Michell Solution

Michell Solution

The Michell solution is a general solution to the elasticity equations in polar coordinates . The solution is such that the stress components are in the form of a Fourier series in .

Michell showed that the general solution can be expressed in terms of an Airy stress function of the form

 \begin{align} \varphi &= A_0~r^2 + B_0~r^2~\ln(r) + C_0~\ln(r) + D_0~\theta \\ & + \left(A_1~r + B_1~r^{-1} + B_1^{'}~r~\theta + C_1~r^3 + D_1~r~\ln(r)\right) \cos\theta \\ & + \left(E_1~r + F_1~r^{-1} + F_1^{'}~r~\theta + G_1~r^3 + H_1~r~\ln(r)\right) \sin\theta \\ & + \sum_{n=2}^{\infty} \left(A_n~r^n + B_n~r^{-n} + C_n~r^{n+2} + D_n~r^{-n+2}\right)\cos(n\theta) \\ & + \sum_{n=2}^{\infty} \left(E_n~r^n + F_n~r^{-n} + G_n~r^{n+2} + H_n~r^{-n+2}\right)\sin(n\theta) \end{align}

The terms and define a trivial null state of stress and are ignored.

Read more about Michell Solution:  Stress Components, Displacement Components

Famous quotes containing the word solution:

    Coming out, all the way out, is offered more and more as the political solution to our oppression. The argument goes that, if people could see just how many of us there are, some in very important places, the negative stereotype would vanish overnight. ...It is far more realistic to suppose that, if the tenth of the population that is gay became visible tomorrow, the panic of the majority of people would inspire repressive legislation of a sort that would shock even the pessimists among us.
    Jane Rule (b. 1931)