Issue 47

D. Benasciutti et alii, Frattura ed Integrità Strutturale, 47 (2019) 348-366; DOI: 10.3221/IGF-ESIS.47.26 365 analysis. Also the S-N material properties are specified at the beginning of the analysis. At the end of second phase, results are displayed as a contour plot (damage map), or written into a text file (function “PbPresults2text.mac”). Figure 10 : Flowchart of the APDL script to implement the PbP in Ansys software. The relationship with the previous Matlab-based procedure (sketched on the right) is shown. The first phase must be run one time only. Once stress PSDs have been calculated and stored, the second analysis phase is performed to compute the fatigue damage. This phase is repeated as many times as are the combinations of S-N properties that need to be scrutinized. In terms of computation time, the first phase may be slightly longer than the second one (especially with low RAM memory). Just to provide an order-of-magnitude estimate, for the model in Fig. 6, determining the nodal stress PSDs takes about 4 minutes, while applying the PbP method takes about 3 minutes on a 64- bit workstation (CPU 3.80 GHz, 32 GB RAM). Compared to the Ansys/Matlab mixed procedure, the new approach entirely based on Ansys has the great advantage to exploit the graphical capabilities of the commercial software in displaying the damage contour maps, especially in 3D complex finite element models. Another little advantage, though trivial, is that only one type of software is needed to carry out the whole calculation. On the other hand, the main disadvantage of using Ansys as the only computation tool is due to a greater complexity and less flexibility of APDL language in performing the fatigue damage calculations required in the PbP method. Although the APDL language – as Matlab – can execute a lot of algebraic and trigonometric functions, and it can even manage “DO/ENDO” and “DOWHILE/ENDO” loops, it does not have functions to compute the eigenvalues/eigenvalues of a square matrix or the gamma function Γ ( - ) directly. Therefore, an APDL macro (called “eigen.mac”) has been written to deal with eigenvalues/eigenvalues computation. This macro took the cue from the software library EISPACK, written in Fortran [22,23]. In particular, the functions involved are: TRED2 for tridiagonalization of a symmetric matrix [24], TQL2 for the QR eigenvalue algorithm [25]. Instead, the gamma function Γ ( – ) was computed by means of Stirling’s approximation formula, see for example [26]. To conclude, it is worth emphasizing that the flowchart here described for Ansys software is very general and it can easily be adapted to any other finite element code that perhaps the reader knows better. NOMENCLATURE A matrix of constants