We do not characterize materials by their E mnpq The Emnpa are useful in doing transformations, manipulations, etc. We characterize materials by their \ENGINEERING CONSTANTS\ (or, Elastic Constants)
Let's first review a bit... from Unified, saw that there are basic considerations in elasticity: 1. Equilibrium 2. Strain-Displacement 3. Stress- Strain Relations (Constitutive Relations)
The logical extension of discrete mass systems is one of an infinite number of masses. In the limit, this is a continuous system. Take the generalized beam-column as a generic representation:
Previously saw (in Unit 19)that a multi degree-of-freedom system has the same basic form of the governing equation as a single degree-of-freedom system The difference is that it is a matrix equation
For a number of cross-sections we cannot find stress functions. However, we can resort to an analogy introduced by Prandtl(1903) Consider a membrane under pressure p, Membrane\. structure whose thickness is small compared to surface