Introduction to the Variational Formulation in Mechanics

9Plates and Shells

9.1 Introduction

As highlighted in the introduction to Part III, Roman architects built aqueducts to convey water from remote locations covering large distances over rivers and valleys through arches. This arrangement enabled the loads over the structure to be transferred to the foundations through a fully compressive stress state in the whole structure, which was particularly appropriate for the material available at the time. An example of this structure is the Pont du Gard in the south of France. This structure was built before the Christian age to allow the Nîmes aqueduct (approximately in length) to cross the Gard river. The architects and hydraulic engineers who designed this aqueduct in the ancient Roman empire created an unprecedented piece of technical art.

In contemporaneous civilization (20th and 21st centuries) shells (considering beams and plates as particular cases) are thin (slender) structural components when compared to the gargantuan areas they are capable of covering thanks to their shape (curvature), and can be adapted to the different demands from civil, mechanical, nuclear, naval, and aerospace engineering, among others.

These slender structural components become marvelous artworks combining architectonic needs, light weight, and beauty. Many famous European and Latin American architects made use of these components in the last century ...