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2017 | OriginalPaper | Buchkapitel

Modeling, Minimizing and Managing the Risk of Fatigue for Mechanical Components

verfasst von : L. Bittner, H. Gottschalk, M. Gröger, N. Moch, M. Saadi, S. Schmitz

Erschienen in: Stochastic Geometric Mechanics

Verlag: Springer International Publishing

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Abstract

Mechanical components that are exposed to cyclic mechanical loading fail at loads that are well below the ultimate tensile strength. This process is known as fatigue. The failure time, that is the time when a first crack forms, is highly random. In this work we review some recent developments in the modelling of probabilistic failure times, understood as the time to the formation of a fatigue crack. We also discuss how probabilistic models can be used in shape design with the intent of optimizing the components’ reliability. We review a recent existence result for optimal shapes and we discuss continuous and discrete shape derivatives. Another application is optimal service scheduling. The mathematical fields involved range from reliability statistics over stochastic point processes, multiscale modeling, PDEs on variable geometries, shape optimization and numerical analysis to operations research.

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Here, \(\nabla [M]_{\text {vM}}\) denotes the gradient of the von Mises stress at the value of a matrix \(M\in \mathbb {R}^{3\times 3}\).

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Titel: Modeling, Minimizing and Managing the Risk of Fatigue for Mechanical Components
verfasst von: L. Bittner
H. Gottschalk
M. Gröger
N. Moch
M. Saadi
S. Schmitz
Verlag: Springer International Publishing
Buch: Stochastic Geometric Mechanics
Print ISBN: 978-3-319-63452-4

Electronic ISBN: 978-3-319-63453-1

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-319-63453-1_10

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