The stochastic perturbation method for computational mechanics

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Title:

Personal Author:

Kaminski, M. M. (Marcin M.), 1969-

Publication Information:

Hoboken : John Wiley & Sons Inc., 2013

Physical Description:

xvii, 330 p. : ill. ; 25 cm.

ISBN:

9780470770825

Subject Term:

Engineering -- Statistical methods

Perturbation (Mathematics)

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010306164	TA340 K36 2013	Open Access Book	Book	Searching... Unknown

Probabilistic analysis is increasing in popularity and importance within engineering and the applied sciences. However, the stochastic perturbation technique is a fairly recent development and therefore remains as yet unknown to many students, researchers and engineers. Fields in which the methodology can be applied are widespread, including various branches of engineering, heat transfer and statistical mechanics, reliability assessment and also financial investments or economical prognosis in analytical and computational contexts.

Stochastic Perturbation Method in Applied Sciences and Engineering is devoted to the theoretical aspects and computational implementation of the generalized stochastic perturbation technique. It is based on any order Taylor expansions of random variables and enables for determination of up to fourth order probabilistic moments and characteristics of the physical system response.

Key features:

Provides a grounding in the basic elements of statistics and probability and reliability engineering Describes the Stochastic Finite, Boundary Element and Finite Difference Methods, formulated according to the perturbation method Demonstrates dual computational implementation of the perturbation method with the use of Direct Differentiation Method and the Response Function Method Accompanied by a website (www.wiley.com/go/kaminski) with supporting stochastic numerical software Covers the computational implementation of the homogenization method for periodic composites with random and stochastic material properties Features case studies, numerical examples and practical applications

Stochastic Perturbation Method in Applied Sciences and Engineering is a comprehensive reference for researchers and engineers, and is an ideal introduction to the subject for postgraduate and graduate students.

Author Notes

Marcin Kaminski is a professor within the Faculty of Civil Engineering, Architecture and Environmental Engineering at the Technical University of Lodz, Poland. Having obtained a PhD in the field of stochastic finite elements in 1997 he has continued his research work in the area, winning the John Argyris award in computational mechanics of solids and fluids in 2001 at ECCOMAS. He currently lectures in the stochastic perturbation method at Lodz. His monograph Computational Mechanics of Composite Materials: Sensitivity, Randomness and Multiscale Behaviour was published in 2002 by Springer, and he has authored over 150 research papers.

Acknowledgments	p. vii
Introduction	p. ix
1 Mathematical Considerations	p. 1
1.1 Stochastic Perturbation Technique Basis	p. 1
1.2 Least-Squares Technique Description	p. 26
1.3 Time Series Analysis	p. 40
2 The Stochastic Finite Element Method	p. 69
2.1 Governing Equations and Variational Formulations	p. 69
2.1.1 Linear Potential Problems	p. 69
2.1.2 Linear Elastostatics	p. 72
2.1.3 Non-linear Elasticity Problems	p. 75
2.1.4 Variational Equations of Elastodynamics	p. 76
2.1.5 Transient Analysis of the Heat Transfer	p. 77
2.1.6 Thermopiezoelectricity Governing Equations	p. 80
2.1.7 Navier-Stokes Equations	p. 83
2.2 Stochastic Finite Element Method Equations	p. 87
2.2.1 Linear Potential Problems	p. 87
2.2.2 Linear Elastostatics	p. 88
2.2.3 Non-linear Elasticity Problems	p. 92
2.2.4 SFEM in Elastodynamics	p. 97
2.2.5 Transient Analysis of the Heat Transfer	p. 100
2.2.6 Coupled Thermo-piezoelectrostatics SFEM Equations	p. 104
2.2.7 Navier-Stokes Perturbation-Based Equations	p. 106
2.3 Computational Illustrations	p. 110
2.3.1 Linear Potential Problems	p. 110
2.3.1.1 1D Fluid Flow with Random Viscosity	p. 110
2.3.1.2 2D Potential Problem with the Response Function Method	p. 114
2.3.2 Linear Elasticity	p. 118
2.3.2.1 Simple Extended Bar with Random Stiffness	p. 118
2.3.2.2 Elastic Stability Analysis of the Steel Telecommunication Tower	p. 124
2.3.3 Non-linear Elasticity Problems	p. 131
2.3.4 Stochastic Vibrations of the Elastic Structures	p. 135
2.3.4.1 Forced Vibrations with Random Parameters for a Simple 2 DOF System	p. 135
2.3.4.2 Eigenvibrations of the Steel Telecommunication Tower with Random Stiffness	p. 139
2.3.5 Transient Analysis of the Heat Transfer	p. 142
2.3.5.1 Heat Conduction in the Statistically Homogeneous Rod	p. 142
2.3.5.2 Transient Heat Transfer Analysis by the RFM	p. 147
3 Stochastic Boundary Element Method	p. 155
3.1 Deterministic Formulation of the Boundary Element Method	p. 156
3.2 Stochastic Generalized Perturbation Approach to the BEM	p. 160
3.3 The Response Function Method in the SBEM Equations	p. 164
3.4 Computational Experiments	p. 168
4 The Stochastic Finite Difference Method	p. 195
4.1 Analysis of the Unidirectional Problems	p. 196
4.1.1 Elasticity Problems	p. 196
4.1.2 Determination of the Critical Moment for the Thin-Walled Elastic Structures	p. 209
4.1.3 Introduction to Elastodynamics with Finite Differences	p. 214
4.1.4 Advection-Diffusion Equation	p. 220
4.2 Analysis of Boundary Value Problems on 2D Grids	p. 225
4.2.1 Poisson Equation	p. 225
4.2.2 Deflection of Thin Elastic Plates in Cartesian Coordinates	p. 230
4.2.3 Vibration Analysis of Elastic Plates	p. 239
5 Homogenization Problem	p. 241
5.1 Composite Material Model	p. 243
5.2 Statement of the Problem and Basic Equations	p. 249
5.3 Computational Implementation	p. 256
5.4 Numerical Experiments	p. 258
6 Concluding Remarks	p. 297
Appendix	p. 303
References	p. 319
Index	p. 329

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Table of Contents