2016/09/16
Friday, September 16, 2016
10:10 AM
For elastic solid bar
we want to minimize the functional
To obtain the exact solution.
However, to minimize a functional we cannot compute derivative. Instead,
we can use the concept of first variation.
For functionals we can define the same concept:
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For functionals we can define the same concept:
How could we evaluate first variation of a functional?
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What is the use of this?
Remember for a function to extremum (e.g. minimum) at a point we
need the function derivative to be zero (or alternatively its first
variation to be zero)
For a functional to be extremum (e.g. minimum) for the exact solution y, we need the first variation
to be zero
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Important relation
To minimize a functional we must have (meaning that it is an essential
condition),
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This looks like the weak statement we obtained from balance law
approach
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The minimization condition from the energy approach:
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Continuation of comparison of energy approach and balance law approach:
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Continuation of comparison of energy approach and balance law approach:
Same approach can be applied to the beam problem
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