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.