1. Reference problem#

1.1. Geometry#

Consider the slender recessed free-free cylindrical bar described below:

_images/10000000000003EE0000008C0B1383EAC9A98A1E.png

Length

: \(l=4m\)

Radius

: \(r=0.1m\)

End 1

: recessed (\(x=0\))

End 2

: free (\(x=l\))

1.2. Material properties#

The characteristics of the material are as follows:

Young’s module: \(E=2.1{10}^{11}\mathrm{Pa}\)

Poisson’s ratio: \(\nu \mathrm{=}0.3\)

Density: \(\rho =7800\mathrm{kg}/{m}^{3}\)

1.3. Boundary conditions and loading#

The boundary condition is that the \(1\) end of the bar must be embedded. This embedment is of the beam type to allow Poisson effects on the section.

The load applied for the response calculation is an axial force, constant under tension, distributed over the section of the end \(2\):

\(P(t)=\)

\(0\)

if \(t<0\)

\({P}_{0}={10}^{6}N\)

if \(t\ge 0\)