A proposal on a course on Real-Time Structural Dynamics

 The following is a tree with the key concepts that, although already at reach of any graduated structural engineer, need to be tied together, maybe in a course, in order to achieve a proper scope on how to simulate real-time structural dynamics:

• Main time integration methods (ODE), their limitations (drawbacks), advantages, motivation, references, illustrations, year, all related to the three disciplines applied physics, maths and applied computing:
• 1st order
• Euler
• Backward Euler
• Semi-implicit Euler
• Exponential Euler
• 2nd order
• Verlet
• Velocity Verlet
• Midpoint Method
• Heun's
• Newmark-beta
• Leapfrog
• Higher order
• Runge-Kutta
• Linear multistep
• Main constraint/collision (DAE) integration methods, their limitations (drawbacks), advantages, motivation, references, illustrations, year, all related to the three disciplines applied physics, maths and applied computing.
• Coordinate Partitioning
• Constraint Orthogonalization
• Udwadia-Kalaba
• Main matter/continuum (PDE) integration methods, their limitations (drawbacks), advantages, motivation, references, illustrations, year, all related to the three disciplines applied physics, maths and applied computing.
• MESH BASED METHODS
• Finite Element
• Finite Differences
• Finite Volume
• Boundary Element
• Mass-spring systems
  
• MESH FREE METHODS
• SPH
• Diffuse Element Method
• Partition of Unity
• Moving Least Square
• Reproducing Kernel Method

A graphical approach to ths subject, not so tied to complex formalisms and formulation, would be a real help to attract more researchers into this fascinating discipline.
It also would reinforce the interest on the very differential equations, as these are a very abstract concept explained and taught on a very abstract basis. This makes them first candidate to be either forgotten or banned into the minds of students.

I will try to develop these subjects with more care in future issues...

Se vidimo!

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.

Discipline Overview

Holidays are over already. I am now living in Slovenia, Ljubljana, and developing the thesis in the Faculty of Architecture (lovely place, by the way...).

Last June I presented my Thesis Proposal to the jury of the Computational and Applied Physics Department in the UPC and...it was accepted!!

After the long pause I have had to prepare an overview of all the studied subjects, just to get some scope on what is coming and where we are now. The following diagrams give some idea on how it is:

And with a bit more of detail:

These diagrams derive from the need of disentangling disciplines that more often than seldom get mixed in the literature and make it fairly hard to follow.
The literature I am talking about is that of the computational simulation of physics, where numerical methods meet with very different origins.