Overview

Test Case

Determine the free-body moments (MX, MY, MZ) about the origin and the rotational accelerations (ω_x, ω_y, ω_z) at the center of mass of an aluminum block due to the forces FX and FY shown.

Figure 300: Counter-Balanced Loads on a Block Problem Sketch

Material Properties	Geometric Properties	Loading
E = 70 x 109 N/m2 ρ = 2712 kg/m3	h = 3 m = 2 m d = 300 m	FX = -2000 N FY = 3000 N

Analysis Assumptions and Modeling Notes

The problem is solved in three different ways:

The block must be constrained such that no rigid body motions occur. In a 3D structure, six DOF must be constrained to prevent free-body motion by translation or rotation. The inertia relief algorithm is used to calculate accelerations to counterbalance the applied loads resulting in net zero values for the sum of the reaction forces. The substructure analysis is performed using the component mode synthesis method (CMSOPT) and the inertia relief results are retrieved after the use pass analysis.

Results Comparison