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A stress-based formulation of the free material design problem with the trace constraint and multiple load conditions PDF Drukuj Email
 A stress-based formulation of the free material design problem with the trace constraint and multiple load conditions. structurak o f
S. Czarnecki, T.Lewiński,
Structural and Multidisciplinary Optimization, 2014 in press
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The paper deals with minimization of the weighted sum of compliances related to the load cases applied non-simultaneously. The design variables are all components of the Hooke tensor, subject to the isoperimetric condition bounding the integral of the sum of the Kelvin moduli. This free material design problem is reduced to an equilibrium problem – in two formulations – of an effective body with locking. The stress-based formulation reduces to minimization of an integral of a certain norm of stress fields over the stress fields which equilibrate the given loads. The equivalent displacement-based formulation involves a locking locus defined by using a norm being dual to the previous one. The optimal Hooke tensor is determined by using the stress fields solving the auxiliary locking problem. To make the optimal Hooke tensor positive definite one should consider at least 3 load conditions in the 2D case and not less than 6 load conditions in the 3D case.
 
Recovery of two-phase microstructures of planar isotropic elastic composites PDF Drukuj Email
10th World Congress on Structural and Multidisciplinary Optimization
May 19-24,2013, Orlando,Florida, USA

Recovery of two-phase microstructures of planar isotropic elastic composites
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Abstract
The isotropic elastic mixtures composed of two isotropic materials of the bulk moduli and shear moduli are characterized by the effective bulk and shear moduli. In the planar problems the theoretically
admissible pairs, for given volume fraction ρ 0 of material, lie within a rectangular domain of vertices determined by the Hashin-Shtrikman bounds. The tightest bounds in 2D known up till now are due to
Cherkaev and Gibiansky (CG). The microstructures corresponding to the interior of the CG area can be of arbitrary rank, in the meaning of the hierarchical homogenization. In the present paper a family of composites is constructed of the underlying microstructures of rank 1. The consideration is confined to the microstructures possessing rotational symmetry of angle 1200. To find the effective moduli the homogenization method is used: the local basic cell problems are set on a cell Y of the shape of a hexagonal domain. The periodicity conditions refer to the opposite sides of Y. Such a non-conventional basic cell choice generates automatically the family of isotropic mixtures. The subsequent points are found by solving the inverse homogenization problems with the isoperimetric condition expressing the amounts of both the materials within the cell. The isotropy conditions, usually explicitly introduced into the inverse homogenization formulation, do not appear, as being fulfilled by the microstructure construction. The method put forward makes it possible to localize each admissible pair by appropriate choice of the layout of both the constituents within the repetitive sub-domain of Y.
Keywords: isotropic composites, inverse homogenization, recovery of microstructures.
 
Two-phase isotropic composites with prescribed bulk and shear moduli PDF Drukuj Email
Two-phase isotropic composites with prescribed bulk and shear moduli.
T. Łukasiak
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ABSTRACT: The paper deals with the inverse homogenization problem: to reconstruct the layout of two elastic and isotropic materials given by bulk and shear  moduli within a hexagonal (2D) pe-
riodicity cell, corresponding to the predefined values of the bulk and shear moduli, of the effective isotropic composite and to the given isoperimetric condition concerning the volume fractions. The effective
isotropic moduli are computed according to the homogenization algorithm, with using appropriate Finite Elements (FE) techniques along with periodicity assumptions. The inverse problem thus formulated can be ef-
fectively solved numerically by the Sequential Linear Programming (SLP) method. The isotropy conditions, usually explicitly introduced into the inverse homogenization formulation, do not appear in the algorithm, as
being fulfilled by the microstructure construconstruction. The rotational symmetry of angle 120o of the resulting representative volume element is assumed.
 
Teoretyczne podstawy budownictwa PDF Drukuj Email
mono-t4-iW serii "Monografie Wydziału Inżynierii Ladowej" ukazał się tom IV monografii "Teoretyczne podstawy budownictwa. Mechanika techniczna", OWPW Warszawa 2013, ISBN 978-83-7814-190-7. W pracy znajdują się następujące rozdziały pracowników naszego Zakładu:
B. Grzeszykowski, G. Jemielita. Nieliniowe zagadnienia belki, s. 55-64
W. Gilewski, A. Kasprzak, Kontynualny opis wpływu samonaprężeń na własności modułów tensegrity, s. 117-126
R. Czubacki, T. Sokół, Optymalizacja kratownic z uwzglednieniem wyboczenia prętów, s. 127-136
T. Łukasiak, Wyznaczanie efektywnych parametrów konstytutywnych kompozytów periodycznych za pomocą systemu Ansys, s. 137-150
K. Hetmański, G. Jemielita, Z. Kozyra, Numeryczna weryfikacja wyznaczania sił przekrojowych w płytach z wykorzystaniem MES, s. 151-158
Z. Kacprzyk, Wstęp do analizy izogeometrycznej, s.159-168

 
Industrial Mathematics PDF Drukuj Email
indu mathBiuro ds. Projektu "Program Rozwojowy Politechniki Warszawskiej" opublikowało pracę "Issues in Industrial Mathematics"   pod redakcją P. Grzegorzewskiego i T. Rzeżuchowskiego, Politechnika Warszawska, Warszawa 2013,  ISBN 978-83-937260-0-4. W pracy znalazły sie dwa referaty pracowników Zakładu:
G. Dzierżanowski, On the Optimal Design of Civil Engineering Structures, pp. 87-97
W. Gilewski, An Introduction to Engineering for Industrial Mathematicians, pp. 23-33
 
Twenty Years of The Dekaban Program at The University of Michigan and Politechnika Warszawska PDF Drukuj Email
dekabanNa seminarium z okazji 20 lecia programu Dekaban z naszego Zakładu prezentowane były następujące referaty:
S.Czarnecki, Edgewort-Pareto optimal trusses of least compliance
, pp.64-76, Mechanics and Materials, ed. S. Jemioło and M. Lutomirska, Warsaw University of Technology, Warsaw 2013
T. Łukasiak, Numerical homogenization of materials with periodic microstructure - computation of effective elastic moduli, pp-77-86, Mechanics and Materials, ed. S. Jemioło and M. Lutomirska, Warsaw University of Technology, Warsaw 2013
T. Sokół, Numerical approximations of exact Michell solutions using the adaptive ground atructure approach, pp. 87-98, Mechanics and Materials, ed. S. Jemioło and M. Lutomirska, Warsaw University of Technology, Warsaw 2013
 
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