finite element method – Randomly distributed mesh points

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I have a mesh bounded by a rectangle:

{w, h} = {400, 300};
r = BoundaryMeshRegion[{{0, 0}, {w, 0}, {w, h}, {0, h}}, Line[{1, 2, 3, 4, 1}]];
meshTriangulated = TriangulateMesh[r, MaxCellMeasure -> 1000]

enter image description here

Notice that the vertices along the edges are evenly distributed:

coord = MeshCoordinates[meshTriangulated];
Sort[Select[coord, #[[2]] == 0 &][[All, 1]]]

(* -> {0., 50., 100., 150., 200., 250., 300., 350., 400.} *)

How can I distribute the vertices more randomly?

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