Consider a special case of Eq (14 1 4) Parameswaran and Shukla (1999) presented a two dimensional study where the shear modulus and Lames constant varied as (x) o (1 ax) and (x) k(x), where o , a, and k are constants For such a material, show that in the absence of body forces the two dimensional N...

u o 222 ax T 20 dv 0 22 2 k2uku dy dx dy Using the new form o ...

Consider a special case of Eq. (14.1.4). Parameswaran and Shukla (1999) presented a two dimensional study where

Question:

Consider a special case of Eq. (14.1.4). Parameswaran and Shukla (1999) presented a two dimensional study where the shear modulus and Lame´’s constant varied as μ(x) = μ_o(1 + ax) and λ(x) = kμ(x), where μ_o, a, and k are constants. For such a material, show that in the absence of body forces the two-dimensional Navier’s equations become:

20 Ju 22 (1 + ax)(10 + 2021 1071 + 2 + 1,0(k++2). + dx 2 Ho(1 +ax) (k where = + v 02v 22 32 +2. + 2 dy