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Low-rank tensors appear to be prosperous in many applications. However, the sets of bounded-rank tensors are non-smooth and non-convex algebraic varieties, rendering the low-rank optimization problems to be challenging. To this end, we…
The use of machine learning techniques to homogenize the effective behavior of arbitrary microstructures has been shown to be not only efficient but also accurate. In a recent work, we demonstrated how to combine state-of-the-art…
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of…
The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…
The geometric form of a building strongly influences its material use, heat losses, and energy efficiency. This paper presents an analytical optimization of L-shaped residential buildings aimed at minimizing the external surface area for a…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
In the present work, a new computational framework for structural topology optimization based on the concept of moving deformable components is proposed. Compared with the traditional pixel or node point-based solution framework, the…
Topology design optimization offers tremendous opportunity in design and manufacturing freedoms by designing and producing a part from the ground-up without a meaningful initial design as required by conventional shape design optimization…
Optimization of large structures of multiple components is essential to many industries for minimizing mass, especially the design of aerospace vehicles. Optimizing a single primary load member independently of all other primary structures…
Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…
Plasticity is inherent to many engineering materials such as metals. While it can degrade the load-carrying capacity of structures via material yielding, it can also protect structures through plastic energy dissipation. To fully harness…
Much work has been done in topology optimization of multiscale structures for maximum stiffness or minimum compliance design. Such approaches date back to the original homogenization-based work by Bends{\o}e and Kikuchi from 1988, which…
This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…
In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…
This paper implements topology optimization on two-dimensional manifolds. In this paper, the material interpolation is implemented on a material parameter in the partial differential equation used to describe a physical field, when this…
This study presents a topology optimization scheme for realizing a bound state in the continuum along an open acoustic waveguide comprising a periodic array of elastic materials. First, we formulate the periodic problem as a system of…
Porous structures are materials consisting of minuscule pores, where the microstructure morphology significantly impacts their macroscopic properties. Integrating different porous structures through a blending method is indispensable to…
Topology optimization methods face serious challenges when applied to structural design with fluid-structure interaction (FSI) loads, specially for high Reynolds fluid flow. This paper devises an explicit boundary method that employs…
A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification…
The area of topology optimization of continuum structures of which is allowed to change in order to improve the performance is now dominated by methods that employ the material distribution concept. The typical methods of the topology…