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Question in deformations, continuum mechanics
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.
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