Elements of Continuum Mechanics

Chapter 1: Introduction

The major objective of our study of mechanics is the formulation and the solution of initial-boundary-value problems that model as realistically as possible a physical phenomenon. There are two equally attractive approaches to mechanics. One is the ad-hoc approach, which takes up specific problems, and devises problem-dependent methods of solution, introducing simplifying assumptions as needed. This approach is used in a sophomore-level course on mechanics of deformable bodies where problems of bending, torsion, and pressure vessel are individually set up under varying assumptions and then solved. The other is the general approach, which explores features of a concept or a theory applicable to a large class of bodies, and considers specific applications at a later stage. By and large, the latter is the quicker way to learn about an entire field, but the former is more concrete and sometimes more easily understood. We will study the general approach in this book.

1.1 What is Mechanics?

Mechanics is the study of the motion, deformation, and temperature changes in a body due to the action of forces. Principles of mechanics have been successfully used to design stents for opening blocked arteries; predict weather patterns; ascertain damage caused to structures by hurricanes; design air bags in cars; predict the flow of fluids around ships, airplanes, bridges, and buildings; manufacture stealth airplanes and satellites; and design smart highways and global positioning systems. Mechanics is based on the concepts of time, space, force, energy, and mass. A knowledge of mechanics is needed for studying physics,...

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