everything is clear about writing the strain tensor as the product of the compliance tensor and the stress tensor according to hooke law, but I cannot do the same for the stress tensor. also, it is not easy to get the inverse of the compliance tensor, since it is a 9x9 matrix. how can i manipulate stiffness matrix from scratch by not taking the inverse of compliance matrix
thanks for the explanation, in the first slide why does it have 2 times epsilon_12 and in the equation above it just have the coefficients without times 2?
I think there is a mistake, the first complete vector epsilon (with the 9 terms )shouldn't have the 2, this is only when terms are grouped (because epsiij=epsiji) that the 2 should appear (in the reduced epsilon vector with 6 terms)
Hi! Thanks a lot for the great explanation! I have a question please, in section "Reduction 2" you mentioned that order of differentiation doesn't matter since its a simple function, so are there other general cases where order of differentiation does matter? (it could be an off-topic question, sorry, I'm just curious to know) Thanks!
It's comes from calculus, which says something along the lines that if the function is continuous, the order of differentiation does not matter. I believe in linear elasticity, the functions will always be continuous. But yeah, there are applications outside linear elasticity where a function might not be continuous, and the order of differentiation does matter.
Wow, well done. I wish my professor would go into this level of detail!
your video is amazing, loved your explanations, a true teacher. Thankyou
Great!
Thanks for making me understand, i appreciate from Uganda Makerere University Structures Masters class 2021/22 Regards
Great video. Thank you Dr. Pettit!
Awesome! Explained all of my confusion. Thank you!
Lad, you are an absolute legend!!
Mr Clayton thank you so much
9:45 love your explanation thanks a lot
nice course, really helpful. thank you!
everything is clear about writing the strain tensor as the product of the compliance tensor and the stress tensor according to hooke law, but I cannot do the same for the stress tensor. also, it is not easy to get the inverse of the compliance tensor, since it is a 9x9 matrix. how can i manipulate stiffness matrix from scratch by not taking the inverse of compliance matrix
May I ask a question why is the component Cijkl, that's gonna be the partial derivative of sigma ij with respect to epsilon kl?
Same question
Thanks a lot for this
thanks for the explanation, in the first slide why does it have 2 times epsilon_12 and in the equation above it just have the coefficients without times 2?
I think there is a mistake, the first complete vector epsilon (with the 9 terms )shouldn't have the 2, this is only when terms are grouped (because epsiij=epsiji) that the 2 should appear (in the reduced epsilon vector with 6 terms)
cool
Hi! Thanks a lot for the great explanation! I have a question please, in section "Reduction 2" you mentioned that order of differentiation doesn't matter since its a simple function, so are there other general cases where order of differentiation does matter? (it could be an off-topic question, sorry, I'm just curious to know) Thanks!
It's comes from calculus, which says something along the lines that if the function is continuous, the order of differentiation does not matter. I believe in linear elasticity, the functions will always be continuous. But yeah, there are applications outside linear elasticity where a function might not be continuous, and the order of differentiation does matter.