Solved: you need to provide typed document as a doc of this/n • Prove that: Th

Question

you need to provide typed document as a doc of this/n • Prove that: The volumetric strain e (change in volume/unit volume) equal to e = εx + εy + ε₂ = 10x + ay + σ₂-2v (ax +ay + a:)] (1.53) e = Ex + Ey + Ez Sub Stituting for Ex, Ey and Ez Using those can's. Ex = ± [6x -v (6y+6z)] Ex: + [64 -V (6x +62)] E = = = ( Oz - ~ (6x + Gy)] 6x-v (6y+62) 6y-v (6x-62) 6t-v(6x-6) 6x +бy +62-2v 6y-2V 62 - 2V6x Ⓒ = = [ 6x + 6x + 6z -2V (6x+6y+6z) P.1.8 Show that the compatibility equation for the case of plane strain, viz. 2²¼xy 2²εy 2²εx + ax ay ar2 ay2 may be expressed in terms of direct stresses σ, and σ, in the form Ex = — (0x-voy) Ej. — (oy-vox) (+)+)-0 2) (ax + ay) = 0 Yey = (xy = 2 (1+0) TxJ E The compatibility condition for Plane Strain is 33YxJ axay Now we Subtitute, we got = ชัย ax² oya 2C1+v) = 8 оходу = 8 (6g - vox ) + 0, (6x-very) Assume that the body Forces Xey are Zovo 86 =06 PJ After differentiating we got. ajax Sj = 0 -(1+v) (x + 1) = (6-Vox) + (x-Vary) Substituting So that = -(IP) 13) - 6718-(1) Which Simplifies to aya (+) (+) = 0 8