Numerical models of random processes and fields and some applications in Monte Carlo methods

1994 ◽  
Vol 9 (2) ◽  
Author(s):  
S. M. PRIGARIN
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Numerical Models ◽  
Random Processes

scholarly journals Dynamic Reliability Evaluation of Road Vehicle Subjected to Turbulent Crosswinds Based on Monte Carlo Simulation

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Bin Wang ◽  
Yongle Li ◽  
Helu Yu ◽  
Haili Liao
Keyword(s):  
Surface Roughness ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Random Process ◽  
Numerical Models ◽  
Random Processes ◽  
Distribution Model ◽  
Vibration System ◽  
Road Vehicle ◽  
Dynamic Reliability

As a vehicle moves on roads, a complex vibration system of the running vehicle is formed under the collective excitations of random crosswinds and road surface roughness, together with the artificial handing by the drivers. Several numerical models in deterministic way to assess the safety of running road vehicles under crosswinds were proposed. Actually, the natural wind is a random process in time domain due to turbulence, and the surface roughness of a road is also a random process but in spatial domain. The nature of a running vehicle therefore is an extension of dynamic reliability excited by random processes. This study tries to explore the dynamic reliability of a road vehicle subjected to turbulent crosswinds. Based on a nonlinear vibration system, the dynamic responses of a road vehicle are simulated to obtain the dynamic reliability. Monte Carlo Simulation with Latin Hypercube Sampling is then applied on the possible random variables including the vehicle weight, road friction coefficient, and driver parameter to look at their effects. Finally, a distribution model of the dynamic reliability and a corresponding index for the wind-induced vehicle accident considering these random processes and variables is proposed and employed to evaluate the safety of the running vehicle.

MODELING OF A TURBULENT ETHYLENE/AIR JET FLAME USING HYBRID FINITE VOLUME/MONTE CARLO METHODS

2009 ◽  
Vol 1 (1) ◽  
pp. 37-53 ◽  
Author(s):  
Ranjan S. Mehta ◽  
Anquan Wang ◽  
Michael F. Modest ◽  
Daniel C. Haworth
Keyword(s):  
Monte Carlo ◽  
Finite Volume ◽  
Monte Carlo Methods ◽  
Jet Flame ◽  
Air Jet

Probabilistic multiscale modeling of fracture in heterogeneous materials and structures

2020 ◽  
Vol 86 (7) ◽  
pp. 45-54
Author(s):  
A. M. Lepikhin ◽  
N. A. Makhutov ◽  
Yu. I. Shokin
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fracture Mechanics ◽  
Multiscale Modeling ◽  
Virtual Work ◽  
Numerical Models ◽  
Heterogeneous Materials ◽  
Heterogeneous Structure ◽  
Generalized Coordinates ◽  
Heterogeneous Structures

The probabilistic aspects of multiscale modeling of the fracture of heterogeneous structures are considered. An approach combining homogenization methods with phenomenological and numerical models of fracture mechanics is proposed to solve the problems of assessing the probabilities of destruction of structurally heterogeneous materials. A model of a generalized heterogeneous structure consisting of heterogeneous materials and regions of different scales containing cracks and crack-like defects is formulated. Linking of scales is carried out using kinematic conditions and multiscale principle of virtual forces. The probability of destruction is formulated as the conditional probability of successive nested fracture events of different scales. Cracks and crack-like defects are considered the main sources of fracture. The distribution of defects is represented in the form of Poisson ensembles. Critical stresses at the tops of cracks are described by the Weibull model. Analytical expressions for the fracture probabilities of multiscale heterogeneous structures with multilevel limit states are obtained. An approach based on a modified Monte Carlo method of statistical modeling is proposed to assess the fracture probabilities taking into account the real morphology of heterogeneous structures. A feature of the proposed method is the use of a three-level fracture scheme with numerical solution of the problems at the micro, meso and macro scales. The main variables are generalized forces of the crack propagation and crack growth resistance. Crack sizes are considered generalized coordinates. To reduce the dimensionality, the problem of fracture mechanics is reformulated into the problem of stability of a heterogeneous structure under load with variations of generalized coordinates and analysis of the virtual work of generalized forces. Expressions for estimating the fracture probabilities using a modified Monte Carlo method for multiscale heterogeneous structures are obtained. The prospects of using the developed approaches to assess the fracture probabilities and address the problems of risk analysis of heterogeneous structures are shown.

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