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## Homework Statement

Given a cylinder in the Ox1x2x3 coordinate system, such that x1 is in the Length direction and x2 and x3 are in the radial directions. The stress components are given by the tensor

$$

[T_{ij}] = \begin{bmatrix}Ax_2 + Bx_3 & Cx_3 & -Cx_2 \\ Cx_3 & 0 & 0 \\ -C_2 & 0 & 0\end{bmatrix}

$$

(a) Verify that in the absence of body forces the equilibrium equations are satisfied.

(b) Show that the stress vector vanishes at all points on the curved surface of the cylinder

(by the way I'm pretty sure that the T_31 is a typo and should be -Cx_2)

## Homework Equations

## The Attempt at a Solution

(a) is simple enough, I think:

$$

\sum \vec{F} = 0 = \nabla \cdot \mathbb{T} = \begin{bmatrix}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{bmatrix}

$$

However I have no idea what they mean or how to go about answering (b). If you did a diagram of an element on the edge, I think you could show there is no shear, but there would still be the compression represented by T_11

Thanks