2. Cube in Gravitational Field

A a solid cube is placed in the gravitational field g=(0, 0, -9.81) at time t=0 and released. The cube must move in 'free fall' along the negative z-axis with

z = 0.5 g z t 2

and the falling speed

v = g z t

with the acceleration a = g z being constant. The model consists of HE8.S, HE20.S.TL, or HE27.S.TL elements. Different mesh densities a tested. The figure below displays the displacement, velocity, and acceleration functions for an integration time of 2s (solid lines are theoretical values).

Solution at node 1 of mesh (blue dots: theoretical solution).

Figure 73. Solution at node 1 of mesh (blue dots: theoretical solution).

The dynamic solution is relatively sensitive with respect to the error tolerance. Values of case options (see input file he.mdl)

tol_residuum 2e-3
tol_solution 1e-4

have been found to lead all element types to convergence.