PDF | This textbook offers an introduction to modeling the mechanical behavior of solids within continuum mechanics and thermodynamics. To illustrate the. PDF | Solid Mechanics | ResearchGate, the professional network for scientists. Downloadable at: smeltitherabpigs.ga . Further, because solid mechanics poses challenging mathematical and.
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Fundamentals of Solid Mechanics. Course at the European School for Advanced Studies in Earthquake Risk Reduction. (ROSE School), Pavia, Italy. Krzysztof. mechanics of deformable solids nor one with a broader and richer history. ferential equations appear in solid mechanics, but requirements for uniqueness. Mechanics of materials is a basic engineering subject that must be .. with the behavior of solid bodies subjected to various types of loading.
As a practising Engineer with a background only in elementary Strength of Materials, I approached that problem initially using the concepts of concentrated forces and superposition. Today, with a rather more extensive knowledge of analytical techniques in Elasticity, I still find it helpful to go back to these roots in the elementary theory and think through a problem physically as well as mathematically, whenever some new and unexpected feature presents difficulties in research.
This way of thinking will be found to permeate this book. My engineering background will also reveal itself in a tendency to work examples through to final expressions for stresses and displacements, rather than leave the derivation at a point where the remaining manipulations would be routine.
Selection procedure and criteria
With the practical engineering reader in mind, I have endeavoured to keep to a minimum any dependence on previous knowledge of Solid Mechanics, Continuum Mechanics or Mathematics. Most of the text should be readily intelligible to a reader with an undergraduate background of one or two courses in elementary Strength of Materials and a rudimentary knowledge of partial differentiation.
Cartesian tensor notation and the summation convention are used in a few places to shorten the derivation of some general results, but these sections are carefully explained, so as to be self-explanatory.
The book is based on a one semester graduate course on Linear Elasticity that I have taught at the University of Michigan since In such a restricted format, it is clearly necessary to make some difficult choices about which topics to include and, more significantly, which to exclude.
The most significant exclusion is the classical complex variable solution of two-dimensional Elasticity, which, if it were to be adequately treated including essential mathematical preliminaries, would need most of a book of this length to itself.
Instead, I have chosen to restrict the two-dimensional treatment to the more traditional real stress function approach, so as to leave room for a substantial amount of material on three-dimensional problems, which are arguably closer to the frontier of current research.
As a researcher in Solid Mechanics, with a primary interest in the physical behaviour of the systems I am investigating, rather than in the mathematical structure of the solutions, I have frequently had recourse to numerical methods of all types and have tended to adopt the pragmatic criterion that the best method is that which gives the most convincing and accurate result in the shortest time.
This is particularly true in three-dimensional problems, where direct numerical methods are extremely computer-intensive if any reasonably accuracy is required, and in problems involving infinite or semi-infinite domains, discontinuities, bonded or contacting material interfaces or theoretically singular stress fields.
By contrast, I would immediately opt for a finite element solution of any two-dimensional problem involving finite bodies with relatively smooth contours, unless it happened to fall into the surprisingly wide class of problems to which the solution can be written down in closed form. The reader will therefore find my choice of topics significantly biassed towards those fields identified above where analytical methods are most useful.
I have provided a representative selection of problems suitable for class use at the end of most of the chapters. This in turn has required me to write the text in such a way that the student can approach problems deductively.
With the greater general availablity of symbolic processors, this will soon cease to be a difficulty, but those without access to such methods might like to simplify some of the three-dimensional problems by restricting the solution to the case At the University of Michigan, we are fortunate in having a very sophisticated computer environment, so I can ask my students to carry the problems as far as plotting graphs CONTENTS xix of stress distributions and performing parametric studies to determine optimum designs for components.
From the engineering perspective, this leads to a significantly greater insight into the nature of the subject, as well as serving as an educational motivation for those students outside the classical Mechanics field.
Foundations of Solid Mechanics (PH, 1965) Fung Y.C.
Over the years, the students attending my course have been drawn from departments of Mechanical, Civil, Aerospace and Materials Engineering as well as Naval Architecture, Applied Mechanics and Mathematics and have therefore generally represented quite a diverse set of points of view.
The questions raised by this very talented group of people have often resulted in vigorous classroom discussions which have had a major impact on my perspective on the subject. It is therefore to my graduate students, past and present, that this book is dedicated. It is traditional at this point also to thank a multitude of colleagues, assistants and family members for their contributions and support.
However, since I developed the text as part of my normal teaching duties and typset it myself using many of these credits would be out of place.
My wife, Maria Comninou, may disagree, but as far as I can judge, my temperament was not significantly soured during the gestation period, but she does deserve my thanks for her technical input during times that we have collaborated on research problems. I am particularly grateful to the Rector and Fellows of Lincoln College, Oxford, who provided me with a stimulating scholarly environment during an important stage in the writing, and to David Hills of that College who made my visit there possible.
The line drawings were prepared by Rodney Hill and Figures I should also like to thank John Dundurs for permission to use Table 9.
In this book, we shall further restrict attention to the case of linear infinitesimal elasticity, in which the stresses and displacements are linearly proportional to the applied loads and the displacements are small in comparison with the characteristic length dimensions of the body.
These restrictions ensure that linear superposition can be used and enable us to employ a wide range of series and transform techniques which are not available for non-linear problems. Most engineers first encounter problems of this kind in the context of the subject known as Mechanics of Materials, which is an important constituent of most undergraduate engineering curricula.
Mechanics of Materials differs from Elasticity in that various plausible but unsubstantiated assumptions are made about the deformation process in the course of the analysis. A typical example is the assumption that plane sections remain plane in the bending of a slender beam. Approximations are often introduced towards the end of the solution, but these are mathematical approximations used to obtain solutions of the governing equations rather than physical approximations that impose artificial and strictly unjustifiable constraints on the permissible deformation field.
However, it would be a mistake to draw too firm a distinction between the two approaches, since practitioners of each have much to learn from the other. Mechanics of Materials, with its emphasis on physical reasoning and a full exploration of the practical consequences of the results, is often able to provide insights into the problem that are less easily obtained from a purely mathematical perspective.
Also, there is little to be said for using an ad hoc approach when, as is often the case, a more rigorous treatment presents no serious difficulty. The second suffix denotes the direction of the stress component and the first the direction of the outward normal to the surface upon which it acts.
This notation is illustrated in Figure 1. The remaining six stress components in Figure 1. However, there is no need for a different symbol, since the suffices enable us to distinguish normal from shear stress components.
Also, we shall find that the use of a single symbol with appropriate suffices permits matrix methods to be used in many derivations and introduces considerable economies in the notation for general results.
The equilibrium of moments acting on the block in Figure 1. In fact, a few books use the opposite convention. Readers who have not encountered three-dimensional problems before should note that there are two shear stress components on each surface and one normal stress component. There are some circumstances in which it is convenient to combine the two shear stresses on a given plane into a two-dimensional vector in the plane — i. An elementary situation where this is helpful is in the Mechanics of Materials problem of determining the distribution of shear stress on the crosssection of a beam due to a transverse shear force2.
For example, we note that in this case, the resultant shear stress on the plane must be tangential to the edge at the boundary of the cross section, since the shear stress complementary to the component normal to the edge acts on the traction-free surface of the beam and must therefore be zero.
This of course is why the shear stress in a thin-walled section tends to follow the direction of the wall. We shall refer to a plane normal to the as an etc.
The only stress components which act on an are those which have an as the first suffix This is an immediate consequence of the definition. Notice also that any can be defined by an equation of the form where C is a constant. The Fundamental Concepts and Principles of Mechanics. The Statics of Particles. The Statics of Rigid Bodies. Surface and Contact Stress.
Fourth M.I.T. Conference on Computational Fluid and Solid Mechanics
Body Forces. Internal Stress. Equilibrium of Stress. Stress Transformation: Further Aspects. Plane Stress.
Stress Boundary Conditions: Plane Strain. Volumetric Strain. Material Behaviour and Mathematical Modelling. Mechanics Modelling. The Response of Real Materials. Material Models.
The Continuum. Linear Elasticity. The Linear Elastic Model.
Homogeneous Problems in Linear Elasticity. Applications of Elasticity. One Dimensional Axial Deformations. Pressure Vessels. Energy and Virtual Work.
Energy in Deforming Materials. Elastic Strain Energy. Material Failure.Find the matrix representations of tensors F.
The molecules may be crystalline or. In order to evaluate f we map. Note that summation can only take place over a dummy or summation index if one index is a subscript and the other is a superscript.
In order to show uniqueness of the polar decomposition we suppose that there exist.