Question

The matrix form of the boundary condition equations is _____________

a.

\(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} σ_{xx} & τ_{xy} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{zy} & σ_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

b.

\(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} σ_{zz} & τ_{xy} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{zy} & σ_{xx} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

c.

\(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} σ_{xx} & τ_{zz} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{zy} & σ_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

d.

\(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} σ_{xx} & τ_{yy} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{yy} & σ_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

Answer: (a).\(\begin{bmatrix} \overline{X}\\ \overline{Y}\\ \overline{Z} \end{bmatrix} = \begin{bmatrix} σ_{xx} & τ_{xy} & τ_{xz} \\ τ_{yx} & σ_{yy} & τ_{yz} \\ τ_{zx} & τ_{zy} & σ_{zz} \end{bmatrix} \begin{bmatrix} l \\ m \\ n \end{bmatrix}\)

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Q. The matrix form of the boundary condition equations is _____________

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