Efficient and Robust Topology Optimization of Compliant Mechanisms using Perturbed Geometrically Non-Linear Analysis

Paper Title: "Structural Topology Optimization using Bayesian-Enhanced Perturbed Non-Linear Analysis"

Master Thesis (2023)
Author(s)

C. Kerkhove (TU Delft - Mechanical Engineering)

Contributor(s)

M. Langelaar – Mentor (TU Delft - Computational Design and Mechanics)

Stijn Koppen – Mentor (TU Delft - Computational Design and Mechanics)

F. van van Keulen – Graduation committee member (TU Delft - Mechanical Engineering)

Faculty
Mechanical Engineering
Copyright
© 2023 Casper Kerkhove
More Info
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Publication Year
2023
Language
English
Copyright
© 2023 Casper Kerkhove
Graduation Date
11-12-2023
Awarding Institution
Delft University of Technology
Programme
['Mechanical Engineering | Precision and Microsystems Engineering']
Faculty
Mechanical Engineering
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Abstract

The recent success of - and demand for - compliant mechanisms has increased rapidly within the micro-electromechanical systems-, aircraft-, spacecraft-, surgical-, and precision-instrument industries. Yet, even greater success may be achieved by overcoming the computational cost and instability of the mechanisms' design methodology. This involves large-scale topology optimization, geometrically non-linear structural analysis, and particularly integrating the latter into the former. Therefore, a novel framework is proposed that extends the powerful design freedom of topology optimization with most of the geometrically non-linear qualities, without as much of the computational ramifications. Utilizing a Bayesian-enhanced perturbed analysis, the equilibrium curve is locally approximated by an asymptotic expansion, satisfying the curve's higher-order geometric derivatives at the undeformed state. Each of the latter is recursively and efficiently obtained through a linear solve with the same, Cholesky-factorized stiffness matrix. Furthermore, a tensor reformulation and -decomposition of the four-noded bilinear element's Green-Lagrange strain energy model are successfully exploited. A tight error estimator is derived to govern the Bayesian analysis and balance approximation efficiency and accuracy during optimization. Design-sensitivities of this error-estimator and other design-dependent responses are analytically obtained through the adjoint method, and applied in a few classical density-based topology optimizations; While Bayesian-enhanced perturbed analysis required noticeably less computational effort compared to Newton-Raphson analysis under mildly non-linear conditions, it often resulted in practically identical performance improvements compared to linear analysis.

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