extract_ed

Purpose:

Extract element nodal quantities from a global solution vector.

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Syntax:

ed = extract_ed(edof, a)
Description:

The extract_ed function extracts element displacements or corresponding quantities \(\mathbf{a}^e\) from the global solution vector \(\mathbf{a}\), stored in a.

Input variables are the element topology matrix edof, defined in assem, and the global solution vector a.

The output variable

ed\(= (\mathbf{a}^e)^T\)

contains the element displacement vector.

If Edof contains more than one element, Ed will be a matrix

Ed\(= \begin{bmatrix} (\mathbf{a}^e)_1^T \\ (\mathbf{a}^e)_2^T \\ \vdots \\ (\mathbf{a}^e)_{nel}^T \end{bmatrix}\)

where row \(i\) gives the element displacements for the element defined in row \(i\) of Edof, and \(nel\) is the total number of considered elements.

Example:

For the two-dimensional beam element, the extract_ed function will extract six nodal displacements for each element given in Edof, and create a matrix Ed of size \((nel × 6)\).

Ed\(= \begin{bmatrix} u_1 & u_2 & u_3 & u_4 & u_5 & u_6 \\ u_1 & u_2 & u_3 & u_4 & u_5 & u_6 \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ u_1 & u_2 & u_3 & u_4 & u_5 & u_6 \end{bmatrix}\)