There is no area of applied science more diverse and powerful than the mechanics of deformable solids nor one with a broader and richer history. From Galileo and Hooke through Coulomb, Maxwell, and Kelvin to von Neuman and Einstein, the question of how solids behave for structural applications has been a basic theme for physical research exciting the best minds for over 400 years.
From fundamental questions of solid-state physics and material science to the mathematical modeling of instabilities and fracture, the mechanics of solids remains at the forefront of today’s research.
At the same time, new innovative applications such as composites, prestressing, silicone chips, and materials with memory appear everywhere around us.
To present to a student such a wonderful, multifaceted, mental jewel in a way that maintains the excitement while not compromising elegance and rigor, is a challenge no teacher can resist.
It is not too difficult at the undergraduate level where, in a series of courses, the student sees that the simple solutions for bending, torsion, and axial load lead directly to analysis and design of all sorts of aircraft structures, machine parts, buildings, dams, and bridges.
However, it is much more difficult to maintain this enthusiasm when, at the graduate level, the next layer of sophistication is necessary to handle all those situations, heretofore glassed over and postponed, where the strength-ofmaterials approach may be inaccurate or where a true field theory is required immediately.
This book has evolved from over 30 years of teaching advanced seniors and first-term graduate students a core course on the application of the full-range field theory of deformable solids for analysis and design.
It is presented to help teachers meet the challenges of leading students in their exciting discovery of the unifying field theories of elasticity and plasticity in a new era of powerful machine computation for students with little experimental experience and no exposure to drawing and graphic analysis.
The intention is to concentrate on fundamental concepts, basic applications, simple problems yet unsolved, inverse strategies for optimum design, unanswered questions, and unresolved paradoxes in the hope that the enthusiasm of the past can be recaptured and that our continued fascination with the subject is made contagious.
In its evolution this book has, therefore, become quite different from other texts covering essentially the same subject matter at this level.2 First, by including plastic as well as elastic behavior in terms of a unified theory, this text is wider in scope and more diverse in concepts.
I have found that students like to see the full range, nonlinear response of structures and more fully appreciate the importance of their work when they realize that incompetence can lead to sudden death.
Moreover, limit analysis by Galileo and Coulomb historically predates elastic solutions and is also becoming the preferred method of analysis for design not only in soil mechanics, where it has always dominated, but now in most codes for concrete and steel structures.
Thus in the final chapters, the hyperbolic field equations of plasticity for a general Mohr-Coulomb material and their solution in closed form for special cases is first presented.
The more general case requiring slip-line theory for a formal plasticity solution is then developed and applied to the punch problem and others for comparison with approximate upper-bound solutions.
Secondly, while the theory presented in the first three chapters covers familiar ground, the emphasis in its development is more on visualization of the tensor invariants as independent of coordinates and uncoupled in the stress–strain relations.
The elastic rotations are included in anticipation of Chapter 4 where they are shown to be the harmonic conjugate function to the first invariant leading to flow nets to describe the isotropic field and closed-form integration of the relative deformation tensor to determine the vector field of displacements.