At the turn of the century, although few realized it, the ingredients were in place for a flowering of the natural sciences with the development of field theory.

**Field Theory **

At the turn of the
century, although few realized it, the ingredients were in place for a
flowering of the natural sciences with the development of field theory. This
was certainly the case in the study of the mechanics of fluids and solids,
which led the way for the new physics of electricity, magnetism, and the
propagation of light.

An uncharitable
observer of the solid-mechanics scene in 1800 might, with the benefit of
hindsight, characterize the state of knowledge then as a jumble of incorrect
solutions for collapse loads, an incomplete theory of bending, an unclear
definition for Young's modulus, a strange discussion of the frictional strength
of brittle materials, a semigraphical solution for arches, a theory for the
longitudinal vibration of bars that was erroneous when extended to plates or
shells, and the wrong equation for torsion. However, this assess-ment would be
wrong. While no general theory was developed, 120 years of research from
Galileo to Coulomb had developed the basic mental tools of the scientific method
(hypothesis, deduction, and verification) and compiled the necessary
ingredients to formulate the modern field theories for strain, stress, and
displacement.

The differentiation
between shear and normal displacement and the gener-alization of equilibrium at
a point to the cross-section of a beam were both major steps in the logic of
solid mechanics as, of course, was Young's insight in relating strain and
stress linearly in tension or compression. Newton first proposed bodies made up
of small points or 'molecules' held together by self-equilibriating forces and
the generalization of calculus to two and three dimensions allowed the
mathematics of finite linear transformation to be reduced to an arbitrarily
small size to describe deformation at a differential scale. Thus the stage was
set. The physical concepts and the mathematical tools were available to produce
a general field theory of elasticity. Historical events conspired to produce it
in France.

The French Revolution
destroyed the old order and replaced it with republican chaos. The great number
of persons separated at the neck by Dr. Guillotine's invention is symbolic of
the beheading of the Royal Society as the leader of an elite class of
intellectuals supported by the King's treasury and beholden to imperial
dictate.

The new school, L'Ecole
Polytechnique founded in 1794, was unlike any seen before. Based on
equilitarian principles, entrance was by competitive examination so that boys
without privileged birth could be admitted. More-over, the curriculum was
entirely different. Perhaps because there were so may unemployed scientists and
mathematicians available, Gospareed Monge (1746-1818), who organized the new
school, was able to select a truly remarkable faculty including among others,
Lagrange, Fourier, and Poisson. Together they agreed on a new concept of
engineering education.They would, for the first two years, concentrate on
instruction in the basic sciences of mechanics, physics, and chemistry, all
presented with the fundamental language of mathematics as the unifying theme.
Only in the third year, once the fundamentals that apply to all branches of
engineering were mastered, would the specific training in applications be
covered.*

Thus the modern
'institute of technology' was born and the consequences were immediate and
profound. The basic field theory of mathematical elas-ticity would appear
within 25 years, developed by Navier and Cauchy not only as an intellectual
construction but for application to the fundamental problems left by their predecessors.*
The first generation of graduates of the Ecole Polytechique such as Navier and
Cauchy, became professors and edu-cated many great engineers who would come to
dominate structural design in the later half of the 19th century.**

The French idea of amalgamating the
fundamental concepts of mathe-matics and mechanics as expressed by field theory
for engineering applica-tions, is the theme of this text. Today, two centuries
of history have proven this concept not only as an educational approach, but as
a unifying princi-ple in thinking about solid mechanics.*** In bygone days, the
term 'Ratio-nal Mechanics' was popular to differentiate this perspective of
visualizing fields graphically with mathematics and experiments so as to
understand how structures work rather than just solving specific boundary value
prob-lems. The phrase 'Rational Mechanics' is now old-fashioned, but
historically correct for the attitude adopted in succeeding chapters of
combining elastic and plastic behavior as a continuous visual progression to
yield and then collapse.

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Civil : Principles of Solid Mechanics : Introduction : Field Theory |

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