Structural optimization for frictionless contact
Sjövall, Filip LU
(2025)
- Abstract
- Structural optimization aims to find the geometry of the best performing design in a predefined setting, using mathematical techniques. The motivation for this study can be categorized into three main benefits: efficient material usage, enhancing existing designs and enabling new technologies. All of these benefits are crucial for solving contemporary technological and environmental challenges.
An important topic of mechanical analysis is contact mechanics, which has been considered scarcely in structural optimization. Previous works have mainly considered linear elastic structures, often in contact with rigid supports, which limits the applicability to practical examples. The research herein investigates new structural... (More) - Structural optimization aims to find the geometry of the best performing design in a predefined setting, using mathematical techniques. The motivation for this study can be categorized into three main benefits: efficient material usage, enhancing existing designs and enabling new technologies. All of these benefits are crucial for solving contemporary technological and environmental challenges.
An important topic of mechanical analysis is contact mechanics, which has been considered scarcely in structural optimization. Previous works have mainly considered linear elastic structures, often in contact with rigid supports, which limits the applicability to practical examples. The research herein investigates new structural optimization methodologies that combine state-of-the-art contact models with established optimization frameworks to develop methods capable of handling non-smooth contact interactions between deformable bodies. For this purpose, two contact models are investigated: the mortar method and the third medium contact method.
This thesis presents the underlying theory of frictionless contact, starting from the continuum formulation where both the mortar and third medium contact formulations are described as optimization problems. Numerical aspects of the contact modeling are discussed, after which the structural optimization framework is described. The proposed research methods are then presented in five appended papers.
Papers A and E explore the third medium contact model. In paper A the model is used to design metamaterials that can utilize internal contact using inverse homogenization and both shape and topology optimization. Paper E develops a new regularization method based on a rotation measure in the third medium that improves the efficacy of the model. In paper B, the mortar method is used to design axisymmetric structures for energy absorption using spline-based shape optimization. A contact aware shape optimization technique is developed in paper C which provides additional robustness to the optimization. This method is extended in paper D where the contact aware shape optimization is combined with topology optimization to provide additional design freedom.
(Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/a6b5b98c-0b19-481c-824f-578838b2cf72
- author
- Sjövall, Filip
LU
- supervisor
- opponent
-
- Prof. Duysinx, Pierre, University of Liege, Belgium.
- organization
- publishing date
- 2025
- type
- Thesis
- publication status
- published
- subject
- keywords
- Structural Optimization, Shape Optimization, Topology Optimization., Contact mechanics, Frictionless contact, Finite strains
- publisher
- Division of Solid Mechanics, Box 118, 221 00 Lund, Sweden,
- defense location
- Lecture Hall M:E, building M, Ole Römers väg 1F, Faculty of Engineering LTH, Lund University, Lund.
- defense date
- 2026-01-23 09:00:00
- ISBN
- 978-91-8104-751-6
- 978-91-8104-752-3
- language
- English
- LU publication?
- yes
- id
- a6b5b98c-0b19-481c-824f-578838b2cf72
- date added to LUP
- 2025-12-15 10:46:21
- date last changed
- 2025-12-17 03:34:09
@phdthesis{a6b5b98c-0b19-481c-824f-578838b2cf72,
abstract = {{Structural optimization aims to find the geometry of the best performing design in a predefined setting, using mathematical techniques. The motivation for this study can be categorized into three main benefits: efficient material usage, enhancing existing designs and enabling new technologies. All of these benefits are crucial for solving contemporary technological and environmental challenges. <br/><br/>An important topic of mechanical analysis is contact mechanics, which has been considered scarcely in structural optimization. Previous works have mainly considered linear elastic structures, often in contact with rigid supports, which limits the applicability to practical examples. The research herein investigates new structural optimization methodologies that combine state-of-the-art contact models with established optimization frameworks to develop methods capable of handling non-smooth contact interactions between deformable bodies. For this purpose, two contact models are investigated: the mortar method and the third medium contact method. <br/><br/>This thesis presents the underlying theory of frictionless contact, starting from the continuum formulation where both the mortar and third medium contact formulations are described as optimization problems. Numerical aspects of the contact modeling are discussed, after which the structural optimization framework is described. The proposed research methods are then presented in five appended papers. <br/><br/>Papers A and E explore the third medium contact model. In paper A the model is used to design metamaterials that can utilize internal contact using inverse homogenization and both shape and topology optimization. Paper E develops a new regularization method based on a rotation measure in the third medium that improves the efficacy of the model. In paper B, the mortar method is used to design axisymmetric structures for energy absorption using spline-based shape optimization. A contact aware shape optimization technique is developed in paper C which provides additional robustness to the optimization. This method is extended in paper D where the contact aware shape optimization is combined with topology optimization to provide additional design freedom.<br/>}},
author = {{Sjövall, Filip}},
isbn = {{978-91-8104-751-6}},
keywords = {{Structural Optimization; Shape Optimization; Topology Optimization.; Contact mechanics; Frictionless contact; Finite strains}},
language = {{eng}},
publisher = {{Division of Solid Mechanics, Box 118, 221 00 Lund, Sweden,}},
school = {{Lund University}},
title = {{Structural optimization for frictionless contact}},
url = {{https://lup.lub.lu.se/search/files/235901234/e.spik_ex_Filip.pdf}},
year = {{2025}},
}