Page 231 - Introduction to Continuum Mechanics

216 Problems

4.37. For the stress field given in Example 4.9.1, determine the constants A and B if the inner
cylindrical wall is subjected to a uniform pressurep 0 and the outer cylindrical wall is subjected
to a uniform pressure p 0.
438. Verify that Eq. (4.8.2b) and (4.8.2c) are satisfied by the stress field given in Example 4.9.2.
439. In Example 4.9.2, if the spherical shell is subjected to an inner pressure of p/ and an
outer pressure of/? 0, determine the constant^ and B
4.40. Prove that for any tensor A^, ^ 2, ^3)

4.41. The equilibrium configuration of a body is described by

If the Cauchy stress tensor is given by TU = 1000 MPa., all other T^ = 0.

(a) Calculate the first Piola-Kirchoff stress tensor.
(b) Calculate the second Piola-Kirchoff stress tensor.
4.42. The equilibrium configuration of a body is described by

If the Cauchy stress tensor for this body is

(a) What is the corresponding first Piola-Kirchhoff stress tensor?
(b) What is the corresponding second Piola-Kirchhoff stress tensor?
(c) Calculate the pseudo stress vector associated with the first Piola-Kirchhoff stress tensor on
the 63 - plane in the deformed state.
(d) Calculate the pseudo stress vector associated with the second Piola-Kirchhoff stress tensor
on the 63 - plane in the deformed state.