Create and solve optimization-FEM models.
Optimization-FEM consists in optimising a target function (here called the cost function) under the constraint that a FEM model be exactly verified. This in turn implies that the problem has more unknowns than the model has equation (or at least: more unknowns than linearly independent equations, as would be the case with “insufficient” boundary conditions).
The unknowns that are dual to the FEM equations are noted X-dofs (the response of the model). The rest of the unknowns can be separated into U-dofs (varying with time, generaly unknown loads) and A-dofs (constant over time, generaly unknown model parameters). The conditions for such a constrained optimization problem to be well-posed are the Babushka-Brezzi conditions, which say, in essence “if you do not restrain, then at least measure”.
Besides solving well-posed FEM problems (obtaining the response of a system, given adequate boundary conditions and known loading terms), many applications can be, or should be, possible within Muscade.
Reliability analysis: Finding a design point. What is the most probable combination of external loads U and strength of the structure A that may cause the response X to exceed, in one of many ways, the acceptable?
Design optimization: What is the cheapest way to engineer a system (for example a structure) that will survive a set of loading conditions?
Load identification and monitoring: Given incomplete and noisy measurements of the response of a system, what are the loads that are most likely to cause a response close to what has been measured?
Optimal control: how to steer a system with many dofs into a wanted behaviour?
Model identification: given enough measurements on the response of a system responding to at least partly unknown load, is it possible to adjust the model of the system (model calibration, damage detection)?
Sensor array optimization: how best to place sensors in a system in order to support the above applications?
See the documentation.
In the REPL, type ] (to go into package management mode), followed by
add Muscade.- Press the
backspacekey to leave the package manager.