Stochastic Mechanics Of Discrete Media
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Stochastic Mechanics Of Discrete Media
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Author : David R. Axelrad
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic Mechanics Of Discrete Media written by David R. Axelrad and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
For the past three decades the mechanics of structured media, frequently called micromechanics, has been recognized as an important new approach in the analysis of material behaviour. This book discusses the modern use of mathematical analysis to the stochastic mechanics of discrete media. The theoretical study is therefore based on set and measure theory and the application of point processes.
Foundations Of The Probabilistic Mechanics Of Discrete Media
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Author : D. R. Axelrad
language : en
Publisher: Elsevier
Release Date : 2016-03-16
Foundations Of The Probabilistic Mechanics Of Discrete Media written by D. R. Axelrad and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-16 with Science categories.
This latest volume in the Foundations & Philosophy of Science & Technology series provides an account of probabilistic functional analysis and shows its applicability in the formulation of the behaviour of discrete media with the inclusion of microstructural effects. Although quantum mechanics have long been recognized as a stochastic theory, the introduction of probabilistic concepts and principles to classical mechanics has in general not been attempted. In this study the author takes the view that the significant field quantities of a discrete medium are random variables or functions of such variables. Hence the probabilistic mechanics of discrete media are based on the mathematical theory of probability and the axiomatics of measure theory.
Computational Stochastic Mechanics
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Author : P.D. Spanos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational Stochastic Mechanics written by P.D. Spanos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
Over a period of several years the field of probabilistic mechanics and com putational mechanics have progressed vigorously, but independently. With the advent of powerful computational hardware and the development of novel mechanical techniques, the field of stochastic mechanics has progressed in such a manner that the inherent uncertainty of quite complicated systems can be addressed. The first International Conference on Computational Stochastic Mechanics was convened in Corfu in September 1991 in an ef fort to provide a forum for the exchanging of ideas on the current status of computational methods as applied to stochastic mechanics and for identi fying needs for further research. The Conference covered both theoretical techniques and practical applications. The Conference also celebrated the 60th anniversary of the birthday of Dr. Masanobu Shinozuka, the Sollenberger Professor of Civil Engineering at Princeton University, whose work has contributed in such a great measure to the development of Computational Stochastic Mechanics. A brief sum mary of his career and achievements are given in the Dedication. This book comprises some of the papers presented at the meeting and cov ers sections on Theoretical Reliability Analysis; Damage Analysis; Applied Reliability Analysis; Theoretical Random Vibrations; Stochastic Finite Ele ment Concept; Fatigue and Fracture; Monte Carlo Simulations; Earthquake Engineering Applications; Materials; Applied Random Vibrations; Applied Stochastic Finite Element Analysis, and Flow Related Applications and Chaotic Dynamics. The Editors hope that the book will be a valuable contribution to the grow ing literature covering the field of Computational Stochastic Mechanics.
The Stochastic Perturbation Method For Computational Mechanics
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Author : Marcin Kaminski
language : en
Publisher: John Wiley & Sons
Release Date : 2013-01-17
The Stochastic Perturbation Method For Computational Mechanics written by Marcin Kaminski and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-17 with Science categories.
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.
Discrete Stochastic Processes
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Author : Robert G. Gallager
language : en
Publisher: Springer
Release Date : 1995-10-31
Discrete Stochastic Processes written by Robert G. Gallager and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-31 with Technology & Engineering categories.
Stochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understanding and intuition necessary to apply stochastic process theory in engineering, science and operations research. The book approaches the subject via many simple examples which build insight into the structure of stochastic processes and the general effect of these phenomena in real systems. The book presents mathematical ideas without recourse to measure theory, using only minimal mathematical analysis. In the proofs and explanations, clarity is favored over formal rigor, and simplicity over generality. Numerous examples are given to show how results fail to hold when all the conditions are not satisfied. Audience: An excellent textbook for a graduate level course in engineering and operations research. Also an invaluable reference for all those requiring a deeper understanding of the subject.
Mechanics Of Granular Media And Its Application In Civil Enginenering
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Author : I.I. Kandaurov
language : en
Publisher: Routledge
Release Date : 2022-03-02
Mechanics Of Granular Media And Its Application In Civil Enginenering written by I.I. Kandaurov and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-02 with Technology & Engineering categories.
Systematic approach to the construction of a probabilistic simulation model for distribution of pressure in granular media. Pressure fields & compressive deformations from that model presented for a thrustless granular medium & homogeneous or stratified earth foundation. General solutions incorporating partial cases of thrustless & thrusting granular media.
Discrete Time Stochastic Systems
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Author : Torsten Söderström
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Discrete Time Stochastic Systems written by Torsten Söderström and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This comprehensive introduction to the estimation and control of dynamic stochastic systems provides complete derivations of key results. The second edition includes improved and updated material, and a new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control.
Analysis Of Stochastic Systems With Discrete Elements
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Author : Roger George Ghanem
language : en
Publisher:
Release Date : 1988
Analysis Of Stochastic Systems With Discrete Elements written by Roger George Ghanem and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
Two new methods for the solution of problems involving material variability are proposed. Medium properties are modeled as second order stochastic processes defined by their mean and convariance functions. Both methods make use of the Karhunen-Loeve expansion which is a mean-square convergent orthogonal expansion of a continuous process in terms of a countable set of uncorrelated random variables. The first of the proposed methods relies on implementing the Karhunen-Loeve expansion for the medium property in conjunction with a Neumann expansion of the inverse operator. This results in an explicit expression for the response process as a multivariate polynomial functional of a set of uncorrelated random variables. The second method treats the solution process as an element in the Hilbert space of random functions, in which a sequence of projection operators is identified as the Polynomial Chaoses of consecutive order. The solution process is then determined by its projection onto the spaces spanned by these polynomials. These concepts can be construed as extensions of the deterministic finite element methods to the space of random functions. Both of the proposed methods are exemplified by three problems from the field of engineering mechanics. The corresponding results are found in agreement with those obtained by a Monte-Carlo simulation solution of the problems. In addition to the two methods mentioned above, a new formulation is presented for a class of problems involving deterministic media subjected to random external excitations. The formulation involves a combination of the boundary element method with the Karhunen-Loeve expansion for the exciting process. Namely, the boundary element method is used as a discretization tool to restate the problem as a set of discrete equations. Further, the Karhunen-Loeve expansion is utilized to represent the random processes in a manner conducing their optimal discretization.
Nonlinear Dynamics And Stochastic Mechanics
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Author : Wolfgang Kliemann
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Nonlinear Dynamics And Stochastic Mechanics written by Wolfgang Kliemann and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
Engineering systems have played a crucial role in stimulating many of the modern developments in nonlinear and stochastic dynamics. After 20 years of rapid progress in these areas, this book provides an overview of the current state of nonlinear modeling and analysis for mechanical and structural systems. This volume is a coherent compendium written by leading experts from the United States, Canada, Western and Eastern Europe, and Australia. The 22 articles describe the background, recent developments, applications, and future directions in bifurcation theory, chaos, perturbation methods, stochastic stability, stochastic flows, random vibrations, reliability, disordered systems, earthquake engineering, and numerics. The book gives readers a sophisticated toolbox that will allow them to tackle modeling problems in mechanical systems that use stochastic and nonlinear dynamics ideas. An extensive bibliography and index ensure this volume will remain a reference standard for years to come.
Nonlinear Stochastic Mechanics
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Author : Nicola Bellomo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Stochastic Mechanics written by Nicola Bellomo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The Symposium, held in Torino (lSI, Villa Gualino) July 1-5, 1991 is the sixth of a series of IUTAM-Symposia on the application of stochastic analysis to continuum and discrete mechanics. The previous one, held in Innsbruck (1987), was mainly concentrated on qual itative and quantitative analysis of stochastic dynamical systems as well as on bifurcation and transition to chaos of deterministic systems. This Symposium concentrated on fundamental aspects (stochastic analysis and mathe matical methods), on specific applications in various branches of mechanics, engineering and applied sciences as well as on related fields as analysis of large systems, system identifica tion, earthquake prediction. Numerical methods suitable to provide quantitative results, say stochastic finite elements, approximation of probability distribution and direct integration of differential equations have also been the object of interesting presentations. Specific topics of the sessions have been: Engineering Applications, Equivalent Lineariza tion of Discrete Stochastic Systems, Fatigue and Life Estimation, Fluid Dynamics, Numerical Methods, Random Vibration, Reliability Analysis, Stochastic Differential Equations, System Identification, Stochastic Control. We are indebted to the IUTAM Bureau for having promoted and sponsored this Sympo sium and the Scientific Committee for having collaborated to the selection of participants and lecturers as well as to a prompt reviewing of the papers submitted for publication into these proceedings. A special thank is due to Frank Kozin: the organization of this meeting was for him ';ery important; he missed the meeting but his organizer ability was present.
