Consider the mapping in 2-D only = X1 +7X2 = X1+ uz *2 = (1+e)X2 = X2+ Uz. (1) 1. In terms of y and a compute F, i.c. the Fij's and then compute the Cy = FF.; recall F = F. Now do the following. 2. Take two fibers, viz. dX = e; and dY = e2, that is two fibers of unit length along the e, and ez axes, respectively in the reference state. Compute the stretch of dX and dY. 3. Compute the small strains from this mapping with u = X2 and uz = eX, from above. What would these small strains suggest for the change in lengths of dX and dY?

Consider the mapping in 2-D only = X1 +7X2 = X1+ uz *2 = (1+e)X2 = X2+ Uz. (1) 1. In terms of y and a compute F, i.c. the Fij's and then compute the Cy = FF.; recall F = F. Now do the following. 2. Take two fibers, viz. dX = e; and dY = e2, that is two fibers of unit length along the e, and ez axes, respectively in the reference state. Compute the stretch of dX and dY. 3. Compute the small strains from this mapping with u = X2 and uz = eX, from above. What would these small strains suggest for the change in lengths of dX and dY?

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter1: Introduction To Statics

Section: Chapter Questions

Problem 1.12P: A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance...

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