MT-1620 al.2002 If we recall a little mathematics, the Laplace Operator in 2-D is x4+20 This is the biharmonic operator(also used in fluids) So the f)equation can be written Ey4AT)-(1=y2v() Finally, in the absence of temperature effects and body forces this becomes v4=0 homogeneous form What happened to E, v?? Paul A Lagace @2001 Unit 8-p. 9MIT - 16.20 Fall, 2002 If we recall a little mathematics, the Laplace Operator in 2-D is: ∇2 ∂2 ∂2 = + ∂x2 ∂y2 ∂4 ∂4 ∂4 ⇒ ∇2∇2 = ∇4 = ∂x4 + 2 2 2 + ∂y4 ∂ ∂ x y This is the biharmonic operator (also used in fluids) So the (*) equation can be written: ∇4φ = −Eα∇2 (∆T) − (1 − ν) ∇2 V (*) Finally, in the absence of temperature effects and body forces this becomes: ∇4φ = 0 homogeneous form What happened to E, ν?? Paul A. Lagace © 2001 Unit 8 - p. 9