Studies in Mechanics of Solids Homework 4

Studies in Mechanics of Solids
Homework 4
1.- Explain the meaning and the differences between the shear strain tensor components and the
engineering shear strains.
2.- Explain why the displacement vector components corresponding to real, unique solutions of
linear elastic problems must be such that the equations of compatibility must always be satisfied.
3.- Consider the problem of simple twist of a long elastic bar of circular cross section of unit
radius. Under these conditions, to a good approximation, the only stress components are the
shear stresses acting on the plane the cross section. Consider a stress function given by the
expression ψ = k (x2 + y2 -1) with k = - G α /2. Here α is the twist angle per unit length.
a) Plot the function for the case G=1e10 Pa and α= 0.01π .
b) Obtain the laplacian of the stress function.
b) Compute and plot the values of the stresses inside the bar.