Question

Q2 For the displacement field given below, obtain the strain energy and kinetic energy based on a plane stress problem. Ow(x, y,0) Ow(x, y, t) U(x,y,2,t) = u(x, y,t) - 2 12; V(x, y, 2, 1) = v(x,y,t) -2- 62; V(x,y,z, t) = w(x,y,t) дх

Answer 1

Given,

The given displacement is,

Figure

In above figure shows the displacement field. obtain the strain energy and kinetic energy based on a plane stress problem.

The given equation are,

( ۶٫۷) لال U (x,y,2, t)= u(x,7,t)-22 N(X,Y,2,1)= V(X,7,4), z dw X,1,1) w (X,4,3,4+) = Wix,M,t) For stain energy: The all the plane stress in tension X2 het, r = Stress in x- direction 02 - Stress in yo clirection 33 - Stress in 2-direction The force in x-direction fx= (oxbh) The force in y-direction fy = (62Xbh) The force in 2 -direction foz (63Xbh)

E The Slogin in the x-direction Ex = a 1 u. 2 u 1 da The strain in the y-elirection Eye-le-4 - The strain in the 2-direction Ey = - cu cele mash ... The total strain Energy is U = 1 1 [opt 27 - 21 (9,82 +0203 630 ] for kinetic energy : The Velocity in x- direction, u(x,y,z,t) = U (,4,2,4)= ULX,1,) - 2 8W (x,y,) The velocity in y-direction u(x,1,2,t) is NOX,1,2,t) = V(X,Y,t)-2 dw (x,y,t) SX The velocity in 2-direction w(x,1,2,t) WIX,Y, 2,t) - W1%,9,4) The Kinetic energy in x-direction is m kg. CK.87 = € Hua Lumpucx,4,4) - 2 540 6X791); (K. €), ampak ma v19,-2. Pax 245 94 )2- The total Kinetic energy, Οχ

Above place stress problem to solve the strain energy and kinetic energy.

The total kinetic energy, (KE) dotal = 1 m [u?ur w²] The needed values of u (X,19,4)= 32+ Sxy+3tror any others.