Page 360 - Introduction to Continuum Mechanics

344 The Elastic Solid

Fig. P5.5

5.68. Consider the stress function

(a) Verify that this stress function is a possible one for plane strain.
(b) Determine the stresses and sketch the boundary tractions on the rectangular boundary
xi = 0, x\ — a , x-i = 0, Jt2 = b.
2
5.69. Consider the stress function <p = a x\ *i
(a) Is this a possible stress function for plane strain?
(b) Determine the stresses.
(c) Determine and sketch the boundary traction on the boundary defined by

5.70. Consider the stress function <p = a x\ + ft X2-
(a) Is this a possible stress function for plane strain?
(b) Determine and sketch the boundary tractions on the rectangular boundary of the previous
problem.
2 -J
5.71. Consider the stress function <p = a xi KI + fixi X2
(a) Is this a possible stress function for plane strain?
(b) Determine the stresses.
(c) Find the condition necessary for the traction on *2 = b to vanish and sketch the stress
traction on the remaining boundaries xi = 0, x\ = 0, x\ —a,
5.72. By integration, obtain Eq. (5.17.13)