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.
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.
Methods
Initialize a plane section.
Initialization can be done either by a list of points or a set of line segments.
Methods
planeSection objects have the following methods:
Functions defined in the 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