# Static condensation or Guyan reduction

## Main Question or Discussion Point

Hey all,

I was going through a few video lectures on youtube. To be specific, this is the video I watched.
Now, the professor in the video talks about Dynamic reduction techniques and puts Guyan reduction in that category. For a fact, Guyan reduction is also called Static condensation and when I come to think of 'Static' condensation as a 'Dynamic' reduction technique I am confused.

The term dynamic stands for something that varies linearly with time. Somwehow I can't correlate this with Static Condensation where we ignore the inertial (mass) terms and assume static equilibrium between the master nodes and slave nodes while solving this equation: [K]{u} = {F}.

Thanks.

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AlephZero
Homework Helper
Somwehow I can't correlate this with Static Condensation where we ignore the inertial (mass) terms and assume static equilibrium between the master nodes and slave nodes while solving this equation: [K]{u} = {F}.
As a simple example, think about the vibration of a cantilever beam. You can write the equation of motion of the beam with the mass distributed along its length, and solve to get the "exact" frequencies and mode shapes. Or you can make an approximate model by lumping the mass properties at the two ends of the beam, and assuming the deflected shape along the length of the beam is the same as for statics (i.e. described by a cubic function).

That's the basic idea behind Guyan reduction, and why it is called "static condensation".

Consider the statement " 'Static' Condensation is a 'Dynamic' reduction technique."
Now, 'reduction' and 'condensation' are synonyms, technique is a neutral word and then you have 'dynamic' and 'static' which are poles apart.

I have still not clearly understood the role of the word 'dynamic' in Static condensation. Yes, lumping of mass is done but again why call it 'dynamic' in first place. Why couldn't it just be called a reduction technique that lumps the mass properties?

Hoping to hear from you soon.

AlephZero
Homework Helper
I think this is more a question about English than about math.

"dynamic reduction" = "reducing the number of degrees of freedom in a model so a dynamic analyiss runs faster".

"static condensation" = "assuming the slave degrees of freedom move in the same way as for a static analysis, by ignoring the inertia forces on them".

These are two-word names for single ideas. Trying to parse "dynamic" as an adjective describing "reduction" and "static" as an adjective describing "condensation" doesn't add much to the meaning.

Why couldn't it just be called a reduction technique that lumps the mass properties?
You could call it that, but there are many different reduction techniques that lump the mass properties in dufferent ways. "Static condensation" is the name of one one way to do it.

Thanks AlephZero.

Your answers have certainly cleared some of my doubts. Will get back to you sooner or later with more doubts. Thanks once again! :)