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I do not know how much the non-linearity will affect your results. It depends on how much the non-linearity affects the calculated stresses. Constant Amplitude and Time Series load providers use linear superposition to combine stresses. They do not check if the analysis was linear. They essentially just assume that the stresses are from linear analysis. If the non-linearity has a small effect on the calculated stresses, then CA and TS might produce reasonable results even with non-linear analysis. However, if the non-linearity has a large effect on the calculated stresses, then CA and TS might produce incorrect results.