If the current step is a steady-state dynamic analysis, the value of an output variable such as stress (S) or displacement (U) can be a complex number with both real and imaginary components. Complex number results are saved during the analysis as pairs of real and imaginary data. When you use ABAQUS/CAE to display complex results, you can choose any of the following forms to view the analysis data:
Magnitude displays the combined magnitude of both the real and imaginary portions of the result value. This option is the default setting.
Phase angle displays the angle between the positive horizontal axis and the plotted point (real, imaginary). This selection is valid only for scalars or for vector and tensor components.
Real displays only the real component.
Imaginary displays only the coefficient of the imaginary component of the complex result.
Value at angle displays the combined value of the real and imaginary portion of the result at an angle that you specify. When the angle is 0°, the real part of the result is displayed; when the angle is 90°, the imaginary part of the result is displayed.
The Magnitude is calculated after any invariants, such that the magnitude value is the square root of the sum of the squares of the real and imaginary invariant components. Similarly, the other complex forms are also calculated after invariants. Value at angle is the only exception; it is calculated prior to invariants to preserve the proper physical meaning.
You can also choose to animate complex results using harmonic animation. This technique animates complex field output by displaying the Value at angle through a sequence of angles. ABAQUS/CAE generates angles ranging from 0° to 180° or from 0° to 360°, according to your specification, and displays the value of the complex results at each angle.
The magnitude and phase angle are related to the real and imaginary components with the usual expressions. For example, the real and imaginary displacement components, and , are related to the magnitude, , and phase angle, , as follows: