VM-WB-MECH-038

VM-WB-MECH-038
Crashing Blocks Simulation with Transient Structural Analysis

Overview

Reference: Any basic kinematics book
Solver(s):

Ansys Mechanical

Analysis Type(s): Flexible Dynamic Analysis
Element Type(s): Solid

Test Case

Three blocks are resting on a base. A left block of mass 2.355 x 10-4 kg is given a constant initial velocity of 100 mm/sec to collide with a middle block of mass 1.1775 x 10-4 kg. Frictionless supports are applied as shown in the figure and also on the bottom faces of the left and middle blocks. The right block is fixed using a fixed support and the base is fixed by applying a fixed joint.

Find the velocity of both the moving blocks after impact.

Figure 50: Schematic

Schematic

Material PropertiesGeometric PropertiesLoading
E = 2 x 105 MPa
ν = 0.3
ρ = 7.85 x 10-6 kg/mm3
Left block = 3 mm x 2 mm x 5 mm
Middle block = 2.5 mm x 2 mm x 3 mm
Right block =3 mm x 6 mm x 4 mm
Base = 3 mm x 8.607 mm x 75.15 mm
Left block initial velocity = 100 mm/s (X direction)

Analysis

For a perfectly elastic collision between the blocks, the following equations are true:

where:

and = mass of the left and middle blocks in kg
and = initial and final velocity of the left block in mm/sec
= initial velocity of the middle block in mm/sec
= final velocity of the middle block after impact in mm/sec

Results Comparison

ResultsTargetMechanicalError (%)
Velocity of the left block after impact (mm/sec)33.333.6290.988
Velocity of the middle block after impact (mm/sec)133.4132.74-0.495