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This work puts forth a new optimal design formulation for planar elastic membranes. The goal is to minimize the membrane's compliance through choosing the material distribution described by a positive Radon measure. The deformation of the…
The paper outlines novel variational technique for finding microstructures of optimal multimaterial composites, bounds of composites properties, and multimaterial optimal designs. The translation method that is used for the exact…
This paper settles the existence question for a rather general class of convex optimal design problems with a volume constraint. In low dimensions, we prove the existence of an optimal configuration for general convex minimization problems…
This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed structures can be realised in a two-step process. One first…
Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…
Optimal packing of objects in containers is a critical problem in various real-life and industrial applications. This paper investigates the two-dimensional packing of convex polygons without rotations, where only translations are allowed.…
We investigate the problem of computing a minimal-volume container for the non-overlapping packing of a given set of three-dimensional convex objects. Already the simplest versions of the problem are NP-hard so that we cannot expect to find…
Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set representation for 2-dimensional data. The first one is an exact…
We introduce a new approach for identifying and characterizing voids within two-dimensional (2D) point distributions through the integration of Delaunay triangulation and Voronoi diagrams, combined with a Minimal Distance Scoring algorithm.…
The design of minimum-compliance bending-resistant structures with continuous cross-section parameters is a challenging task because of its inherent non-convexity. Our contribution develops a strategy that facilitates computing all…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
We prove weak duality between two recent convex relaxation methods for bounding the optimal value of a constrained variational problem in which the objective is an integral functional. The first approach, proposed by Valmorbida et al. (IEEE…
Reconstructing a composition (union) of convex polytopes that perfectly fits the corresponding input point-cloud is a hard optimization problem with interesting applications in reverse engineering and rigid body dynamics simulations. We…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…
We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…
This manuscript presents an approach for simultaneously optimizing the connectivity and elevation of grid-shell structures acting in pure compression (or pure tension) under the combined effects of a prescribed external loading and the…
One of the challenges encountered in optimization of mechanical structures, in particular in what is known as topology optimization, is the size of the problems, which can easily involve millions of variables. A basic example is the minimum…