1D function definition

@FUNCTION_1D_DEFINITION {
@FUNCTION_1D_NAME {Fun1DName} {
@CHEBYSHEV_POLYNOMIAL_NAME {ChbFunName}
@HARMONIC_FUNCTION_NAME {HarFunName}
@TABULATED_FUNCTION_NAME {TblFunName}
@USER_FUNCTION_NAME {UsrFunName}
@START_TIME {ts}
@END_TIME {te}
@COMMENTS {CommentText}
}
}

Introduction

The 1D function utility defines an arbitrary function of a single variable, F = F(x), where x is the independent variable and F the value of the function. A plot of the function will be generated if plotting control parameters are defined. The functions can be represented in four mutually exclusive manners.

  1. If keyword @CHEBYSHEV_POLYNOMIAL_NAME appears, the function is represented as a Chebyshev function, ChbFunName. This approach is the simplest is the function has a simple polynomial expression.
  2. If keyword @HARMONIC_FUNCTION_NAME appears, the function is represented as a harmonic function, HarFunName. This approach is the simplest is the function has a simple harmonic expression.
  3. If keyword @TABULATED_FUNCTION_NAME appears, the function is represented as a tabulated function, TblFunName. This approach is the simplest is the function is defined by experimental measurements. If desired, these experimental measurements can be approximated through Chebyshev approximation.
  4. If keyword @USER_FUNCTION_NAME appears, the function is represented as a user function, UsrFunName. This approach is the simplest is the function has a given analytical expression that can be programmed easily.

NOTES

  1. Various types of functions can be defined to be used by various objects of the model. The list of allowable function types is given below.
  2. Optionally, a start time, ts, and an end time, te, can be defined for the 1D function. Default values: tsi = - DBL_MAX and tei = DBL_MAX. These start and end times are used in the following manner
    F(t) = F(ts), if t < ts,
    F(t) = F(t), if ts < t < te,
    F(t) = F(te), if te < t.
  3. It is possible to attach comments to the definition of the object; these comments have no effect on its definition.

List of function types

The recognized types of Fun1DType are listed in the first column of table 1. The second column describes the context in which the 1D function is used. If the 1D function is defined by means of a single-entry table, column 3 and 4 list the required XentryType and DataType for the table.

Fun1DType Description XentryType DataType
FORCE_ALONG_i1
FORCE_ALONG_i2
FORCE_ALONG_i3

Applied force distribution along i1, i2, i3

η

Force/span
HYDRAULIC_ORIFICE Flow-pressure relationship for hydraulic orifices Pressure Flow
MOMENT_ABOUT_i1
MOMENT_ABOUT_i2
MOMENT_ABOUT_i3

Applied moment distribution about i1, i2, i3

η

Moment/span
RECTILINEAR_DAMPER Force-velocity relationship for rectilinear dashpots or
elastomeric dampers
Force Stroke rate
RECTILINEAR_SPRING Force-stretch relationship for rectilinear springs or
elastomeric dampers
Force Stroke
TIME_FUNCTION Function of time for dead loads, prescribed displacements,
edge loads
Time Time function
TORSIONAL_DAMPER Moment-angular velocity relationship for torsional dashpots Moment Angular velocity
TORSIONAL_SPRING Moment-rotation relationship for torsional springs Moment Rotation
Table 1. List of recognized Fun1DType.