Linearized Elasticity

Abstract

Rather special, but anyhow frequently occurred situations in many engineering applications exhibit deformations whose gradient is relatively very close to identity. In other words, displacement gradient is very small and often even the displacement itself is relatively small. It allows us with a reasonable accuracy to neglect higher order terms and simplified a lot of aspects related to geometrical nonlinearities very substantially. It also facilitates computational algorithms substantially, and there is no wonder that most engineering computations in solid mechanics are just based on such hypotheses. As we will see, linearized elasticity provides us with unique solutions and strongly relies on convexity assumptions.

The first mathematician to consider the nature of resistance of solids to rupture was Galileo ... Undoubtedly, the two great landmarks are the discovery of Hook’s law in 1660 and the formulation of the general equations by Navier (1821).

Augustus Edward Hough Love (1863–1940)