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# 36. `section2d` — Some functions operating on 2D structures.

This is a plugin for pyFormex. (C) 2002 Benedict Verhegghe

See the Section2D example for an example of its use.

`Classes defined in module section2d`

class `section2d.``PlaneSection`(F)

  A class describing a general 2D section.

  The 2D section is the area inside a closed curve in the (x,y) plane. The curve is decribed by a finite number of points and by straight segments connecting them.

`Functions defined in module section2d`

`section2d.``sectionChar`(F)

  Compute characteristics of plane sections.

  The plane sections are described by their circumference, consisting of a sequence of straight segments. The segment end point data are gathered in a plex-2 Formex. The segments should form a closed curve. The z-value of the coordinates does not have to be specified, and will be ignored if it is. The resulting path through the points should rotate positively around the z axis to yield a positive surface.

  The return value is a dict with the following characteristics:

  - L : circumference,
  - A : enclosed surface,
  - Sx : first area moment around global x-axis
  - Sy : first area moment around global y-axis
  - Ixx : second area moment around global x-axis
  - Iyy : second area moment around global y-axis
  - Ixy : product moment of area around global x,y-axes

`section2d.``extendedSectionChar`(S)

  Computes extended section characteristics for the given section.

  S is a dict with section basic section characteristics as returned by sectionChar(). This function computes and returns a dict with the following:

  - xG, yG : coordinates of the center of gravity G of the plane section
  - IGxx, IGyy, IGxy : second area moments and product around axes through G and parallel with the global x,y-axes
  - alpha : angle(in radians) between the global x,y axes and the principal axes (X,Y) of the section (X and Y always pass through G)
  - IXX, IYY : principal second area moments around X,Y respectively. (The second area product is always zero.)

`section2d.``princTensor2D`(Ixx, Iyy, Ixy)

  Compute the principal values and directions of a 2D tensor.

  Returns a tuple with three values:

  - alpha : angle (in radians) from x-axis to principal X-axis
  - IXX,IYY : principal values of the tensor

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