Modelling of Mechanical Systems: Structural Elements

Francois Axisa, Philippe Trompette

• Publisher: Butterworth-Heinemann
• Year: 2005
• Print ISBN: 9780750668460
• eBook ISBN: 9780080461366
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

The modelling of mechanical systems provides engineers and students with the methods to model and understand mechanical systems by using both mathematical and computer-based tools. Written by an eminent authority in the field, this is the second of four volumes which provide engineers with a comprehensive resource on this cornerstone mechanical engineering subject. Dealing with continuous systems, this book covers solid mechanics, beams, plates and shells. In a clear style and with a practical rather than theoretical approach, it shows how to model continuous systems in order to study vibration modes, motion and forces. Appendices give useful primers on aspects of the mathematics introduced in the book. Other volumes in the series cover discrete systems, fluid-structure interaction and flow-induced vibration.*Axisa is a world authority in the modelling of systems*Comprehensive coverage of mathematical techniques used to perform computer-based analytical studies and numerical simulations*A key reference for mechanical engineers, researchers and graduate students in this cornerstone subject

Chapter 1

Solid mechanics

François Axisa; Philippe Trompette

Abstract

Real mechanical systems generally comprise an assembly of deformable solids which must be modelled within the framework of the theory of continuum mechanics. Accordingly material is assumed to be distributed continuously in a 3D domain. However in most instances the engineer deals with structural elements endowed with geometrical particularities which allow for further simplification in modelling based on the concept of 2D or even 1D equivalent continuous media. Before embarking on the presentation of such models which is the central object of this book it is appropriate to review first a few fundamental concepts definitions laws of continuum mechanics. This vast subject is restricted here to a few important aspects of linear elasticity elastodynamics of solids.

1.1 Introduction

The mechanics of solid bodies is concerned with the motion of deformable media, in which solid matter is continuously distributed over a domain of the three-dimensional Euclidean space, bounded in every direction. Accordingly, it extends the mechanics of discrete particles, dealing with the new following aspects:

1. To describe the motion, use is made of an infinite, and even more significant, an uncountable set of degrees of freedom (D...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright page
• Preface
• Introduction
• Chapter 1: Solid mechanics
• Chapter 2: Straight beam models: Newtonian approach
• Chapter 3: Straight beam models: Hamilton’s principle
• Chapter 4: Vibration modes of straight beams and modal analysis methods
• Chapter 5: Plates: in-plane motion
• Chapter 6: Plates: out-of-plane motion
• Chapter 7: Arches and shells: string and membrane forces
• Chapter 8: Bent and twisted arches and shells
• Appendices
• References
• Index
• Color plate