Fundamentals of Dimensional Analysis

Fundamentals of Dimensional Analysis PDF

Author: Alberto N. Conejo

Publisher: Springer Nature

Published: 2021-05-31

Total Pages: 384

ISBN-13: 9811616027

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This is the first book which systematically describes an integral approach on dimensional analysis. The amount of textbooks on dimensional analysis is huge, however most of the books start with the definition of the relevant variables. When the variables are given to the reader without prior knowledge on each problem it has serious consequences: the usefulness of dimensional analysis is not appreciated, is not possible to understand the real challenges of this subject and the result, which is a general relationship with dimensionless groups is useless. This book closes the hole in previous books because in addition to describe step by step how to reach the general relationship with dimensionless groups, which creates solid basis of different metallurgical problems to understand the role of the relevant variables. It provides a full description on how to obtain the experimental data and applies the experimental data to transform the general relationship in a particular solution. Once the reader learns how to design the experimental work and uses that information to define the particular solution, it is possible to asses if the selection of variables was adequate or not. The book is useful for both undergraduate and graduate students.

Dimensional Analysis for Engineers

Dimensional Analysis for Engineers PDF

Author: Volker Simon

Publisher: Springer

Published: 2017-02-09

Total Pages: 144

ISBN-13: 3319520288

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This monograph provides the fundamentals of dimensional analysis and illustrates the method by numerous examples for a wide spectrum of applications in engineering. The book covers thoroughly the fundamental definitions and the Buckingham theorem, as well as the choice of the system of basic units. The authors also include a presentation of model theory and similarity solutions. The target audience primarily comprises researchers and practitioners but the book may also be suitable as a textbook at university level.

A Student's Guide to Dimensional Analysis

A Student's Guide to Dimensional Analysis PDF

Author: Don S. Lemons

Publisher: Cambridge University Press

Published: 2017-03-16

Total Pages: 115

ISBN-13: 1107161150

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This introduction to dimensional analysis covers the methods, history and formalisation of the field. Utilising topics including mechanics, hydro- and electrodynamics, and thermal and quantum physics, it illustrates the possibilities and limitations of dimensional analysis, making it perfect for students on introductory courses in physics, engineering and mathematics.

Applied Dimensional Analysis and Modeling

Applied Dimensional Analysis and Modeling PDF

Author: Thomas Szirtes

Publisher: Butterworth-Heinemann

Published: 2007-04-27

Total Pages: 853

ISBN-13: 0080555454

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Applied Dimensional Analysis and Modeling provides the full mathematical background and step-by-step procedures for employing dimensional analyses, along with a wide range of applications to problems in engineering and applied science, such as fluid dynamics, heat flow, electromagnetics, astronomy and economics. This new edition offers additional worked-out examples in mechanics, physics, geometry, hydrodynamics, and biometry. Covers 4 essential aspects and applications: principal characteristics of dimensional systems, applications of dimensional techniques in engineering, mathematics and geometry, applications in biosciences, biometry and economics, applications in astronomy and physics Offers more than 250 worked-out examples and problems with solutions Provides detailed descriptions of techniques of both dimensional analysis and dimensional modeling

Dimensional Analysis

Dimensional Analysis PDF

Author: Percy Williams Bridgman

Publisher: Theclassics.Us

Published: 2013-09

Total Pages: 40

ISBN-13: 9781230226217

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1922 edition. Excerpt: ...between the number of fundamental units and the number of variables, which determines the number of arguments of the unknown function, is the same in either case, because when the number of units is augmented by one by including the force, the number of variables is also augmented by one by including the dimensional constant, and the difference remains constant. If, however, the problem were such that the experimental relation between force, mass, and acceleration is not involved in the equations of motion of the system, then the ordinary mechanical units would be inappropriate, because we would obtain less information when using them. For we could in this case use four fundamental units without introducing a corresponding dimensional constant into the list of variables, so that the difference between the number of variables and the units would be less by one when using four than when using three fundamental units, and the arguments of the function would be fewer in number, which is desirable. We shall meet an example illustrating this point later. KEFERENCES (1) Fourier, Theorie de Chaleur, 160. As dealing with the general question of the proper number of fundamental units may be mentioned E. Buckingham, Nat. 96, 208, and 396, 1915. CHAPTER VI EXAMPLES ILLUSTRATIVE OF DIMENSIONAL ANALYSIS Let us in the first place recapitulate the results of the preceding chapter. Before undertaking a dimensional analysis we are to imagine ourselves as making an analysis to the extent of deciding the nature of the problem, and enumerating the physical variables which would enter the equations of motion (in the general sense) and also the dimensional coefficients required in writing down the equations of motion. The dimensions of all these variables are...

Fundamentals of Finite Element Analysis

Fundamentals of Finite Element Analysis PDF

Author: Ioannis Koutromanos

Publisher: John Wiley & Sons

Published: 2018-02-12

Total Pages: 724

ISBN-13: 1119260086

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An introductory textbook covering the fundamentals of linear finite element analysis (FEA) This book constitutes the first volume in a two-volume set that introduces readers to the theoretical foundations and the implementation of the finite element method (FEM). The first volume focuses on the use of the method for linear problems. A general procedure is presented for the finite element analysis (FEA) of a physical problem, where the goal is to specify the values of a field function. First, the strong form of the problem (governing differential equations and boundary conditions) is formulated. Subsequently, a weak form of the governing equations is established. Finally, a finite element approximation is introduced, transforming the weak form into a system of equations where the only unknowns are nodal values of the field function. The procedure is applied to one-dimensional elasticity and heat conduction, multi-dimensional steady-state scalar field problems (heat conduction, chemical diffusion, flow in porous media), multi-dimensional elasticity and structural mechanics (beams/shells), as well as time-dependent (dynamic) scalar field problems, elastodynamics and structural dynamics. Important concepts for finite element computations, such as isoparametric elements for multi-dimensional analysis and Gaussian quadrature for numerical evaluation of integrals, are presented and explained. Practical aspects of FEA and advanced topics, such as reduced integration procedures, mixed finite elements and verification and validation of the FEM are also discussed. Provides detailed derivations of finite element equations for a variety of problems. Incorporates quantitative examples on one-dimensional and multi-dimensional FEA. Provides an overview of multi-dimensional linear elasticity (definition of stress and strain tensors, coordinate transformation rules, stress-strain relation and material symmetry) before presenting the pertinent FEA procedures. Discusses practical and advanced aspects of FEA, such as treatment of constraints, locking, reduced integration, hourglass control, and multi-field (mixed) formulations. Includes chapters on transient (step-by-step) solution schemes for time-dependent scalar field problems and elastodynamics/structural dynamics. Contains a chapter dedicated to verification and validation for the FEM and another chapter dedicated to solution of linear systems of equations and to introductory notions of parallel computing. Includes appendices with a review of matrix algebra and overview of matrix analysis of discrete systems. Accompanied by a website hosting an open-source finite element program for linear elasticity and heat conduction, together with a user tutorial. Fundamentals of Finite Element Analysis: Linear Finite Element Analysis is an ideal text for undergraduate and graduate students in civil, aerospace and mechanical engineering, finite element software vendors, as well as practicing engineers and anybody with an interest in linear finite element analysis.

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