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Intermediate Mechanics of Materials - 2nd Edition


Springer has just published the second edition of my book
`Intermediate Mechanics of Materials'. The book covers a selection of topics appropriate to a second course in mechanics of materials. Many books with titles like 'Advanced Mechanics of Materials' are pitched at a much higher level than most introductory courses and this can present a significant barrier to undergraduate students. My intention in this book is to make this transition smoother by discussing simple examples before introducing general principles and by restricting the mathematical level to topics that can be treated using ordinary differential equations rather than PDEs.


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Elasticity, 3rd edition, J.R.Barber

Springer has just published the third edition of my book
`Elasticity'.


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Optimal structural design against elastic instability


In the classical Euler buckling problem, the critical buckling load can be increased by a factor of four if the first mode is suppressed by placing an additional simple support at the mid-point.

If we solve the more general problem where the additional support is placed at some different point z=a in 0<z<L, the critical load will be found to increase above that for the unspported first mode, but the maximum increase is achieved when the support is at the mid-point and buckling then occurs of course in what would have been the second mode of the unsupported beam.


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Three-dimensional anisotropic elasticity - an extended Stroh formalism

Tom Ting and I have recently developed a method of extending Stroh's anisotropic formalism to problems in three dimensions. The unproofed paper can be accessed at http://www-personal.umich.edu/~jbarber/Stroh.pdf .


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IINTERMEDIATE MECHANICS OF MATERIALS

J.R.BARBER: INTERMEDIATE MECHANICS OF MATERIALS

Many of you may know my book on Elasticity, but may not be aware that I also wrote an undergraduate book on Intermediate Mechanics of Materials (Published by McGraw-Hill - ISBN 0-07-232519-4). This picks up from the typical elementary Mechanics of Materials course and deals with the next range of topics such as energy methods, elastic-plastic bending, bending of axisymmetric cylindrical shells and axisymmetric thick-walled cylinders. A full Table of Contents and the Preface are given below.


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ASYMPTOTIC ELASTIC STRESS FIELDS AT SINGULAR POINTS

Singular elastic stress fields are generally developed at sharp re-entrant corners and at the end of bonded interfaces between dissimilar elastic materials. This behaviour can present difficulties in both analytical and numerical solution of such problems. For example, excessive mesh refinement might be needed in a finite element solution.

Williams (1952) pioneered a method for determining the strength of the dominant singularity by expressing the local field as an asymptotic expansion. The same method has since been used for a variety of situations leading to singular points, including bonded dissimilar wedges and frictionless or frictional contact between bodies with sharp corners.


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Surface Roughness and Electrical Contact Resistance

J.R.Barber The contact of rough surfaces Surfaces are rough on the microscopic scale, so contact is restricted to a few `actual contact areas'. If a current flows between two contacting bodies, it has to pass through these areas, causing an electrical contact resistance. The problem can be seen as analogous to a large number of people trying to get out of a hall through a small number of doors.

Classical treatments of the problem are mostly based on the approximation of the surfaces as a set of `asperities' of idealized shape. The real surfaces are represented as a statistical distribution of such asperities with height above some datum surface. However, modern measurement techniques have shown surfaces have multiscale, quasi-fractal characteristics over a wide range of length scales. This makes it difficult to decide on what scale to define the asperities.


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