1D function definition
- @FUNCTION_1D_DEFINITION {
- @FUNCTION_1D_NAME {Fun1DName} {
- @FUNCTION_1D_TYPE {Fun1DType}
- @CHEBYSHEV_POLYNOMIAL {
- @APPROXIMATION_RANGE {x_{lo}, x_{hi}}
- @CHEBYSHEV_COEFFICIENTS {c_{1}, c_{2},..., c_{N}}
- }
- @TABLE_1D_NAME {Tbl1DName}
- @COMMENTS {CommentText}
- }
- }
NOTES
- 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.
- 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.
- 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.
- The lower and upper bounds of the approximation, denoted x_{lo} and x_{hi}, 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.
- The N coefficients of Chebyshev's polynomial expansion, c_{1}, c_{2},... , c_{N}.
- 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.
- 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.