Hello,
This is perhaps more of a math question than an engineering question, but here goes:
I am attempting to derive the Airy Stress Function, d^4(phi)/dx^4 + 2*d^4(phi)/dx^2dy^2+d^4(phi)/dy^4
I think that from the compatibility equations I can get to del^4(phi). Every book/website I can find then says that this can be expanded as the above equation. I was just wondering how exactly that is the case? I thought del^4(x) = d^4(x)dx^4 + d^4
dy4 . Where does the other term come in? I guess what I am asking for is the definition/explanation of the higher order gradient operator. Is it correct that del(x) = d/dx + d/dy?
Thanks for any help!
This is perhaps more of a math question than an engineering question, but here goes:
I am attempting to derive the Airy Stress Function, d^4(phi)/dx^4 + 2*d^4(phi)/dx^2dy^2+d^4(phi)/dy^4
I think that from the compatibility equations I can get to del^4(phi). Every book/website I can find then says that this can be expanded as the above equation. I was just wondering how exactly that is the case? I thought del^4(x) = d^4(x)dx^4 + d^4
dy4 . Where does the other term come in? I guess what I am asking for is the definition/explanation of the higher order gradient operator. Is it correct that del(x) = d/dx + d/dy? Thanks for any help!
