MT-1620 Fall 2002 Note that deformations(um) must be continuous single-valued functions for continuity (or it doesn't make physical sense!) Step 2: Now consider the case where there are gradients in the strain field 812≠0,。y2 12 0 This is the most general case and most likely in a general structure ake derivatives on both sides 12 1(0。u 2 0yy22(叫yny2"y7y2 Step 3: rearrange slightly and recall other strain-displacement equations du 2 Paul A Lagace @2001 Unit 4-p.8∂ ∂ ∂ ∂ ∂ ∂ MIT - 16.20 Fall, 2002 Note that deformations (um) must be continuous single-valued functions for continuity. (or it doesn’t make physical sense!) Step 2: Now consider the case where there are gradients in the strain field ∂ε12 ≠ 0, ∂ε12 ≠ 0 ∂y1 ∂y2 This is the most general case and most likely in a general structure Take derivatives on both sides: ∂2ε12 1  ∂3u1 ∂3u2  ⇒ = 2 + 2 y y2 2  y y2 y y2  1 1 1 Step 3: rearrange slightly and recall other strain-displacement equations ∂u1 = ε1 , ∂u2 ε = 2 ∂y1 ∂y2 Paul A. Lagace © 2001 Unit 4 - p. 8