Michell Solution - Displacement Components

Displacement Components

Displacements can be obtained from the Michell solution by using the stress-strain and strain-displacement relations. A table of displacement components corresponding the terms in the Airy stress function for the Michell solution is given below. In this table

$\kappa = \begin{cases} 3 - 4~\nu & \rm{for~plane~strain} \\ \cfrac{3 - \nu}{1 + \nu} & \rm{for~plane~stress} \\ \end{cases}$

where is the Poisson's ratio, and is the shear modulus.

Note that you can superpose a rigid body displacement on the Michell solution of the form

$\begin{align} u_r &= A~\cos\theta + B~\sin\theta \\ u_\theta &= -A~\sin\theta + B~\cos\theta + C~r\\ \end{align}$

to obtain an admissible displacement field.

Read more about this topic: Michell Solution

Famous quotes containing the word components:

“Hence, a generative grammar must be a system of rules that can iterate to generate an indefinitely large number of structures. This system of rules can be analyzed into the three major components of a generative grammar: the syntactic, phonological, and semantic components.”
—Noam Chomsky (b. 1928)