Introduction to the Variational Formulation in Mechanics

Part IIIModeling of Structural Components

Throughout the development of humanity, and each time compelled by the need for the design and construction of increasingly intricate structural elements inherent to this development, engineers, architects, physicists, and mathematicians have realized the necessity for the idealization of accurate mechanical models capable of adequately representing the functional response of such components, while maintaining a level of simplicity such that the calculation of analytical solutions is feasible. In increasing degree of complexity we cite archs, vaults, beams, plates, and shells. The facilities provided by such simplified models, together with the capacity of these components to provide proper support when subjected to diverse loading conditions, have been fundamental pillars for such applications to spread to diverse and different areas of the engineering domain.

Unfortunately, it is rather common to find, in the specialized scientific literature, the presentation of such mechanical models within a theoretical framework commingling the foundational mechanical aspects of the model with the complexity of the material behavior. By employing such an approach, the reader can easily get confounded in separating basic concepts/principles, which are valid for any kind of material, and the aspects underlying the description of the material response. Usually, the former go unnoticed given the intricacy posited by the mathematical representation ...