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Question in deformations, continuum mechanics
Mon, 2013-12-30 22:16 - AP
Hello,
I have a question in intoductory continuum mechanics, in strains and deformations.
Source of image: wikipedia, http://en.wikipedia.org/wiki/Deformation_(mechanics)
In above image, point B in reference configuration becomes b in current configuration. Vertical displacement of b is given by uy + (duy/dx)*dx.
After a lot of thinking and efforts, I am not able to understand why (duy/dx)*dx i.e. uy vertical displacement then why derivative w.r.t. x and why multiplied by x?
Any help much appreciated. Thanks in advance.
Forums:
Question in deformations
Any comments or explanation?
The displacement components
The displacement components (ux and uy) depend on both x and y coordinates.
When you carry out Taylor series expansion of uy(x,y+dy)=uy(x,y)+(duy/dx)dx+(duy/dy)dy to the first order. (duy/dx) is the rate of change in the displacement in y direction with x coordinate.
B