The two- and three-dimensional truss examples presented in this chapter demonstrate the complex and often unexpected load deflection behavior exhibited when, in particular, geometrical nonlinearity is included in structural analysis. Each point on the various graphs shown below represents an equilibrium configuration; however, these configurations may be structurally stable or unstable. For a chosen load it can be observed that the structure can be in a variety of equilibrium configurations. For most structures subjected to “in service” loadings, this is clearly unacceptable (not to say alarming), nevertheless such analysis can indicate possible collapse scenarios. While the points on a load deflection graph refer to equilibrium configurations, it must not be assumed that connecting adjacent points necessarily represents smooth continuity of the motion of the structure as the loading changes. However, such smooth motion is likely to be the case if a large number of load increments are employed in the solution, but it cannot be guaranteed.

A situation where a small change in load leads to a dramatic change in configuration is known as “snap-through” behavior. There are “structures” that rely on snap-through behavior to fulfill a useful function. Indeed such structures are vastly more numerous than everyday structures; for example, a shampoo container cap when opened carefully will suddenly “flick” into a fully opened position. A child's hair clip often employs snap-through behavior to lock into position, while perhaps the most common item is the simple light switch.

This worked examples text is intended primarily as a companion to the second edition of the textbook Nonlinear Continuum Mechanics for Finite Element Analysis by Javier Bonet and Richard D. Wood. However, to be reasonably self-contained, where necessary key equations from the textbook are replicated in each chapter.

Textbook equation numbers given at the beginning of each chapter are indicated in square brackets.

Exercises are presented in a mix of direct (tensor), matrix, or indicial notation, whichever provides the greater clarity. Indicial notation is used only when strictly necessary and with summations clearly indicated.

The textbook is augmented by a website, www.flagshyp.com, which contains corrections, software, and sample input data. Updates to this worked examples text will also be included on the website as necessary.

This book clearly exhibits some remarkable and unusual features. The central theme addresses one of the primary research challenges at present in solid and structural mechanics. In fact, research on nonlinearities owing to large deformations and inelastic behaviours of materials now has to be tackled for many systematic applications in mechanical and civil engineering because the evaluation of safety margins has become computationally possible, with obvious advantages when compared with “admissible stress” criteria, popular in past structural engineering practice.

The content of this book reflects the intensive and successful research work carried out by the author and his co-workers both at the University of Trento and at other institutions. The detailed introduction includes several clear illustrative descriptions of experiments and, hence, solid links with practical motivation and application for the book's content. It seems that in his writing, Davide Bigoni has been mindful of Cicero's admonition not always implemented in books on mechanics: ‘Non enim paranda nobis solum, sed fruenda sapientia est’ (‘The knowledge should not only be acquired; it should be utilized as well’). Isaac Newton expanded on Cicero's advice when he wrote, ‘Exempla docent non minus quam praecepta’ (‘Examples are not less instructive than theories’). In fact, the subsequent chapters include many examples to clarify notions of applied mathematics and theoretical continuum mechanics.

The mathematics and physics covered in this volume are not easily found in the existing engineering-oriented literature in the consistent manner presented herein.