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The objective of this paper is to demonstrate that frequency domain methods for calculating structural response and fatigue damage can be more widely applicable than previously thought. This will be demonstrated by comparing results of time domain vs. frequency domain approaches for a series of fatigue/durability problems with increasing complexity. These problems involve both static and dynamic behavior. Also, both single input and multiple correlated inputs are considered. And most important of all, a variety of non-stationary loading types have been used. All of the example problems investigated are typically found in the automotive industry, with measured loads from the field or from the proving ground.

The fatigue analysis of a full car body requires the sheet metal (sheet fatigue), spot welds (spot weld fatigue) and seam welds (seam weld fatigue) to be thoroughly evaluated for durability. Traditionally this has always been done in the time domain, but recently new frequency domain techniques are able to perform these tasks with numerous advantages. This paper will summarize the frequency domain process and then compare the results and performance against the more usual time domain process.

Frequency domain methods of analysis are now being used for the evaluation of fatigue for large vehicle systems and these methods offer advantages over equivalent time domain approaches in a number of ways, including analysis efficiency and the usefulness of derived results. One big potential advantage is to be able to do localized sub-component analysis using “cascaded” loads. Such sub-components can be analysed with refined parameters such as more sophisticated damping or a different frequency range. Local parts can also be re-analysed at a different phase in the design program. This paper will demonstrate the approach and show examples of the method.

The time domain is currently the most widely chosen option in fatigue testing to fully represent random events occurring in multiple simultaneous input channels. In vehicles for example, time domain tests can represent the same conditions of the road, by applying the same loads at the hard points of the vehicle along a time history. The main drawback of this methodology is the extensive testing duration and hardware cost. Time domain based fatigue tests are composed of a complex hardware, which requires servo motors to work, in order to induce the specific amount of load at a specific time window. These tests are time consuming, since they require the same length duration of the event they are reproducing, times the required repetitions. The frequency domain method for fatigue testing, on the other hand, requires simpler hardware, since there are no need for servomotors and the test length is reduced, since there is no need to run the full event times the required repetitions.

Conventional approaches for the fatigue life evaluation of automotive parts like headlamps involves the evaluation of random stress conditions in either the time or frequency domain. If one is working in the frequency domain the fatigue life can be evaluated using one of the available methods like the Rayleigh (Narrow Band) approach or the more recent Dirlik method. Historically, the random stresses needed as input to these methods have been evaluated by the FEA solver (eg Abaqus, or Nastran) and these “in built” stress evaluations have limitations which relate to the fact that the stress conditions are complex and so the common “equivalents” for stress like von-Mises or Principal have not been available. There have also been limitations in the location and method of averaging for such stresses. In addition, the fatigue calculation approach for doing the evaluation has been constrained to the linear stress based (S-N) method.

For many automotive systems it is required to calculate both the durability performance of the part and to rule out the possibility of collision of individual components during severe base shake vibration conditions. Advanced frequency domain methods now exist to enable the durability assessment to be undertaken fully in the frequency domain and utilizing the most advanced and efficient analysis tools (refs 1, 2, 3, 4, 5). In recent years new capabilities have been developed which allow hyper-sized models with multiple correlated loadcases to be processed. The most advanced stress processing (eg, complex von-Mises) and fatigue algorithms (eg, Strain-Life) are now included. Furthermore, the previously required assumptions that the loading be stationary, Gaussian and random have been somewhat relaxed. For example, mixed loading like sine on random can now be applied.

It has been recognised since the 1960's that the frequency domain method for structural analysis offers superior qualitative information about structural response (refs 1, 2, 3, 4); But computational and technological issues have held back the implementation for fatigue calculation until now. Recent technological developments (see refs 5, 6, 7, 8, 9) have now enabled the practical implementation of the frequency domain approach and this paper will focus on the accuracy of the approach when compared with the traditional time based (transient dynamic) approach.