MT-1620 Fall 2002 One other point Are all these equations/unknowns independent? NO Why?--> Relations between the strains and displacements(due to geometrical considerations result in the Strain Compatibility equations (as you saw in Unified) General form is dymdy+aN, amdy dyn少。0 m This results in 6 strain-compatibility (in 3-D) What a mess !!! What do these really tell us??? The strains must be compatible, they cannot be prescribed in an arbitrary fashion ets consider an example Step 1 consider how shear strain (E)is related to displacement 12 Paul A Lagace @2001 Unit 4-p. 7∂ ∂ ∂ ∂ MIT - 16.20 Fall, 2002 One other point: Are all these equations/unknowns independent? NO Why? --> Relations between the strains and displacements (due to geometrical considerations result in the Strain Compatibility Equations (as you saw in Unified) General form is: ∂2εnk + ∂2εml − ∂2εnl − ∂2εmk = 0 y yl ∂ ∂yk y yk ∂ ∂y m l yn m yn This results in 6 strain-compatibility (in 3-D). What a mess!!! What do these really tell us??? The strains must be compatible, they cannot be prescribed in an arbitrary fashion. Let’s consider an example: Step 1: consider how shear strain (ε12) is related to displacement: 1  ∂u1 ∂u2  ε  +  12 = 2  ∂y2 ∂y1  Paul A. Lagace © 2001 Unit 4 - p. 7