The *AMPLITUDE option 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 *AMPLITUDE, DEFINITION=TABULAR option uses a nonfixed time increment, which requires that pairs of time-amplitude data be supplied. The *AMPLITUDE, DEFINITION=EQUALLY SPACED option 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 *AMPLITUDE, DEFINITION=PERIODIC option uses the Fourier series to define the function. The *AMPLITUDE, DEFINITION=MODULATED option uses the product of two sine functions. The *AMPLITUDE, DEFINITION=DECAY option uses an exponential function. The *AMPLITUDE, DEFINITION=SMOOTH STEP option uses a fifth-order polynomial equation to ramp up/down smoothly from one amplitude value to the next. The *AMPLITUDE, DEFINITION=SOLUTION DEPENDENT option (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 CONTROL option.

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. The SMOOTH parameter 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 using the END STEP parameter. A simple truss model is used. Various nodal degrees of freedom are prescribed with the *BOUNDARY option, and loads are applied using the *CLOAD and *DLOAD options. In all of these cases the prescribed quantities are defined using the *AMPLITUDE option. 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 use the END STEP parameter, 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 option.

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 an amplitude with DEFINITION=SOLUTION DEPENDENT.