lunes, 22 de noviembre de 2010

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!

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