I recommend to use our stochastic package SARA (with ATENA Engineering, limited to randomizing material parameters and some geometry) or RLACS (with ATENA Science, not yet the final release version).
To change the coordinates of volume elements (in 3D, surface elems. in 2D), a user in Portugal has done this by preparing a special .inp file manually. The problem is that in normal .inp or .ixt files, there are already mesh nodes, but you have to modify the geometry coordinates before meshing (otherwise, some elements will have bad shapes or will be turned "inside-out" unless the coordinate shifts are kept very small). The solution is to prepare a special inp. file where the mesh is replaced by mesh generator commands.
If you are a bit familiar with programming in BASIC, you might also write a script in GiD to prepare a set of models with the desired modifications.