Physics Engines Benchmarking

The target was to devise in some manner the way different computational physics simulation models/engines/environments performed against a canonical one.

For such purpose, I have reviewed the paper "Beam Benchmark Problems For Validation Of Flexible Multibody Dynamic Codes" by A.L. Schwab and J.P. Meijgaard.
The following is an outline of the proposed in this paper:

• 1.- Introduction
• The paper presents some basic problems for which analytic solution is known
• 2.- Beam benchmark problems
• Tests to be performed
• Static analyses in small displacements for the validation of the correct formulation of elastic forces
• Static analyses for large displacements and rotations, on straight and curved beams
• Buckling tests in normal, lateral and torsional directions to check the way geometric stiffness due to prestress is taken into account
• Eigenfrequency analyses for the validation of the combination of elastic forces and distributed inertia forces
• Mesh refinement tests for all the above to prove convergence of the results
• Underlying model: Timoshenko beam with large displacements and large rotations
• Finite Element Method Beam Element
• Shear flexible based on the elastic line concept
• Slender beam, cross section doubly symmetric
• Large rotation and displacements, but small deformations
• Isotropic and linearly elastic
• BEAM model: standard strain-displacement relations
• BEAMNL model: additional quadratic terms included in the strain-displacement for better performance in the pre-stress cases

Interestingly enough, the analytical solution is provided for each of the tests, and the proposed model is simple enough so as not having too much trouble in introducing it in a few characteristic ready made softwares currently available.

The implementation of such a benchmark over some of the most popular engines revised lately would surely make a nice contribution.

Integration Overview

In order to get some scope I have prepared a new diagram where the different integration fields of any multibody physics engine can be fit.

Normally we have to integrate time, via ODEs, for which any of the available schemes can be chosen, but then also the Differential Algebraic Equations for constraints (related to collisions) and the Partial Differential Equations related to the continuum have to be solved.

Of course, not every engine implements the continuum part (limiting to rigid solid) and some matter integration schemes already consider the very collisions so the constraint integration is explicitly sorted...

The associated disciplines where each concept fits are represented by the horizontal blocks.