Materials and Structures under Shock and Impact E-Book

Patrice Bailly

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 275

Veröffentlichungsjahr: 2013

Beschreibung

Materials and Structures under Shock and Impact In risk studies, engineers often have to consider the consequences of an accident leading to a shock on a construction. This can concern the impact of a ground vehicle or aircraft, or the effects of an explosion on an industrial site. This book presents a didactic approach starting with the theoretical elements of the mechanics of materials and structures, in order to develop their applications in the cases of shocks and impacts. The latter are studied on a local scale at first. They lead to stresses and strains in the form of waves propagating through the material, this movement then extending to the whole of the structure. The first part of the book is devoted to the study of solid dynamics where nonlinear behaviors come into play. The second part covers structural dynamics and the evaluation of the transient response introduced at the global scale of a construction. Practical methods, simplified methods and methods that are in current use by engineers are also proposed throughout the book.

Leseprobe

Table of Contents

Introduction

PART 1: Dynamics of Solids

Chapter 1: Motion within Solids

1.1. Representation of the medium

1.2. Elastodynamic equations

1.3. One-dimensional waves

1.4. Harmonic waves

1.5. Viscoelasticity

Chapter 2: Shocks in Solids

2.1. Discontinuity of stress and velocity

2.2. Wave course

2.3. Shocks of solids

2.4. Shocks on viscoelastic solids

Chapter 3: Waves and Shocks in a Nonlinear Medium

3.1. Irreversible phenomena

3.2. Adiabatic shear

3.3. Propagation in uniaxial stress state

3.4. Uniaxial strain state

3.5. Shock waves

Chapter 4: Dynamic Materials Testing

4.1. Dynamic testing

4.2. Hopkinson pressure bars

4.3. Testing by direct impact

4.4. Taylor impact test

4.5. Plate impact

PART 2: Dynamic of Structures

Chapter 5: Impact on a Simple Structure

5.1. Basic structure

5.2. Shock response spectrum

5.3. Iso-damage curves

5.4. Modeling a real structure

Chapter 6: Collisions of Structures

6.1. Shocks on elastic structures

6.2. Shock with crushing

6.3. Classification of shocks

Chapter 7: Explosions and Blasts

7.1. Accidental explosions

7.2. Pressure waves

7.3. Action of an explosion on a structure

7.4. Blast-structure coupling

Chapter 8: Mechanical Response of Beams

8.1. Dynamic beam models

8.2. Impacts on beams

8.3. Calculation by modal superposition

8.4. Dynamic buckling

Chapter 9: Responses of Multiple Degree of Freedom Structures

9.1. Modeling through a discrete system

9.2. Resolution by modal superposition

9.3. Fluid–structure coupling

Chapter 10: Response of a Nonlinear Structure

10.1. Nonlinear behavior of structures

10.2. Nonlinear system with one degree of freedom

10.3. The case of elastoplastic behavior

10.4. Approach of response to a violent impact

Bibliography

Index

First published 2014 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUK

www.iste.co.uk

John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA

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© ISTE Ltd 2014The rights of Patrice Bailly to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2013951423

British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN: 978-1-84821-651-8

Introduction

In risk studies, engineers may be required to consider the consequences of an accident resulting in a shock on a building. This may be, for example, the impact of a vehicle or aircraft, or the effects of an explosion on an industrial site.

This book combines elements of applied mechanics from which practical and sometimes simplified methods used in such studies arise. It is aimed at Master’s students or students of engineering schools with a fairly general mechanical training. It can also be used by practicing engineers who wish to enter the field of structural resistance to accidental mechanical actions. This book is an intermediary between two types of scientific literature: on the one hand, bibliographic resources on the areas of mechanics involved in studies of shocks on structures, i.e. the waves in continuous systems, behavior of materials, resistance calculations of structures, vibrations, structural dynamics, etc., and on the other hand, technical manuals devoted to practical calculation methods and design of structures to withstand shocks or explosions. These manuals may be technically very accurate, especially regarding the constructive arrangements. Just like regulations related to the calculation of reinforced concrete or metal structures, their effective use requires knowledge of the theoretical mechanical elements that led to the methods they advocate. It is also important to have a basic understanding of the physical phenomena involved in the predicted accidental events. For example, concerning the effects of explosions on a building, the engineer responsible for the structural design must understand the physical parameters involved in the explosion process, their relationship with the extreme effect of the explosion, that is the blast wave, and the manner in which the interaction with a building leads to a dynamic load on the latter. In this book, the proposed approach is to provide the elements of fairly general and theoretical mechanics in order to develop their applications to cases of shocks and impacts. Throughout the developments, hypotheses and limitations of the models used will appear. The engineering methods discussed in this book are not based on the use of important digital codes for structure calculations.

Impact on a building is primarily a local phenomenon that causes stress and strain in the form of propagating waves in the material. The movement then extends to the entire structure. Both local and global phases of the mechanical response have different time characteristics. This book follows this chronology: Part 1 is devoted to the study of the dynamics of solids that come into play during the local phenomena. Part 2 deals with the dynamics of structures in response to a global impact on a building.

In Part 1, the propagation of movements in a continuous system is first presented in the context of linear behavior such as elasticity and viscoelasticity. Shocks on solids induce stress waves, the amplitude of which is related to impact velocity. These waves propagate and diffract and are reflected within the solids. The impact velocities during accidental events are sufficient for the level of stress to exceed the yield strength of the construction materials. It is then necessary to understand how the nonlinear aspects of behavior influence the propagation of stress and strain. A feature of shocks is to provoke pressure levels much higher than those commonly found in materials under static loads. The study of behavior, in this case, is quite specific to the field of shock.

In Part 2, the case of a simple structure (modeled by a mechanical system with one degree of freedom) is used to introduce the engineering tools of the shock response spectrum and iso-damage curves. Two types of short-term dynamic loading are then introduced: collisions and explosions. Collisions of structures, or crashes, are discussed with the aim of clarifying the load imposed on the structure that is affected. The case of explosions is approached by defining some basic knowledge of dynamics, which is necessary to understand the phenomenon. The goal is to achieve the characteristic elements of dynamic loading that can be imposed on a structure. The basic construction element is usually a beam. A study on the evolution of stress and movements in beams during impacts is considered in order to identify the various possible levels of modeling and their areas of relevance. To study the overall response, structures of buildings or industrial buildings can be modeled by mechanical systems with several degrees of freedom, as it is customary to do in earthquake studies. The nonlinear behavior phase of structures can be achieved. In metal or reinforced concrete structures, it is most often through the formation of plastic hinges that these nonlinearities occur. The response to the shock of a structure with plastic hinges is considered.

Despite its compact size, this book covers various significant and representative aspects of problems related to studies on shocks on buildings. Not all types of materials and structures are covered in this book, for example composite materials, plates and shells are not included. Finally, it should be noted that an educational approach guided the organization of this book.

PART 1

Dynamics of Solids

Chapter 1

Motion within Solids

The concept of stress and strain waves emerges from the equations of motion in elastic continuum. Uniaxial propagation is particularly well-studied because of its practical importance. The waves can be altered within their propagation by dispersion and dissipation. For viscoelastic solids, we can address the effects of behavior sensitive to strain in a linear framework.

1.1. Representation of the medium

1.1.1. Framework of continuum mechanics

The problem for the engineer is to describe the position (or displacement) of solids and fluids. This mechanism is of a macroscopic scale. On this macroscopic scale, solid or fluid matter can be seen as continuous, which is not the case at the microscopic level of particles, molecules and atoms. The macroscopic scale is not the same for all materials: a fraction of a millimeter for a metal, a few inches for geomaterials such as rock or concrete.

In this book, we only refer to classical mechanical engineering knowledge of continuum mechanics and structural strength. This chapter intends to recall the basics of continuum motion when these can be described by linear equations, such as in the context of small strains and elastic or viscoelastic material behavior.

1.1.2. Representation of motion

The motions in matter are identified in an affine Euclidean space. A point in matter which occupies position M0 at time 0, defined by the vector is in position Mt at time t, defined by the vector . A certain amount of matter that occupies the simply connected domain Ω0 at time 0, also occupies the simply connected domain Ωt at time t (Figure 1.1).

[1.1]

Figure 1.1.Material field in its initial position and after transformation

The description of these movements can be given from two points of view: one is called “Lagrangian” and the other is called “Eulerian”. The Lagrangian description involves following the matter points in their motion. The current position, or displacement, is expressed depending on the initial position and t, using a continuous vector function [1.2] that defines the trajectories (this is a bijection of Ω to Ω, due to the continuity of displacement of the system):