Beam property definition

@BEAM_PROPERTY_DEFINITION {
@BEAM_PROPERTY_NAME {BldPropName} {
@PROPERTY_DEFINITION_TYPE {PropertyType}
@COORDINATE_TYPE {CoordinateType}
@ETA_COORDINATE {η} {
@SECTION_BUILDER_SECTION_NAME {SbSecName}
}
@ETA_COORDINATE {η} {
...
}
@DAMPING_COEFFICIENT {μs}
@MESH_OPTIMIZATION_FLAG {YES/NO}
@COMMENTS {CommentText}
}
}

Introduction

The physical mass and stiffness sectional properties of beams are defined in this section. The physical properties of the beam are allowed to vary along its span. To describe this variation, tables of beam sectional properties are defined. Beam properties are defined in the plane of the cross-section as defined by the beam geometry. Plots of the beam sectional properties will be generated, if requested in the plotting control parameters data section.

It is possible to attach comments to the definition of the object; these comments have no effect on its definition.

Property definition type

The sectional properties of the beam are defined in the local axis system attached to the curve defining the geometry of the beam. Axis e1 is tangent to the curve, and axes e2 and e3 define the plane of the cross-section. These properties describe the mass and stiffness characteristics of the section in the form of a 6 x 6 mass matrix and a 6 x 6 stiffness matrix, respectively.

Beam sectional properties can be defined in two alternative manners, depending on the value of the PropertyType parameter.

  1. If PropertyType = SECTION_BUILDER, the sectional properties are defined in the SectionBuilder section data, SbSecName. This option allows the automatic transfer of the stiffness and mass characteristics of a beam's cross-section computed by SectionBuilder to Dymore.
  2. If PropertyType = SECTIONAL_PROPERTIES, the data must appear in the format defined in section Sectional properties format. This format focuses on the definition of engineering sectional properties such as sectional bending and torsional stiffnesses. When experimental measurements of the sectional physical properties are available, this is the preferred data input format.

Typically, the viscous damping coefficient, μs, of the section is estimated, not calculated rigorously. Hence, it is convenient to provide an estimated default value of this coefficient. If a default value of μs is defined here, it will be used for the sectional properties defined at all span-wise locations along the beam's curve. If a viscous damping coefficient is defined at a particular station, that values overrides the default. A default viscous damping coefficient can be defined for the two options of parameter PropertyType.

Coordinate definition type

Since beam properties are given along the curve that defines the geometry of the beam, table entries are associated with a parameterization of this curve. Coordinates can be defined in three alternative manners depending on the flag CoordinateType.

  1. If CoordinateType = ETA_COORDINATE, positions along the curve are defined by means of the η coordinate. Each new property set must be introduced by the keyword @ETA_COORDINATE. The beam sectional properties will be defined in a table. Table entries define a sequence of η-coordinates. Property sets are defined at each specific η-entry, as illustrated in fig. 1.

    The table entries are mapped to physical locations along the beam curve by letting the η-coordinate be the coordinate that parameterizes the curve defining the geometry of the beam.
  2. Figure 1. Beam property definition using η-coordinate. The circles indicate the table entries.
  3. If CoordinateType = CURVILINEAR_COORDINATE, positions along the curve are defined by means of the curvilinear coordinate, s. Each new property set must be introduced by the keyword @CURVILINEAR_COORDINATE. The beam sectional properties will be defined in a table. Table entries are define a sequence of s-coordinates. Property sets are defined at each specific s-entry, as illustrated in fig. 2.

    The table entries are mapped to physical locations along the beam curve by letting the s-coordinate be the coordinate that parameterizes the curve defining the geometry of the beam.
    Figure 2. Beam property definition using s-coordinates.
    At the root end point of the beam curve, curvilinear variable s is zero. When the beam is defined, an offset, si, can be specified. In such case, the curvilinear variable along the beam becomes si + s, allowing the beam to use a subset of the entries of the property table, as illustrated in fig. 2. At the end point of the beam curve, the curvilinear variable is sf = si + L, where L is the length of the beam. Clearly, the following inequalities must hold: sbeg <= si < send and sbeg < sf <= send. When using the s-coordinate option, different beams are allowed to refer to the same beam property table, typically using adjacent portions of the table.
  4. If CoordinateType = AXIAL_COORDINATE, positions along the curve are defined by means of the axial coordinate, x. Each new property set must be introduced by the keyword @AXIAL_COORDINATE. The beam section properties will be defined in a table. Table entries are define a sequence of x-coordinates. Property sets are defined at each specific x-entry. All the features of this option are identical to those detailed for the s-coordinate option.

Sharp gradients in sectional properties

Beam often present sharp gradients in sectional property distributions. The accuracy of finite element models rapidly degrades when these sharp gradients occur within a single finite element. If the @MESH_OPTIMIZATION_FLAG flag is set to YES, this situation can be remedied using the procedure described below. When the beam properties are defined by tables this flag is automatically set to YES.

  1. Mesh optimization. To remedy the problem, it seems rational to use smaller elements in the areas of high property gradients. In general, the size of the elements within a beam is controlled by the curve mesh parameters, which allow the definition of the size of each element. In this first step, the element sizes will be automatically computed: smaller elements will be used in regions of high property gradient. Note that this option will automatically erase the element size defined by the curve mesh parameters. The element size ratio, Er, the ratio of the largest to the smallest element of the mesh can be defined for the corresponding beam.
  2. Property smoothing. Within each element, a sectional property smoothing technique will then be used that is based on conservation arguments for mass properties and energy considerations for stiffness properties.