Benchmark UP1

Pressure Loaded Beam (Small Strains)


A cantilever of length l, depth and width z0, loaded by a uniform pressure load p1 from above. The cantilever is supposed to be fixed at x=0 and x=l. The depicted boundary conditions do not restrict transverse deformation which occurs due to the nonzero Poisson’s number. The maximum deflection of the structure is tested.

Two cantilever materials are used:

  • Neo-Hookean
  • Gent
Image depicts cantilever dimensions, loading and boundary conditions.

l = 0.11 m z0 = 0.00275 m p1 = 5 Pa κ = 108 Pa μ = 3 .33¯ · 106 Pa

where κ is the bulk modulus and μ is the shear modulus.


The maximum deflection is given by u max = 164 p1 z0 μ ( 1 + ν ) ( l z0 ) 4 , where the Poisson's number is given by ν = 3κ-2μ 6κ+2μ .

FE Model

In ANSYS the problem is solved using 2×2×80=320 quadratic elements (SOLID186). In femCalc the same number of BRICK60 elements with linear pressure interpolation was used.

Material Theory ANSYS (SOLID186) femCalc (BRICK60)
Type κ [Pa] ν [-] umax [m] umax [m] Ratio umax [m] Ratio
Neo-Hookean 108 0.483516 0.000111 0.000112 1.009 0.000112 1.009
Gent 108 0.483516 0.000111 0.000112 1.009 0.000112 1.009