Control of bifurcation structures using shape optimization
Many problems in engineering can be understood as controlling the bifurcation structure of a
given device. For example, one may wish to delay the onset of instability or bring forward a …
given device. For example, one may wish to delay the onset of instability or bring forward a …
Higher-order moving mesh methods for PDE-constrained shape optimization
We present a new approach to discretizing shape optimization problems that generalizes
standard moving mesh methods to higher-order mesh deformations and that is naturally …
standard moving mesh methods to higher-order mesh deformations and that is naturally …
Reproducing kernel Hilbert spaces and variable metric algorithms in PDE-constrained shape optimization
In this paper we investigate and compare different gradient algorithms designed for the
domain expression of the shape derivative. Our main focus is to examine the usefulness of …
domain expression of the shape derivative. Our main focus is to examine the usefulness of …
Level-set based shape optimization for plane elastic structures using radial basis functions and Hilbertian descent direction
P Sobczak, T Sokół - Structural and Multidisciplinary Optimization, 2024 - Springer
Structural optimization problems are often associated with the so-called shape functionals
depending on a shape through its geometry and the state being a solution of given partial …
depending on a shape through its geometry and the state being a solution of given partial …
A priori error analysis of shape derivatives of linear functionals in structural topology optimization
We provide theoretical analyses and numerical comparisons of boundary-based and
volumetric shape derivative expressions of linear objective functionals encountered in …
volumetric shape derivative expressions of linear objective functionals encountered in …
The strip method for shape derivatives
A major challenge in shape optimization is the coupling of finite element method (FEM)
codes in a way that facilitates efficient computation of shape derivatives. This is particularly …
codes in a way that facilitates efficient computation of shape derivatives. This is particularly …