# Homework_4 - AE 321 Homework 4 Due in class on September 27...

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AE 321 Homework 4 Due in class on September 27 1. Assume that the stress state everywhere in the interior of a body is given in Cartesian coordinates by: σ ij [] = P 00 0 P 0 P KPa Note: This stress state is called isotropic or hydrostatic. (a) Does this stress state satisfy equilibrium? (b) Show that the normal stresses are – P and the shear stresses vanish for any other Cartesian coordinate system. (c) What are the principal stresses for this stress state (everywhere in the body)? (d) Consider a cube of a material subjected to a uniform external pressure P on all sides as shown below (e.g. by submerging the cube in water). Does the above stress state satisfy the boundary conditions (i.e. Cauchy’s equation) on all external surfaces of the cube? 1

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2. The stress tensor at a point P in a material is given by: σ ij [] = 311 102 120
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Homework_4 - AE 321 Homework 4 Due in class on September 27...

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