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IKP - Mechanics

Topology Optimization

Researcher: Mikael Thellner

Supervisor: Anders Klarbring

Co-supervisor: Joakim Petersson, Bo Torstenfelt

Industrial advisor: Gunnar Björkman Volvo Technological Development

Funding: Intergral Vehicle Structures (IVS)


Designing a product starts with a need to fulfill. The need is developed into requirements for the product. Based on the requirements, concepts for the product are generated and evaluated. The best concepts are further developed ending with the final product. If the concepts fail to fulfill the requirements, new concepts need to be generated. For structural design, this process can be improved by using structural optimization. Using structural optimization will in one sense reverse the design process. Based on the objectives and constraints an optimization problem is formulated and the unknown design is computed instead of first developing a concept and analyzing it to see whether it fulfills the requirements.

Structural optimization means determining the structure with the best objective given a set of constraints. The variables in the optimization are called design variables. Depending on what properties the design variables are describing structural optimization can be divided into different subfields. In shape optimization the design variables are parameters which control the shape of part of the boundary of the structure. If the design variables are some sizing parameters like cross-section area, thickness of beams or plates we talk of size optimization. The most general subfield in structural optimization is topology optimization. In topology optimization a limited amount of material is distributed within a specified design domain. The design variables takes either the value 0, meaning no material, or the value 1, meaning material. Only the design domain and the boundary conditions are specified prior to the optimization and the structure is free to take any shape within the design domain.


Since the initiation in 1988 the development of topology optimization has been steady. Today several commercial software are available. However, to be a flexible and useful tool in structural design, topology optimization needs to be interfaced with other optimization methods such as shape and sizing optimization. Also, the design process needs to be studied, so as to allow for early use of computational methods such as topology optimization. Methods for integrated shape and topology optimization have been studied and further have simultaneous shape and thickness optimization been investigated.

For many years now, structural optimization has become a widely used tool in industry. All these major advances do concern problems where in general there is only one objective function to minimize under constraints. As an example, the most well known case is the minimization of the structural compliance under mass or volume constraint. There is however an increasing need from industry to deal with multidisciplinary optimization, involving multiple objectives and models. In one project multidisciplinary topology optimization is formulated in the game theory framework.

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