Function 1D definition

@FUNCTION_1D_DEFINITION {

@FUNCTION_1D_NAME {Fun1dName} {

@FUNCTION_1D_TYPE {Fun1DType}

@CHEBYSHEV_POLYNOMIAL_NAME {ChbFunName}

@HARMONIC_FUNCTION_NAME {HarFunName}

@TABULATED_FUNCTION_NAME {TblFunName}

@USER_FUNCTION_NAME {UsrFunName}

@START_TIME {t_s}

@END_TIME {t_e}

@COMMENTS {CommentText}

}

}

Introduction

The function 1D 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, t_s, and an end time, t_e, can be defined for the 1D function. Default values: t_si = - DBL_MAX and t_ei = DBL_MAX. These start and end times are used in the following manner
   F(t) = F(t_s), if t < t_s,
   F(t) = F(t), if t_s < t < t_e,
   F(t) = F(t_e), if t_e < 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.

Fun1DType	Description	XentryType	DataType
DISTRIBUTED_FORCE_ALONG_i1 DISTRIBUTED_FORCE_ALONG_i2 DISTRIBUTED_FORCE_ALONG_i3	Distributed applied forces along i1, i2, i3	η	Force/span
HYDRAULIC_ORIFICE	Flow-pressure relationship for hydraulic orifices	Pressure	Flow
DISTRIBUTED_MOMENT_ABOUT_i1 DISTRIBUTED_MOMENT_ABOUT_i2 DISTRIBUTED_MOMENT_ABOUT_i3	Distributed applied moments 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
PRESSURE_ALONG_i1 PRESSURE_ALONG_i2 PRESSURE_ALONG_i3	Applied pressure along i1, i2, i3	η	Pressure
TIME_FUNCTION	Function of time for applied loads, prescribed displacements, rigid rotations	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.