Design and analysis are intertwined concepts for the engineer. The Theory of Elasticity is now complete with 15 equations and 15 unknowns and a pure mathematician, after some discussion of uniqueness and existence, would at this point go on to other things.

**Strategies for Elastic Analysis and Design**

**Rational
Mechanics **

Design and analysis are
intertwined concepts for the engineer. The Theory of Elasticity is now complete
with 15 equations and 15 unknowns and a pure mathematician, after some discussion
of uniqueness and existence, would at this point go on to other things. To the
engineer, the fun has just begun.

How can we solve these
equations for specific structures-the classic 'boundary-value problem'? Better
yet, can we control the internal stresses flowing through a structure and its
displacements by adjusting its shape or composition or support conditions? This
is the 'inverse problem' or 'design problem' and is fundamentally much more
obscure, difficult, and rewarding.

For all intents and
purposes, textbooks and the literature today deal with the first
question-finding solutions to the boundary value problem.* It is more
man-ageable, particularly with the increasing power of the computer with
refined numerical models. Compared to 'the design problem' it may not be as
much fun, but it is easy to do and easy to teach. Moreover, for most engineers,
design is thought of exclusively as a process of trial and error using
successive boundary-value solutions for different shapes, materials, or support
conditions.

To imaginative
engineers, the great designers, solving boundary value problems is a prelude
necessary but not sufficient for creating new and better structures. For them
the object is to understand solid mechanics at the more profound level of
discovering 'how structures work.' Solving boundary-value problems can produce
this fundamental understanding from which creativity springs but only if the
mathematics is thought of as a means to explore the phys-ical truths hidden in
the equations and only if the results are completed through plots of the most
revealing field variables with sensitivity studies of the material properties
and boundary parameters. All this is then coupled with comparison to simple
cases, approximate solutions from strength of materials, and evidence from
structural models tested in the laboratory or at full scale in the field.

This sort of visual
approach is sometimes called 'Rational Mechanics.' In this and succeeding
chapters, the approach of rational mechanics* will be empha-sized. This theme
differentiates this text from others that cover the same material. We will not
present an in-depth development of all the closed-form solution techniques for
the field equations or a compilation of known results. There are many wonderful
books on elasticity with hundreds of solutions and references to hundreds
more.** The field of plasticity and limit analysis is nearly as rich. Nor will
we do more than comment on the various numerical methods such as Finite
Difference solutions for differential equations or finite modeling techniques
such as the Boundary Element and Finite Element methods, which dominate the
liter-ature today. These are already extremely powerful tools for analysis and
becom-ing more so, but they require a clear understanding of the fundamentals
of elasticity and plasticity to be appreciated and applied properly.

Similarly the entire
subject of experimental analysis must be omitted even though observation of
real behavior is of paramount importance in developing a physical feel for the
flow of stress and strain through structures. Photographic results from models
using such experimental methods as Moire, holographic interferometry, and
photoelasticity will, on occasion, be given for comparison to analytic solutions.
All these techniques produce optical, full-field interference patterns, which
are actually contour maps of the various displacement or stress components
(more precisely, strain components). Unfortunately, however, no real
explanation of these wonderful methods is possible.***

Instead we will concentrate on a few
classical structures such as beams, rings, and wedges primarily in their
two-dimensional idealizations. We will explore their behavior in both the
elastic and plastic range from both an anal-ysis and a design perspective.
Because the regular geometry of such struc-tures can be described by simple
coordinate systems, closed-form solutions can often be found that best
illustrate strategies at a level where the student can appreciate the intricacy
of the concepts involved and their interrelation-ships. Subsequent courses on
numerical or physical modeling to consider structures with irregular geometry,
time-dependent boundary or thermal loading, built perhaps of anisotropic,
inhomogeneous, or nonlinear materials will then be based on a firm foundation.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

Civil : Principles of Solid Mechanics : Strategies for Elastic Analysis and Design : Rational Mechanics |

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