Amplitude

The amplitude curve is used to specify a function that defines arbitrary time variations of prescribed variables throughout an analysis. The user can specify this function with a variety of methods. Two of the methods use tabulated values that define a continuous function of linear segments. The tabular amplitude definition uses a nonfixed time increment, which requires that pairs of time-amplitude data be supplied. The equally spaced amplitude definition uses a fixed time increment that is specified once, and only the values of the function are required. Two other amplitude types use trigonometric functions to define the function. The periodic amplitude definition uses the Fourier series to define the function. The modulated amplitude definition uses the product of two sine functions. The exponential decay amplitude definition uses an exponential function. The smooth-step amplitude definition uses a fifth-order polynomial equation to ramp up/down smoothly from one amplitude value to the next. A solution-dependent amplitude definition (available only in Abaqus/Standard) accepts a starting value and lets Abaqus calculate subsequent values based on the evolution of solution parameters. Currently there is only one solution parameter available, the maximum equivalent creep strain rate, which is compared to target values entered in the creep strain rate.

If the function describes either a displacement or velocity in a dynamic analysis, the derivatives and integrations of the function are required. For the three amplitude types that use trigonometric or exponential functions, the derivatives are continuous and available. For the amplitude type that uses a fifth-order polynomial equation, the derivatives are continuous and available; however, both the first and second derivatives are zero at the data point. For the two types that use tabulated values, the linear segments do not have continuous derivatives, and the second derivative will be infinite at the segment intersections. An amplitude curve with smoothing allows the user to define an interval about the data points in which a quadratic function is interpolated to give a continuous first derivative and a finite second derivative. The use of this parameter is verified within these tests.

Input files xampmult.inp (Abaqus/Standard) and xamptest.inp (Abaqus/Explicit) are analyses performed over multiple steps during which several loads and displacements are applied in terms of defined amplitudes with various settings of the parameters. xampresm.inp (Abaqus/Standard) and xamprest.inp (Abaqus/Explicit) restart the analyses from the previous step. A simple truss model is used. Various nodal degrees of freedom are prescribed with the boundary conditions, and loads are applied. In all of these cases the prescribed quantities are defined using the amplitude curve. The purpose of this test is to ensure that the initial value of the function to be applied in the next step is interpolated properly from the amplitude definitions. Since xampresm.inp and xamprest.inp restart the analysis from the previous step, the results will show that the initial value at the beginning of the restart step is obtained from the point on the amplitude curve at which the restart was done; the value will be ramped to the new value defined in the new step. The output variables corresponding to the prescribed input are checked to verify the use of the amplitude curve.

xampsdep.inp and xampress.inp simulate the superplastic forming of a rectangular pan in Abaqus/Standard. The pressure applied to a sheet that forces it to acquire the shape of a die is determined by solution-dependent amplitude.