Question

Show that the following stress components satisfy the equations of equilibrium with zero body forces, but are not the solution to a problem in elasticity. c is a nonzero constant.

σₓₓ=c[y²+v(x²-y²)]
​σyy=c[x²+v(y²-x²)]
​​σzz=cv(x²+y²)
​τₓy=-2cvxy
τyz=τzₓ=0

Answer 1

The given stress components satisfy the equations of equilibrium with zero body forces, but they are not the solution to a problem in elasticity.

Step-by-step explanation:

The given stress components satisfy the equations of equilibrium with zero body forces because the sum of the forces acting in each direction is equal to zero. However, they are not the solution to a problem in elasticity because they do not satisfy the constitutive equations that relate stress to strain for a given material.