If the displacement field is given by Ux = kxy, uy = kxy, uz = 2k(x +y)z where k is a constant small enough to ensure applicability of the small deformation theory, (a) write down the strain matrix %3D (b) what is the strain in the direction nx = ny = nz =1//3 ?

If the displacement field is given by Ux = kxy, uy = kxy, uz = 2k(x +y)z where k is a constant small enough to ensure applicability of the small deformation theory, (a) write down the strain matrix %3D (b) what is the strain in the direction nx = ny = nz =1//3 ?

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.6.13P: A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean...

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Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external force and cross-section of the object. Mathematically, the evaluation of strain can be obtained with the help of elastic constants.

Question

Exercise 3
If the displacement field is given by
Ux = kxy, uy = kxy, uz = 2k(x + y)z
where k is a constant small enough to ensure applicability of the
small deformation theory,
(a) write down the strain matrix
(b) what is the strain in the direction nx = ny = n, =1//3 ?

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