Random fatigue methods

When you perform a random fatigue analysis, you can choose between the narrow-band (Miles) method and the wide-band (Dirlik) method NOTE.

For both methods, the durability solvers uses only:

• The von Mises stress PSD from the random event of the Response Dynamics solution process.From the von Mises stress PSD, the durability solver computes up to the first four moments of the stress PSD to use in the random fatigue methods. The nth moment of stress PSD, mn is computed numerically using quadrature from the following equation NOTE:where σ(f) is the stress amplitude as a function of frequency, f.

• Fatigue strength coefficient, σ'f, and fatigue strength exponent, b, from the stress-life material properties.If you define an S-N curve for the material, the durability solver uses the least square method to fit the specfied S-N curve and find the values for σ'f and b.

Narrow-band (Miles) method

The narrow-band (Miles) method computes the expected damage, E{D(t)}, for a specified period of time of excitation, t, as follows:

where:

• νo+ is the positive zero crossing, given in terms of the 2nd and 0th moment of the stress PSD, defined as:

• σrms is the root-mean square value of the stress response:

• Γ is the Gamma function, defined as:

Wide-band (Dirlik) method

The wide-band (Dirlik) method computes the expected damage, E{D(t)}, for a specified period of time of excitation, t, as follows:

where:

• νp is the expected rate of peaks defined as:

• The constants D1, R, D2, D3, and Q are defined in terms of the irregularity factor, γ and Xm as:

Random fatigue analysis results

For element nodes that are on a free face, the durability solver can compute:

• The event damage result set, which is the expected damage E{D(t)} for a specified period of time of excitation, t.

• The event life result set, which is the fatigue life computed by solving for the time value T for which E{D(T)} = 1.

Look up more details

Introduction to durability analysis

Understanding the strength evaluation

Strength calculations for orthotropic failure criteria

Fatigue evaluation on element free faces

Fatigue life criteria

Biaxial fatigue evaluation on element free faces

Using a notch factor for modeling the local plastic behavior

Understanding cyclic stress-strain behavior

Understanding the fatigue safety evaluation

Cumulative damage

Strain and stress calculations from strain gage leg data

Strain gage transverse corrections for rosette legs

Scientific literature references for durability

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Random fatigue methods, Simcenter 3D 2021.1 Series

© 2020 Siemens

Wijker, J.J., “Random Vibrations in Spacecraft Structure Design: Theory and Applications”, Chapter 2, Spring Verlag, 2009.

Bonte, M., de Boer, A., and Liebregts, R., “Determining the von Mises PSD for freqeuncy domain fatigue analysis including out-of-phase stress components”, Journal of Sound and Vibration, Volume 302, 2007, pp. 379-386.

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