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Chapter
One-Dimensional Waves
The one-dimensional wave equation is introduced and its general solution obtained. It is shown that this equation governs one-dimensional motions of a linear elastic material. To aid in visualizing solutions, ...
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Chapter
Transient Waves
Solutions to transient wave problems in elastic materials are obtained by Fourier and Laplace transforms. The discrete Fourier transform is defined and the numerical algorithm called the fast Fourier transform...
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Chapter
Linear Elasticity
The equations governing the motions of linear elastic materials are derived. The deformation of a continuous medium and the internal forces, or stresses, in the material are discussed. An elastic material is d...
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Chapter
Steady-State Waves
Steady-state waves are waves in which the dependent variables are harmonic or oscillatory functions of time. One-dimensional steady-state waves are discussed, then representations of steady-state compressional...
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Chapter
Nonlinear Wave Propagation
Here we summarize the theory of one-dimensional nonlinear elasticity. We first show how the motion and strain of the material are described and then obtain the equations of motion from the postulates for conse...
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Chapter
Mechanics of Systems of Particles
Hamilton’s principle was originally expressed in terms of the classical mechanics of systems of particles. The concepts and the terminology involved in applying Hamilton’s principle to continuum mechanics are ...
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Chapter
Discontinuous Fields
A discussion is given of the application of Hamilton’s principle to a continuous medium containing a surface across which the fields that characterize the medium, or their derivatives, suffer jump discontinuit...
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Chapter
Mechanics of Continuous Media
The application of Hamilton’s principle to a continuous medium is described, beginning with ideal fluids and elastic solids. The general case of a continuum that does not exhibit microstructural effects is pre...
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Chapter
Foundations of Continuum Mechanics
A brief survey of the mathematics and elements of continuum mechanics required in the subsequent chapters is given. The concept of a comparison motion of a continuum is introduced.
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Chapter
Mechanics of Mixtures
As another example of the use of Hamilton’s principle to develop generalized continuum theories, applications to mixtures are described. A mixture of ideal fluids is discussed, using the case of a liquid conta...
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Chapter
Criteria for Failure and Fracture
Structural members may have geometric features (including holes, notches, and corners) that result in localized regions of high stress called stress concentrations. The ratio C of the maximum stress resulting fro...
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Chapter
Introduction
Mechanics of materials is one of the sciences underlying the design of any device that must support loads, from the simplest machines and tools to complex vehicles and structures. Three fundamental questions a...
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Chapter
Axially Loaded Bars
Axially loaded bars are used in many applications, especially as members of truss structures. A prismatic bar is one whose cross section is uniform throughout its length. Suppose that such a bar with cross-sectio...
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Chapter
Internal Forces and Moments in Beams
Consider a straight, horizontal beam with arbitrary supports. Let a cartesian coordinate system be oriented with its origin at the centroid of the beam’s cross section, the x axis extending to the right along the...
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Chapter
States of Stress
The six components σx, σy, σz, τxy, τxz and τyz of the state of stress at a point in terms of a given cartesian coordinate system were defined in Chap. 2. In a state of plane stress, the only nonzero components a...
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Chapter
Deflections of Beams
Let v be the deflection of a prismatic beam’s neutral axis (the line through the centroid of the cross section) relative to the x axis, and let θ be the angle between the neutral axis and the x axis. The objectiv...
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Chapter
Energy Methods
When an archer draws a bow and shoots an arrow, it demonstrates that energy can be stored in an object when work is done to deform it relative to a reference state. Many advanced techniques used in mechanics of m...
