Uniqueness theorem

Uniqueness theorem - Uniqueness theorem Let us consider now...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Uniqueness theorem Let us consider now whether our equations can have more than one correct solution corresponding to given surface and body forces. The equations of equilibrium expressed in terms of stresses have been established as , ij i j f + = (a) In the expanded form, one has xy 0 x xy x xz x y yz y yz xz z z X x y z X y z X x y z + + + = + + + = + + + = (2-12) The kinematic relationships are ( 29 , , 1 2 ij i j j i u u = + (b) In the expanded form, one has xy , , x y u v u v x y y x = = = + (2-2) and xz yz , , z w w u w v z x z y z = = + = + (2-3) With the compatibility constrains of , , , , ij kl kl ij ik jl jl ik + = + (c) Again, in the expanded form 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 2 y xy x y yz z x xz z yz xy x xz y yz xy xz yz xy xz z y x x y z y y z x z x z y z x x y z x z y x y z x y z x y z + = + = + = =- + + =- + = +- (2-13) and the constitutive law is given by ( 29 1 1 ij ij ij kk E = +- (d) In the expanded form ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 11 11 11 11 22 33 1 1 1 1 1 1 xx xx xx yy zz xx yy zz E E E...
View Full Document

Page1 / 7

Uniqueness theorem - Uniqueness theorem Let us consider now...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online