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!