Structural optimisation of diffusion-driven degradation processes
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Date
2021
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Abstract
In the field of structural engineering, structures are developed and calculated. The stresses
and deformations resulting from mechanical loads are determined, and the structures are
dimensioned to ensure load-bearing capacity, usability and durability in accordance with
standards. The application of structural optimisation algorithms enables the development
of more efficient and economical building structures, whereby maximum permissible
stresses can be exhausted. However, standardised calculations take environmental influences,
such as chemical impact, only via so-called exposure classes and resulting material
properties into account. Detailed calculations on the influence of stresses and deformations
of the structures, especially due to the long-term chemical influence and resulting
material degradation, are often neglected. For example, specific stress constraints may be
exceeded.
Within the scope of the present work, a numerical programme is developed, enabling
an efficient optimisation of mechanical structures that are additionally burdened by
degradation processes due to diffusive concentrations. For this purpose, a mechanicalchemical-
degradation coupled model is developed. Within the framework of classical
structural mechanics, the developed material behaviour is presented, taking into account
modified physical principles of continuum mechanics to describe a mechanical-chemicaldegradation
coupled processes. With the help of the fundamentals of the Finite Element
Method (FEM), the solution of the non-linear problem is outlined in detail. Furthermore,
the developed structural analysis is embedded in a mathematical algorithm of
gradient-based structural optimisation. The optimisation allows a deeper analysis and
reduction of the harmful effects due to the influence of acting chemical concentrations.
A variational approach to structural optimisation provides the simultaneous integration
of analytically prepared sensitivity analysis with the structural analysis for embedding
the continuum mechanical formulations. Thus, efficient structural optimisation of the
introduced mechanical-chemical-degradation model is comprehensively presented. The
mathematical model with the required derivations as well as discretisation is documented
and implemented in a computer-based model.
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Keywords
Coupled problems, Mechanical diffusion coupling, Degradation, Shape optimisation
Subjects based on RSWK
Numerisches Verfahren, Finite-Elemente-Methode, Strukturoptimierung