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:

Thus far we have discussed mechanical loading and the stresses and strains caused by that We noted, however, that the environment can have an effect on the behavior of materials and structures. Let's first consider:

Summarizing what we've looked at in elasticity, we have: 15 equations in 15 unknowns 3 equilibrium -6 strains -6 strain-displacement -3 displacements

There are many structural configurations where we do not have to deal with the full 3-D case. First let's consider the models Let's then see under what conditions we can apply them A. Plane Stress

As we've previously noted, we may often want to describe a structure in various axis systems. This involves... Transformations (Axis, Deflection, Stress, Strain, Elasticity Tensors) e.g., loading axes material principal axis Figure 7.1 Unidirectional Composite with Fibers at an Angle

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)

Sources of Stresses and Strains Depends on type of structure Aircraft

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)

Recall the definition of stress: o stress =\intensity of internal force at a point\ Figure 3.1 Representation of cross-section of a general body

Sampling Given a continuous time waveform, can we represent it using discrete samples? How often should we sample? Can we reproduce the original waveform?