Mini-symposium S4

S4: Shape and Topology Optimization With Finite Elements

Co-chairs: 

Alberto Paganini (University of Leicester)*; Philip Herbert (University of Sussex)

Key words: shape optimization, topology optimization, finite elements

ABSTRACT

Shape and topology optimization are ubiquitous in industrial applications. Classical uses are to improve designs of boat hulls and airplane and car fuselages. These examples are optimization problems constrained to partial differential equations (PDEs) that model the physical response of designs, and hence require numerical methods to compute approximate solutions to PDEs.

This minisymposium is dedicated to the recent advances of shape and topology optimization methods in the framework of finite element approximations of PDE constraints. There exist different competing approaches to shape and topology optimization, with differences mainly due to the modelling of shape and topology updates. A few examples are the Solid Isotropic Material with Penalization (SIMP) method [1], the level-set method with Ersatz material approach [2], and the phase-field method [3].

Computational shape and topology optimization is a very active and lively field of research, and this minisymposium will be an opportunity to present and discuss the latest developments in the field.

REFERENCES

[1] Bendsoe, Martin Philip, and Ole Sigmund. Topology optimization: theory, methods, and applications. Springer Science & Business Media, 2013.

[2] Allaire, Grégoire, François Jouve, and Anca-Maria Toader. "Structural optimization using sensitivity analysis and a level-set method." Journal of computational physics 194.1 (2004): 363-393. 

[3] Garcke, Harald, et al. "Numerical approximation of phase field based shape and topology optimization for fluids." SIAM Journal on Scientific Computing 37.4 (2015): A1846-A1871.