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The Linearized Theory of Elasticity (Paperback, Softcover reprint of the original 1st ed. 2002)
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The Linearized Theory of Elasticity (Paperback, Softcover reprint of the original 1st ed. 2002)
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The linearized theory of elasticity has long played an important
role in engineering analysis. From the cast-iron and steel truss
bridges of the eighteenth century to the international Space
station, engineers have used the linearized theory of elasticity to
help guide them in making design decisions effecting the strength,
stiffness, weight, and cost of structures and components. The
Linearized Theory of Elasticity is a modern treatment of the
linearized theory of elasticity, presented as a specialization of
the general theory of continuum mechanics. It includes a
comprehensive introduction to tensor analysis, a rigorous
development of the governing field equations with an emphasis on
recognizing the assumptions and approximations inherent in the
linearized theory, specification of boundary conditions, and a
survey of solution methods for important classes of problems. It
covers two- and three-dimensional problems, torsion of noncircular
cylinders, variational methods, and complex variable methods.The
mathematical framework behind the theory is developed in detail,
with the assumptions behind the eventual linearization made clear,
so that the reader will be adequately prepared for further studies
in continuum mechanics, nonlinear elasticity, inelasticity,
fracture mechanics, and/or finite elements. Prior to linearization,
configurations and general (finite deformation) measures of strain
and stress are discussed. A modern treatment of the theory of
tensors and tensor calculus is used. General curvilinear
coordinates are described in an appendix. An extensive treatment of
important solutions and solution methods, including the use of
potentials, variational methods, and complex variable methods,
follows the development of the linearized theory. Special topics
include antiplane strain, plane strain/stress, torsion of
noncircular cylinders, and energy minimization principles.
Solutions for dislocations, inclusions, and crack-tip stress fields
are discussed. Development of the skills and physical insight
necessary for solving problems is emphasized. In presenting
solutions to problems, attention is focused on the line of
reasoning behind the solution.Topics and Features: * Can be used
without prerequisite course in continuum mechanics * Includes over
one hundred problems * Maintains a clear connection between
linearized elasticity and the general theory of continuum mechanics
* Introduces theory in the broader context of continuum mechanics
prior to linearization, providing a strong foundation for further
studies * Promotes the development of the skills and physical
intuition necessary for deriving analytic solutions * Provides
readers with tools necessary to solve original problems through
extensive coverage of solution methods The book is ideal for a
broad audience including graduate students, professionals, and
researchers in the field of solid mechanics. This new
text/reference is an excellent resource designed to introduce
students in mechanical or civil engineering to the linearized
theory of elasticity.
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