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The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…
This article deals with the multiscale modeling of stress transfer characteristics of nano-reinforced polymer composite reinforced with regularly staggered carbon fibers. The distinctive feature of construction of nano-reinforced composite…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
Cellular solids and micro-lattices are a class of lightweight architected materials that have been established for their unique mechanical, thermal, and acoustic properties. It has been shown that by tuning material architecture, a…
This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…
In this paper, a novel and effective formulation based on isogeometric approach (IGA) and Refined Plate Theory (RPT) is proposed to study the behavior of laminated composite plates. Using many kinds of higher-order distributed functions,…
This paper proposes a computational framework for the design optimization of stable structures under large deformations by incorporating nonlinear buckling constraints. A novel strategy for suppressing spurious buckling modes related to…
Fiber reinforced materials (FRMs) can be modeled as bi-phasic materials, where different constitutive behaviors are associated with different phases. The numerical study of FRMs through a full geometrical resolution of the two phases is…
This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…
Shape-morphing structures possess the ability to change their shapes from one state to another, and therefore, offer great potential for a broad range of applications. A typical paradigm of morphing is transforming from an initial…
A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…
Materials like paper, consisting of a network of natural fibres, exposed to variations in moisture, undergo changes in geometrical and mechanical properties. This behaviour is particularly important for understanding the hygro-mechanical…
Functionally Graded Materials (FGMs) made of soft constituents have emerged as promising material-structure systems in potential applications across many engineering disciplines, such as soft robots, actuators, energy harvesting, and tissue…
A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology…
We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…
The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper…
This work is concerned with the micro-architecture of multi-layer material that globally exhibits desired mechanical properties, for instance a negative apparent Poisson ratio. We use inverse homogenization, the level set method, and the…
This paper presents a density-based topology optimization approach considering additive manufacturing limitations. The presented method considers the minimum size of parts, the minimum size of cavities, the inability of printing overhanging…
In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding…