Question

The σx in terms of stress function is given by __________

(a) \(\frac{∂Φ}{∂z}\)

(b) \(\frac{∂^2 Φ}{∂z^2}\)

(c) \(\frac{∂^2 Φ}{∂x2}\)

(d) \(\frac{∂Φ}{∂x}\)

This question was posed to me by my college director while I was bunking the class.

The question is from Elasticity Elements topic in section Elements of Elasticity of Geotechnical Engineering I

Answer 1

The correct option is (b) \(\frac{∂^2 Φ}{∂z^2}\)

To explain I would say: It is convenient to reduce the compatibility and equilibrium equations into a single equation in terms of stress function Φ.

The stress function for stress in the x-direction is given by,

\(\frac{∂^2 Φ}{∂z^2}.\)