Page 361 - Introduction to Continuum Mechanics

Problems 345

5,73. From Eqs, (5.19.2), show that Eq. (5.19.4) can also be written as:

5.74, Obtain the general solution of Eq. (5.20.6) as

5.75. A hollow sphere is subjected to an internal pressure/?/ only.

(a)Show that T^ is always negative (i.e., compressive) and TQQ is always positive (tensile).
(b) Find the maximum TQQ.

(c) If the thickness t = a 0 -a/ is small, show that the equation obtained in (b) reduces to
Pj^L
2t
5.76. Using Eq. (5.16.6) in Eq. (5.16.7) to obtain Eq. (5.16.8).
5.77. Derive Eq. (5.16.9).

5.78. Obtain the solution for the differential equation, Eq. (5.17.8).
5.79. Obtain^ and U G from Eqs. (5.17.11) and (5.17.12).
5.80. Verify Eq. (5.19.4)
5.81. Find the general solution for Eq. (5.20.6)
5.82. Write stress strain laws for a monoclinic elastic solid whose plane of symmetry is the
xi X2 plane in contracted notation.
5.83. Write stress strain laws for a monoclinic elastic solid whose plane of symmetry is the
x$xi plane in contracted notation.
5.84. Verify any one of the equations in Eqs(iv) of Section 5.26 on transversely isotropic elastic
solid.
r a
5.85. Show from the equation €1233 = 0 that Cu^ = €2233 f° transversely isotropic
material [See Section 5.26]

5.86. Referring to Section 5.26, for a transversely isotropic elastic solid, obtain Eq. (k)
5.87. In Section 5.26 we obtained the reduction in the elastic coefficients for a transversely
isotropic elastic solid by demanding that each Sp plane is a plane of material symmetry. We
can also obtain the same reduction by demanding that C^ be the same for all ft. Verify that
the two procedures lead to the same elastic coefficients.