I tried to understand what you want, but failed.

First, your DensityTop is basically of the form

f[ x ] := (x - a L)^2 +  b  for  0 <= x <= L

that means

f[ 0 ] = ( a L )^2 + b and f[ L ] = L^2 ( 1 - a )^2 + b

and this depends on L, so you will never get the "same" function for different rods.

If you say

?if the fist rod has minimum force at 60%, all others have the same. ?if force density reaches maximum at 30% it has to at all rods. And The difference between minimum and maximum has to be the same for all rods. ?If f(x=0)f(x=L)=0.02 for the first rod, than this has to apply for all other 24 rods.

you can try a function

F[x_] := (D[f[xx], xx, xx] (x - a) (x - b) - D[f[xx], xx] (2 x - a - b) + 2 f[xx]) /. xx -> x

The derivative vanishes at a and b

 D[F[x], x] // Simplify


(a - x) (b - x) f'''[x]

and your other conditions

F[ a ] - F[ b ] == c1

and

F[ 1 ] / F[ 0 ] == c2

may help to find an appropriate f[ x ].

Then F[ x / L ] is a force density applying to all rods.