You said, conventional calculus is used to extremize function and variational calculus is used to extermize Functional. The function returned in calculus of variation is minimum at every point in the domain OR does the minimum is in average sense due to fact we integrate the functional in domain?
I see you have shown many derivations, so one get good understanding of basics. Do you have some class notes or recommended book that follow exactly like your covered the entire topics of fea.
You showed only a single graph for which there is a variation, which we derived. Since in this and in previous case (of last videos based o derivatives) we want to find an extremal function, which will have an infinite number of 'points' along x axis. My question is about eta function we used previously and referred here as well. Do we will need an infinite number of eta functions for each point x for comparison with 'known' assumed function. This will also imply that we will have to make similar calculation for infinite number of x axis points. Am i correct?
I last part of lecture, one see that 1-c1 in sqaure root. We generalized this to A. Would not value to c1 have any constraint on choices of values of c1or A in final u?
What would happen if you were to cool to 400 degrees and wait until you have 50% bainite, and then quench to room temperature? What would the microstructure be?
thank you for this video. Is it possible to implement this without the stiffness matrix, but with the internal force vector Fint(u_(k+1)) ? The factorazation does not work like this to solve for u_(k+1) in the last step
Thank you for interesting video. If we put (6) into (4), we get negative value of pi (if displacement and force have same direction). It's a little bit confusing. Potential energy is negative at equilibrium? Could you please comment, why this happens?
Wow, our continuum mechanics professor had given this expression to prove in the final exam when I was in my first year PG. Now I understand!! Thanks and Cheers!
This is so clear thank you. If energy lost/energy stored = 4 x pi x tan delta, doesn't this imply virtually all energy is lost in vulcanised rubber, where tan delta is around 0.1 at room temperature?
