of the carbon black particle reinforced rubber composites, while the three-dimensional axisymmetric simulations appear to give a better prediction.

A simplified plane strain analysis of lateral wall deflection for excavations with cross walls

2012 ◽  
Vol 49 (10) ◽  
pp. 1134-1146 ◽  
Author(s):  
Pio-Go Hsieh ◽  
Chang-Yu Ou ◽  
Chiang Shih
Keyword(s):  
Plane Strain ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Lateral Wall ◽  
Diaphragm Wall ◽  
Beam Model ◽  
Two Dimensional ◽  
Wall Deflection ◽  
Dimensional Plane ◽  
Proposed Model

Previous studies have shown that installation of cross walls in deep excavations can reduce lateral wall deflection to a very small amount. To predict the lateral wall deflection for excavations with cross walls, it is necessary to perform a three-dimensional numerical analysis because the deflection behavior of the diaphragm wall with cross walls is by nature three dimensional. However for the analysis and design of excavations, two-dimensional plane strain analysis is mostly used in practice . For this reason, based on the deflection behavior of continuous beams and the superimposition principle, an equivalent beam model suitable for two-dimensional plane strain analysis was derived to predict lateral wall deflection for excavations with cross walls. Three excavation cases were employed to verify the proposed model. Case studies confirm the proposed equivalent beam model for excavations with cross walls installed from near the ground surface down to at least more than half the embedded depth of the diaphragm wall. For the case with a limited cross-wall depth, the proposed model yields a conservative predicted lateral wall deflection.

scholarly journals An analysis of two and three dimensional unsteady withdrawal flows, using shallow water theory

2000 ◽  
Vol 41 (3) ◽  
pp. 338-357 ◽  
Author(s):  
A. J. Koerber ◽  
L. K. Forbes
Keyword(s):  
Shallow Water ◽  
Three Dimensional ◽  
Finite Depth ◽  
Two Dimensional ◽  
Shallow Water Theory ◽  
Symmetric Flow ◽  
Dimensional Plane ◽  
Flow Through ◽  
Steady Solutions

AbstractThis paper examines the predictions of shallow water theory for steady and unsteady withdrawal flows through an extended sink from fluid of finite depth. Two-dimensional plane flows and three-dimensional axi-symmetric flow through a circular drain are examined. Shallow water theory indicates the presence of limiting configurations, where the surface of the fluid collapses directly into the sink. In addition, this theory suggests that some previously computed steady solutions may be unstable.

Two-Dimensional Green’s Functions for Elastic Bi-materials

1992 ◽  
Vol 59 (2) ◽  
pp. 321-327 ◽  
Author(s):  
J. L. Carvalho ◽  
J. H. Curran
Keyword(s):  
Boundary Element Method ◽  
Hydraulic Fracturing ◽  
Boundary Element ◽  
Plane Strain ◽  
Three Dimensional ◽  
Fundamental Solutions ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Dimensional Plane ◽  
Element Method

Two-dimensional plane-strain fundamental solutions for elastic bi-materials are developed using the nuclei of strain method. The method is a reduction of the threedimensional approach previously derived by Vijayakumar and Cormack. The structure of the three-dimensional solution is preserved and the two-dimensional nuclei of strain and their corresponding vector functions are reported in this paper. Application of these solutions to the boundary element method is demonstrated via a hydraulic fracturing example.

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