Question

The σz in terms of stress function is given by __________

(a) \(\frac{∂Φ}{∂z}\)

(b) \(\frac{∂^2 Φ}{∂z^2}\)

(c) \(\frac{∂^2 Φ}{∂x^2}\)

(d) \(\frac{∂Φ}{∂x}\)

This question was posed to me at a job interview.

Query is from Elasticity Elements in portion Elements of Elasticity of Geotechnical Engineering I

Answer 1

Right answer is (c) \(\frac{∂^2 Φ}{∂x^2}\)

Explanation: 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 z-direction is given by,

\(σ_z=\frac{∂^2 Φ}{∂x^2}.\)