Consider another 2D displace- ment field measured on the surface of a material using digital image correlation and given by u = [k(2x + y²), k(x² - 3y²), 0]T (T stands for transpose, so that we can think of u as a column vector, as it was introduced in class), where k 10-4. The original configuration of an infinitesimal element in the body is shown in Fig. 1 and has side lengths dx and dy. = (a) Show the distorted configuration and determine the new lengths, da' and dy', angle between each side deformed side using linearized metrics. (b) Find the new location of the point (2,1,0) after displacement. (c) Find the strain tensor at the point (2,1,0) and the rotation of the point (2,1,0) about the axis (0,0,1) after displacement.

Consider another 2D displace- ment field measured on the surface of a material using digital image correlation and given by u = [k(2x + y²), k(x² - 3y²), 0]T (T stands for transpose, so that we can think of u as a column vector, as it was introduced in class), where k 10-4. The original configuration of an infinitesimal element in the body is shown in Fig. 1 and has side lengths dx and dy. = (a) Show the distorted configuration and determine the new lengths, da' and dy', angle between each side deformed side using linearized metrics. (b) Find the new location of the point (2,1,0) after displacement. (c) Find the strain tensor at the point (2,1,0) and the rotation of the point (2,1,0) about the axis (0,0,1) after displacement.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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