Papers by Author: Jan Zeman

Abstract: The Extended Finite Element Method (XFEM) enhances the approximation space of the standard Finite Element Method (FEM) with functions reflecting local features in order to yield more accurate results with less degrees of freedom. XFEM performance is, thus, closely related to the quality of enrichment functions. Analogously to our previous works, in which we have employed the concept of Wang tiles to assembly microstructure geometries, in this contribution we use Wang tiles to assemble microstructure-informed enrichment functions. We compare two ways of generating the enrichments: (i) inspired by the first-order numerical homogenization and (ii) based on spectral analysis of the global stiffness matrix for the whole set. The methodology and performance of both approaches are illustrated through a linear diffusion problem in two dimensions

Abstract: Optimal design of trusses is a widely developed field of structural optimization. In topology optimization the infinite design space is usually discretized into a finite ground structure defining the set of all feasible joints and bars. In this paper we adopt semidefinite programming (SDP) formulation of the topology optimization that enables us to obtain a globally optimal least compliant truss subjected to the constraints on structural volume and on the fundamental eigenvalue of free vibrations. For a model problem of 3D cantilever truss, we present a comparison of six solvers, namely CSDP, MOSEK, PENLAB, SDPA, SDPT3 and SeDuMi, from which it follows, that SDPA delivers the best computational performance.

Abstract: Preliminary outcomes on a novel modular additive manufacturing technology are presentedin this contribution. The capabilities of the proposed system to synthesize materials with conventionalor meta properties are explored. Two limiting and a single mixed compositions are tested in com-pression in order to reveal both, global and local behaviours of the conglomerates. The experimentalmeasurements are supported by DIC (Digital Image Correlation) observations.