Displacements of a body in Equilibrium

[koolraj09]

Hi everyone.
While analyzing for stresses and strains for a body in equilibrium we consider the displacements u(x,y);v(x,y). Why are these displacements functions of x,y? I've got to understand it physically not mathematically.
Thanks in Advance.

 

[Mapes]

The displacements aren't typically the same at every point, so we have the challenge of how displacement varies as we move about the object. One way to keep everything straight is to map or tabulate the displacement as a function of the location (x,y) of the original point. Thus, u and v are functions of x and y. Does this answer your question?

 

[koolraj09]

Hi Mapes. I wanted to know that why the displacements not the same at every point? I mean why they vary from point to point?

 

[Mapes]

If the displacements were the same at every point, the object would be moving (specifically, translating) and not deforming. Deformation means that some part of the object is changing size and/or shape, and this implies that deformation is different in different locations.

 

[darkside00]

If you bend a straight wire (clothes hanger thick) by pulling one end down with your hands. your deflection is not the same over the full length

 

[boneh3ad]

Another way to look at it, at any point in the material, if you start at whatever point is "fixed" (or some reference), as you get farther away, that point's displacements has all of the displacements of the previous point built into it.

 

[darkside00]

displacement is the amount of movement. Strain is looked at a local spot on the material. The best way to look at it is bending energy is distributed