Topology optimization using a continuous-time high-cycle fatigue model

• Published in: Structural and multidisciplinary optimization Vol. 61; no. 3; pp. 1011 - 1025
• Main Authors: Suresh, Shyam, Lindström, Stefan B., Thore, Carl-Johan, Torstenfelt, Bo, Klarbring, Anders
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020; Springer Nature B.V
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Constraint modelling; Damage; Differential equations; Engineering; Engineering Design; Fatigue failure; High cycle fatigue; Load history; Nonproportional loads; Optimization; Ordinary differential equations; Research Paper; Sensitivity analysis; Stiffness; Theoretical and Applied Mechanics; Topology optimization; Endurance surface; Topology optimization; Adjoint sensitivity analysis; Continuous-time approach; High-cycle fatigue; Aggregation function
• ISSN: 1615-147X; 1615-1488; 1615-1488
• DOI: 10.1007/s00158-019-02400-w

We propose a topology optimization method that includes high-cycle fatigue as a constraint. The fatigue model is based on a continuous-time approach where the evolution of damage in each point of the design domain is governed by a system of ordinary differential equations, which employs the concept of a moving endurance surface being a function of the stress and back stress. Development of fatigue damage only occurs when the stress state lies outside the endurance surface. The fatigue damage is integrated for a general loading history that may include non-proportional loading. Thus, the model avoids the use of a cycle-counting algorithm. For the global high-cycle fatigue constraint, an aggregation function is implemented, which approximates the maximum damage. We employ gradient-based optimization, and the fatigue sensitivities are determined using adjoint sensitivity analysis. With the continuous-time fatigue model, the damage is load history dependent and thus the adjoint variables are obtained by solving a terminal value problem. The capabilities of the presented approach are tested on several numerical examples with both proportional and non-proportional loads. The optimization problems are to minimize mass subject to a high-cycle fatigue constraint and to maximize the structural stiffness subject to a high-cycle fatigue constraint and a limited mass.