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ASCE 9780784476864 2012

ASCE 9780784476864 2012

$35.75

Stochastic Models of Uncertainties in Computational Mechanics

Published By Publication Date Number of Pages
ASCE 2012 134
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LNMech 2 presents the main concepts, formulations, and recent advances in the use of a mathematical-mechanical modeling process to predict the responses of a real structural system in its environment.

PDF Catalog

PDF Pages PDF Title
1 Cover
6 Contents
10 1 Introduction
12 2 Short overview of probabilistic modeling of uncertainties and related topics
2.1 Uncertainty and variability
13 2.2 Types of approach for probabilistic modeling of uncertainties
15 2.3 Types of representation for the probabilistic modeling of uncertainties
18 2.4 Construction of prior probability models using the maximum entropy principle under the constraints defined by the available information
20 2.5 Random Matrix Theory
24 2.6 Propagation of uncertainties and methods to solve the stochastic dynamical equations
26 2.7 Identification of the prior and posterior probability models of uncertainties
28 2.8 Robust updating of computational models and robust design with uncertain computational models
30 3 Parametric probabilistic approach to uncertainties in computational structural dynamics
3.1 Introduction of the mean computational model in computational structural dynamics
31 3.2 Introduction of the reduced mean computational model
33 3.3 Methodology for the parametric probabilistic approach of modelparameter uncertainties
34 3.4 Construction of the prior probability model of model-parameter uncertainties
35 3.5 Estimation of the parameters of the prior probability model of the uncertain model parameter
36 3.6 Posterior probability model of uncertainties using output-predictionerror method and the Bayesian method
38 4 Nonparametric probabilistic approach to uncertainties in computational structural dynamics
4.1 Methodology to take into account both the model-parameter uncertainties and the model uncertainties (modeling errors)
39 4.2 Construction of the prior probability model of the random matrices
40 4.3 Estimation of the parameters of the prior probability model of uncertainties
41 4.4 Comments about the applications and the validation of the nonparametric probabilistic approach of uncertainties
44 5 Generalized probabilistic approach to uncertainties in computational structural dynamics
5.1 Methodology of the generalized probabilistic approach
46 5.2 Construction of the prior probability model of the random matrices
5.3 Estimation of the parameters of the prior probability model of uncertainties
47 5.4 Posterior probability model of uncertainties using the Bayesian method
50 6 Nonparametric probabilistic approach to uncertainties in structural-acoustic models for the low- and medium-frequency ranges
51 6.1 Reduced mean structural-acoustic model
55 6.2 Stochastic reduced-order model of the computational structuralacoustic model using the nonparametric probabilistic approach of uncertainties
56 6.3 Construction of the prior probability model of uncertainties
58 6.4 Model parameters, stochastic solver and convergence analysis
6.5 Estimation of the parameters of the prior probability model of uncertainties
59 6.6 Comments about the applications and the experimental validation of the nonparametric probabilistic approach of uncertainties in structural acoustics
60 7 Nonparametric probabilistic approach to uncertainties in computational nonlinear structural dynamics
61 7.1 Nonlinear equation for 3D geometrically nonlinear elasticity
7.2 Nonlinear reduced mean model
63 7.3 Algebraic properties of the nonlinear stiffnesses
7.4 Stochastic reduced-order model of the nonlinear dynamical system using the nonparametric probabilistic approach of uncertainties
65 7.5 Comments about the applications of the nonparametric probabilistic approach of uncertainties in computational nonlinear structural dynamics
66 8 Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data
67 8.1 Definition of the problemto be solved
69 8.2 Construction of a family of prior algebraic probability models (PAPM) for the tensor-valued random field in elasticity theory
79 8.3 Methodology for the identification of a high-dimension polynomial chaos expansion using partial and limited experimental data
85 8.4 Computational aspects for constructing realizations of polynomial chaos in high dimension
87 8.5 Prior probability model of the random VVC
90 8.6 Posterior probability model of the random VVC using the classical Bayesian approach
95 8.7 Posterior probability model of the random VVC using a new approach derived from the Bayesian approach
97 8.8 Comments about the applications concerning the identification of polynomial chaos expansions of random fields using experimental data
98 9 Conclusion
100 References
118 Index
A
B
C
119 D
E
120 F
121 G
H
123 K
L
124 M
125 N
127 O
P
132 R
133 S
T
U
134 V

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ASCE 9780784476864 2012
$35.75