Microstructure emerging in shape optimization of elastic structures

Speaker(s)

Benedikt Wirth

Affiliation

Universität Münster

Language of the talk

English

Date

Nov. 4, 2026, 12:30 p.m.

Room

room 4060

Seminar

Seminarium Zakładu Równań i Analizy

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So-called compliance minimization seeks the optimal geometry of an elastic material to withstand a fixed given mechanical load and, at the same time, to consume as little material as possible. In general this problem is ill-posed: Minimizers may not exist, and microstructure may form along minimizing sequences. However, for some externally applied loads and some loading geometries minimizers actually do exist, sometimes even without microstructure. Indeed, the problem features an interesting dichotomy: If the load has eigenstresses of opposite sign, minimizers do not exist, and the only optimal microstructure consists of a laminate. If both eigenstresses are of the same sign, there is suddenly a plethora of optimal microstructures, and even minimizers of fractal geometry are known. But is microstructure really necessary, and if yes, how does the microstructure of minimizers look like? We will discuss some answers to these problems. The work is joint with Peter Bella and Jonathan Fabiszisky.

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