The computation is based on the theories of [Giavotto et al. (1983)] and [Ghiringhelli et al. (1994)].

A 3D mesh slice (SOLID186 element) of the beam section is generated using section cuts, as represented in the figure below. The computational model of the section cut is automatically converted to the reference coordinate system, where x and y are the beam section in-plane axes, while the beam longitudinal axis follows the global z (positive).

Figure 2.116: 3D Representation of a Beam Slice (with Respect to the Global Coordinate System)

The global FE stiffness and mass matrix of the slice are then computed using the Mechanical APDL Solver.

The global mass matrix is used to compute the equivalent beam mass matrix per unit length.

The global stiffness matrix is used as the starting point to compute all the matrices required by the theory explained in [Giavotto et al. (1983)].

The global stiffness matrix is split into four submatrices (the subscripts 1 and 2 refer to face-1 and face-2 of the solid slice):

These four K-sub-matrices are then combined following the implementation explained in [Ghiringhelli et al. (1994)] to build the system of equations of [Giavotto et al. (1983)], solve them, and finally compute the stiffness matrix of the beam section.

The results of the computation are the stiffness matrix of the cross section, mass matrix, and other section properties such as shear center and center of gravity. The primary results are with respect to the origin of the section cut and the global coordinate system of the section cut which is defined by the normal and reference direction 1.

The standard output stiffness matrix produced by this feature has the following form:

where,

All the represent a stiffness value. The ones on the main diagonal are:

Shear stiffness in x plane
Shear stiffness in y plane
Axial stiffness
Bending stiffness in x plane
Bending stiffness in y plane
Torsional stiffness

This feature also computes the following important quantities:

The results of the computation are the stiffness matrix of the cross section, mass matrix, and other section properties such as shear center and center of gravity.

You can request for the stiffness and mass matrix to be printed out and reordered to follow the specific Ansys beam section type form SECTYPE,,COMB,MATRIX, which can be used to assign the computed equivalent beam properties to an Ansys beam element (such as BEAM188 or BEAM189). See the get_transformed_sectional_properties_matrix() function of the Section Cut. There is an example at the end of this section which generates an input file for Mechanical APDL.

The get_sectional_stiffness_behavior() extracts the equivalent stiffness values from the matrix.

Reordering Example

The value in the standard output becomes the value in position (1,1) of the SECTYPE,,COMB,MATRIX, while the value becomes the value in position (3,3).

For a detailed description of the stiffness and mass matrix form in this case, see Using Preintegrated Composite Beam Sections in the Structural Analysis Guide.

The position and orientation of the section cut are important. Typically, the section cut plane is perpendicular to the mesh and the origin is placed in the center of the mesh. The section cut provides methods to transform points from the global coordinate system to the coordinate system of the section cut, and vice versa.

Export Section Cut Example

Export section cut properties to Mechanical APDL as a preintegrated composite beam.

model = db.active_model
model.update()

with open("D:\\tmp\\composite_sections.cdb", "w") as mapdl_file:
    for index, sc in enumerate(model.section_cuts.values()):
        # compute equivalent beam properties
        results = sc.compute_equivalent_beam_properties(check_status=True)
        sectype_command = sc.get_sectype_command_from_sectional_properties(
            properties=results.properties,
            stiffness_matrix_position="elastic center", 
            stiffness_matrix_angle="elastic axes",
            mass_matrix_position="center of gravity", 
            mass_matrix_angle="principal axes", 
            sectype_id=index+1
        )
        mapdl_file.write(sectype_command)

This feature has the following limitations:

The computation of the respective sectional properties based on Ghiringhelli's theory (see [Ghiringhelli et al. (1994)]) was compared with that of Becas. The comparison contains various cross sections with different materials and layups, and the results are almost identical.