• About Solver
• femGate
• Benchmarks
• • UP1
  • UP2
  • UP3
  • UP4
  • UP5
  • UP6
  • F1

Benchmark UP1

Pressure Loaded Beam (Small Strains)

Description

A cantilever of length $l$, depth and width $z_0$, loaded by a uniform pressure load $p_1$ 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

Parameters

$\begin{array}{ccc}\hfill l& \hfill =\hfill & 0.11\mathrm{m}\hfill \\ \hfill z_0& \hfill =\hfill & 0.00275\mathrm{m}\hfill \\ \hfill p_1& \hfill =\hfill & 5\mathrm{Pa}\hfill \\ \hfill \kappa & \hfill =\hfill & {10}^8\mathrm{Pa}\hfill \\ \hfill \mu & \hfill =\hfill & 3.\overline{33}·{10}^6\mathrm{Pa}\hfill \end{array}$

where $\kappa$ is the bulk modulus and $\mu$ is the shear modulus.

Theory

The maximum deflection is given by $u_{\max }=\frac{1}{64}\frac{p_1{z}_0}{\mu (1+\nu )}{\left(\frac{l}{z_0}\right)}^4$, where the Poisson's number is given by $\nu =\frac{3\kappa -2\mu }{6\kappa +2\mu }$.

FE Model

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

Results