In the engineering sciences, mathematical models are based on the equations of continuum mechanics, heat flow, Maxwell, Navier-Stokes, or some combination of these. These equations have been validated and their domains of calibration are generally much larger than the expected domain of calibration of the model being developed. In the terminology introduced by Lakatos, the assumptions incorporated in these equations are called hardcore assumptions, and the assumptions incorporated in the other constituents of a model are called auxiliary hypotheses. Model development is concerned with the formulation, calibration, and validation of auxiliary hypotheses.
Engineering students and professionals alike want to know: are singularities “real”? And if so, when they appear in our solutions, what are we supposed to do with them?
Regarding the practical question of what to do with singularities; we need to distinguish between cases where singularities are just nuisances and where a singularity is the object of simulation.
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“At DST Group, we have effectively used StressCheck over the last 10 years to determine accurate stress intensity factors. The results have been used to improve our residual strength and structural life estimates for aircraft in service with the Royal Australian Airforce, including C-130, P-3C and F/A-18 A/B. We have found it to be extremely easy to use and a very versatile code with which to create parametric models.
We have recently used StressCheck to obtain improved stress intensity factor solutions (Improved stress intensity factors for selected configurations in cracked plates and Improved stress intensity factors for a single corner crack at a loaded fastener hole) for five key generic configurations. These transferable parametric results have been published externally. One specific example is the non-linear contact analysis of a cracked, filled fastener hole, with both fastener and remote plate loading.”
Dr. Manfred Heller, HeadStructural & Damage Mechanics, DST Group