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I was wondering what is origin of weak form in continuum mechanics.
Tue, 2011-04-26 22:13 - roger84
Last day, I took my class of Nonlinear Analysis of solids and structures.
And I learned about the strong form & weak form in the prilciple of Virtual work.
I can find the origin of those two form that is from Piola-Kirchhoff stress tensor.
but why Integral form is called "weak form"? why Differential form is called "strong form"? why?
I was just wondering.
Forums:
Distribution Theory
Dear Roger,
The answer to your question is rooted in the theory of distributions. In fact relationships involving integral form accept a wider class of solutions; solutions that are not only functions but distributions. On the other hand the strong form requires the solution to be differentiable: it is much more restrictive! In fact distributions have derivatives (they are infinetely differentiable indeed), but in a much more weaker sense that usual functions. I think the terms weak/strong come from this.
My blog on research on Hybrid Solvers: http://mechenjoy.blogspot.com/
Reference
Hi,
There is a discussion in the following link:
http://imechanica.org/node/5570