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andrew-plattandrew-platt
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Merge pull request #2646 from luwang00/f/RectangularMembers
Implementation of rectangular members in HD and SD
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‎docs/source/user/subdyn/theory.rst‎

Lines changed: 8 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -389,17 +389,17 @@ element stiffness and consistent mass matrices can be written as follows
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{\scriptstyle
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[k_e]=
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\begin{bmatrix}
392-
\frac{12 E J_y} {L_e^3 \left( 1+ K_{sy} \right)} & 0 & 0 & 0 & \frac{6 E J_y}{L_e^2 \left( 1+ K_{sy} \right)} & 0 & -\frac{12 E J_y}{L_e^3 \left( 1+ K_{sy} \right)} & 0 & 0 & 0 & \frac{6 E J_y}{L_e^2 \left( 1+ K_{sy} \right)} & 0 \\
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& \frac{12 E J_x}{L_e^3 \left( 1+ K_{sx} \right)} & 0 & -\frac{6 E J_x}{L_e^2 \left ( 1+ K_{sx} \right )} & 0 & 0 & 0 & -\frac{12 E J_x}{L_e^3 \left ( 1+ K_{sx} \right )} & 0 & -\frac{6 E J_x}{L_e^2 \left ( 1+ K_{sx} \right )} & 0 & 0 \\
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\frac{12 E J_y} {L_e^3 \left( 1+ K_{sx} \right)} & 0 & 0 & 0 & \frac{6 E J_y}{L_e^2 \left( 1+ K_{sx} \right)} & 0 & -\frac{12 E J_y}{L_e^3 \left( 1+ K_{sx} \right)} & 0 & 0 & 0 & \frac{6 E J_y}{L_e^2 \left( 1+ K_{sx} \right)} & 0 \\
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& \frac{12 E J_x}{L_e^3 \left( 1+ K_{sy} \right)} & 0 & -\frac{6 E J_x}{L_e^2 \left ( 1+ K_{sy} \right )} & 0 & 0 & 0 & -\frac{12 E J_x}{L_e^3 \left ( 1+ K_{sy} \right )} & 0 & -\frac{6 E J_x}{L_e^2 \left ( 1+ K_{sy} \right )} & 0 & 0 \\
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& & \frac{E A_z}{L_e} & 0 & 0 & 0 & 0 & 0 & -\frac{E A_z}{L_e} & 0 & 0 & 0 \\
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& & & \frac{\left(4 + K_{sx} \right) E J_x}{L_e \left ( 1+ K_{sx} \right )} & 0 & 0 & 0 & \frac{6 E J_x}{L_e^2 \left ( 1+ K_{sx} \right )} & 0 & \frac{\left( 2-K_{sx} \right) E J_x}{L_e \left ( 1+ K_{sx} \right )} & 0 & 0 \\
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& & & & \frac{\left(4 + K_{sy} \right) E J_y}{L_e \left ( 1+ K_{sy} \right )} & 0 & -\frac{6 E J_y}{L_e^2 \left ( 1+ K_{sy} \right )} & 0 & 0 & 0 & \frac{\left( 2-K_{sy} \right) E J_y}{L_e \left ( 1+ K_{sy} \right )} & 0 \\
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& & & \frac{\left(4 + K_{sy} \right) E J_x}{L_e \left ( 1+ K_{sy} \right )} & 0 & 0 & 0 & \frac{6 E J_x}{L_e^2 \left ( 1+ K_{sy} \right )} & 0 & \frac{\left( 2-K_{sy} \right) E J_x}{L_e \left ( 1+ K_{sy} \right )} & 0 & 0 \\
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& & & & \frac{\left(4 + K_{sx} \right) E J_y}{L_e \left ( 1+ K_{sx} \right )} & 0 & -\frac{6 E J_y}{L_e^2 \left ( 1+ K_{sx} \right )} & 0 & 0 & 0 & \frac{\left( 2-K_{sx} \right) E J_y}{L_e \left ( 1+ K_{sx} \right )} & 0 \\
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& & & & & \frac{G J_z}{L_e} & 0 & 0 & 0 & 0 & 0 & -\frac{G J_z}{L_e} \\
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& & & & & & \frac{12 E J_y} {L_e^3 \left( 1+ K_{sy} \right)} & 0 & 0 & 0 & -\frac{6 E J_y}{L_e^2 \left ( 1+ K_{sy} \right )} & 0 \\
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& & & & & & & \frac{12 E J_x}{L_e^3 \left( 1+ K_{sx} \right)} & 0 & \frac{6 E J_x}{L_e^2 \left ( 1+ K_{sx} \right )} & 0 & 0 \\
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& & & & & & \frac{12 E J_y} {L_e^3 \left( 1+ K_{sx} \right)} & 0 & 0 & 0 & -\frac{6 E J_y}{L_e^2 \left ( 1+ K_{sx} \right )} & 0 \\
399+
& & & & & & & \frac{12 E J_x}{L_e^3 \left( 1+ K_{sy} \right)} & 0 & \frac{6 E J_x}{L_e^2 \left ( 1+ K_{sy} \right )} & 0 & 0 \\
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& & & & & & & & \frac{E A_z}{L_e} & 0 & 0 & 0 \\
401-
& & & & & & & & & \frac{\left(4 + K_{sx} \right) E J_x}{L_e \left ( 1+ K_{sx} \right )} & 0 & 0 \\
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& & & & & & & & & & \frac{\left(4 + K_{sy} \right) E J_y}{L_e \left ( 1+ K_{sy} \right )} & 0 \\
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& & & & & & & & & \frac{\left(4 + K_{sy} \right) E J_x}{L_e \left ( 1+ K_{sy} \right )} & 0 & 0 \\
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& & & & & & & & & & \frac{\left(4 + K_{sx} \right) E J_y}{L_e \left ( 1+ K_{sx} \right )} & 0 \\
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& & & & & & & & & & & \frac{G J_z}{L_e} \\
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\end{bmatrix}
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}

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