Introduction to Elasticity/Rotating rectangular beam

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Example : Rotating Rectangular Beam[edit | edit source]

A rotating rectangular beam

The body force potential is given by

Hence,

or,

The compatibility condition (in terms of stress) is

Plug in to get

Since is even in and and BCs are homogeneous, assume

Hence,

The traction BCs are

Apply BCs at .

Therefore,

We then have,

Plug into compatibility equation

to get

or,

Apply BCs at .

Strong BCs imply that

which cannot be true. So weak BCs on need to be applied at .

Hence,

or,

Hence,

The stress field is, therefore,

or,

The displacements can be found in the standard manner.

Stresses () in a rotating rectangular beam
Stresses () in a rotating rectangular beam