## 1D function definition

@FUNCTION_1D_DEFINITION {
@FUNCTION_1D_NAME {Fun1DName} {
@FUNCTION_1D_TYPE {Fun1DType}
@CHEBYSHEV_POLYNOMIAL {
@APPROXIMATION_RANGE {xlo, xhi}
@CHEBYSHEV_COEFFICIENTS {c1, c2,..., cN}
}
@TABLE_1D_NAME {Tbl1DName}
}
}

### NOTES

1. 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. Function F(x) will be represented by expension in terms of Chebyshev polynomials. A plot of the function will be generated if plotting control parameters are defined.
2. 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.
3. The 1D function F(x) can be defined in two mutually exclusive manners.
• If keyword @CHEBYSHEV_POLYNOMIAL appears, the function is defined by the coefficients of its Chebyshev expansion directly. The following two inputs are then required.
1. The lower and upper bounds of the approximation, denoted xlo and xhi, respectively, define the range over which the approximation is valid. If independent variable x falls outside this range during the simulation, a warning message will be printed. As explained in the discussion of Chebyshev polynomials, the coefficients of the expansion depend on the he range over which the approximation is defined.
2. The N coefficients of Chebyshev's polynomial expansion, c1, c2,... , cN.
• If keyword @TABLE_1D_NAME appears, the function is defined by one-dimensional table Tbl1DName. If this case, the function is defined by a set of experimental data points and this discrete relationships is then approximated by its Chebyshev expansion.
4. 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 following function types can be defined.

• If Fun1DType = PRESSURE_DISTRIBUTION, this function describes the load applied along an external edge of the cross-section of the beam.
• If Fun1DType = DISTRIBUTION_FUNCTION, this function describes the load applied along the span of the beam.