Solution of three-dimensional problems of the theory of elasticity using the Monte Carlo method

1988 ◽  
Vol 52 (2) ◽  
pp. 270-274 ◽  
Author(s):  
B.E. Pobedrya ◽  
P.V. Chistyakov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
The Monte Carlo Method

scholarly journals Safety Evaluation of Underground Caverns Based on Monte Carlo Method

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Qifeng Guo ◽  
Zhihong Dong ◽  
Meifeng Cai ◽  
Fenhua Ren ◽  
Jiliang Pan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Three Dimensional ◽  
Safety Evaluation ◽  
Cumulative Distribution ◽  
Three Dimensional Model ◽  
Maximum Displacement ◽  
The Monte Carlo Method ◽  
Underground Caverns ◽  
The Stability

In order to study the influence of joint fissures and rock parameters with random characteristics on the safety of underground caverns, several parameters affecting the stability of surrounding rock of underground caverns are selected. According to the Monte Carlo method, random numbers satisfying normal distribution characteristics are established. A three-dimensional model of underground caverns with random characteristics is established by discontinuous analysis software 3DEC and excavation simulations are carried out. The maximum displacement at the numerical monitoring points of arch and floor is the safety evaluation index of the cavern. The probability distribution and cumulative distribution function of the displacement at the top arch and floor are obtained, and the safety of a project is evaluated.

SIMULATION OF GAS RELEASE FLOWS FROM THE FLOW SURFACES OF TURBOMOLECULAR VACUUM PUMPS

2020 ◽  
pp. 45-48
Author(s):  
M. V. Fomin ◽  
I. M. Fomina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Gas Flow ◽  
Three Dimensional ◽  
Low Density ◽  
Gas Release ◽  
The Monte Carlo Method ◽  
Turbomolecular Pump ◽  
Flow Part

An algorithm for modeling and an example of calculating gas release flows from the surfaces of the flow part of a turbomolecular pump by the Monte Carlo method in a three-dimensional setting low-density gas flow is considered.

The Binary Spatial Partitioning Algorithm for Efficient Tracing of Rays in the Monte Carlo Method for Surface-to-Surface Radiation Transport

2006 ◽  
Author(s):  
Sandip Mazumder
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Binary Tree ◽  
Radiation Transport ◽  
Three Dimensional ◽  
Surface Radiation ◽  
Computational Domain ◽  
Spatial Partitioning ◽  
The Monte Carlo Method ◽  
Discrete Surface

The Binary Spatial Partitioning (BSP) algorithm has found prolific usage within the computer graphics community for efficient tracing of rays. In this paper, the BSP algorithm is described and demonstrated in the context of the Monte Carlo method for surface-to-surface radiation transport. In the BSP algorithm the computational domain is recursively bisected into a set of hierarchically linked boxes that are then made use of to narrow down the number of ray-surface intersection calculations. The geometric information pertaining to these hierarchically linked boxes is stored in the form of a binary tree or table. The algorithm is 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, and is found to result in orders of magnitude gains in computational efficiency over direct calculations that do not employ any acceleration strategy. In theory, the BSP algorithm is expected to scale logarithmically, i.e., the CPU time is expected to increase logarithmically with increase in the number of discrete surface elements (or faces) that the boundaries of the computational domain are broken into. In practice, however, it was found that balancing of the binary tree is critical for logarithmic scaling of the algorithm. Without balancing of the binary tree, only super-linear scaling can be attained.

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