Ever since the publication of the 99-line topology optimization MATLAB code (top99) by
Sigmund in 2001, educational articles have emerged as a popular category of contributions …

A critical step in topology optimization (TO) is finding sensitivities. Manual derivation and
implementation of sensitivities can be quite laborious and error-prone, especially for non …

Shape optimization is used to design flexible mechanical metamaterials. We employ the
higher-order moving-mesh method to arbitrarily parameterize the geometries and tune their …

We propose in this paper two kinds of continuity preserving discrete shape gradients of
boundary type for PDE-constrained shape optimizations. First, a modified boundary shape …

We consider a flexible mechanical metamaterial comprising an elastomeric matrix with an
embedded square array of circular holes. First, we use the deflated continuation technique …

PDE-constrained shape optimization has been playing an important role in a large variety of
engineering applications. Traditional mesh-dependent shape optimization methods often …

Soft materials underpin many domains of science and engineering, including soft robotics,
structured fluids, and biological and particulate media. In response to applied mechanical …

For an educational purpose, we develop the Python package AutoFreeFEM which
generates all ingredients for shape optimization with non-linear multi-physics in FreeFEM …

The solution of optimization problems constrained by partial differential equations (PDEs)
plays an important role in many areas of science and industry. In this work we present …

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 …