1,720,981 research outputs found
A new rational approach to multi-input multi-output 3D topology optimization
No full textA new 3D topology optimization approach is presented that is based on the singular value decomposition of the input/output transfer matrix of the system. To start with, the input and output vectors, i.e. the acting loads and the quantities of interest for the designer, are chosen and the input-output transfer matrix is derived. Such matrix, say G(p), depends on the vector of the design variables p (the densities at the element level). The singular value decomposition of G(p) is the core of the proposed approach. It provides singular values as well as left and right singular vectors. Singular values are shown to uniquely define a few matrix norms that can be conveniently computed and used as goal functions to be minimized. Left and right singular vectors respectively represent the principal input/output pairs of the system whose gain is the associated singular value. Numerical optimization is pursued via the method of moving asymptotes (MMA) [1] that calls for the semi-analytic computations of objective functions and constraints. The results of a few 3D numerical investigations are presented and discussed in much detail. An in-house Matlab code developed for the sake of this paper, and based on the ones presented in [2] and [3], is provided in full as an Appendix to the paper
Topology optimization of dynamic systems under uncertain loads: An H infinity-norm-based approach
No full textAn innovative approach to topology optimization of dynamic system is introduced that is based on the system transfer-function H 1 -norm. As for the structure, the proposed strategy allows to determine the optimal material distribution that ensures the minimization of a suitable goal function, such as (an original definition of) the dynamic compliance. Load uncertainty is accounted for by means of a nonprobabilistic convex-set approach (Ben-Haim and Elishakoff, 1990, Convex Models of Uncertainty in Applied Mechanics, Elsevier Science, Amsterdam). At each iteration, the worst load is determined as the one that maximizes the current dynamic compliance so that the proposed strategy fits the so-called worst case scenario (WCS) approach. The overall approach consists of the repeated solution of the two steps (minimization of the dynamic compliance with respect to structural parameters and maximization of the dynamic compliance with respect to the acting load) until convergence is achieved. Results from representative numerical studies are eventually presented along with extensions to the proposed approach that are currently under development
Using multiple singular values in topology optimization of dynamic systems
No full textWithin the general framework of frequency-domain topology optimization of Multi Input-Multi Output (MI-MO) dynamic systems, suitable norms of the input/output transfer matrix are introduced as possible merit functions to be minimized. Among them, the by now classical H∞-norm (i.e. the supremum of the maximum singular value over the whole frequency range), and the so-called nuclear norm (i.e. the sum of all the positive singular values are considered. Heuristic motivations are given that suggest which norm should one choose according to the practical objective to be pursued alongside a few numerical examples on topology optimization of 2D linear-elastic multiload SI-SO and MI-MO dynamic systems
Static and dynamic topology optimization: an innovative unifying approach
Full text linkThis paper presents a topology optimization approach that is innovative with respect to two distinct matters. First of all the proposed formulation is capable to handle static and dynamic topology optimization with virtually no modifications. Secondly, the approach is inherently a multi-input multi-output one, i.e., multiple objectives can be pursued in the presence of multiple loads. The input-to-output transfer matrix, say G, is the key ingredient that governs the algebraic mapping between applied loads and structural response. In statics G depends on the design variables only, whereas it depends on the frequency variable as well in the dynamic case. The Singular Value Decomposition (SVD) of G represents then the core of the proposed approach. Singular values are shown to be the gains of the input/output mapping and are used to compute proper norms of G that represent the goal functions to be minimized. Singular vectors provide at no extra cost the plant directions, i.e., the load combination factors that stress the structure the most. Numerical examples are discussed in much detail and open issues object of ongoing investigations are highlighted. A full Matlab code handling the static topology optimization problem is provided as an online Appendix to the manuscript. Its extension to the dynamic case may be gathered following the formulation proposed in Sect. 5
Paolo Venini, P. Papini Stati Thebaidos Liber XI. Introduction, texte, commentaire et traduction
No full textVerdière Raoul. Paolo Venini, P. Papini Stati Thebaidos Liber XI. Introduction, texte, commentaire et traduction. In: L'antiquité classique, Tome 41, fasc. 1, 1972. pp. 330-332
Modal identification of storage racks for cheese wheels
Full text linkDuring the Emilia-Romagna earthquake (2012), a great number of steel racks used to store cheese wheels collapsed, causing a non-negligible damage to the Italian economy. Therefore, for similar structures that survived and are in service, a deep investigation towards the assessment of their effective safety is required. In the seismic analysis of these frames, the mechanical constraint acting onto the racks due to the reinforced concrete sidewalls, possible nonlinearities exhibited by the base-plate joints and the in-plane restraint provided by wooden boards that connects adjacent columns should be carefully modelled to ensure realistic design results. In the paper, an experimental activity, based on suitable modal identification techniques, is presented to capture the dynamic behaviour of these peculiar structures. The scope is to collect data useful to calibrate numerical finite element models in order to accurately define the aforementioned unknown parameters. Furthermore, a few numerical models based on ideal restraints are herein discussed stressing out non-negligible differences in terms of expected seismic and static response
A rational H∞-norm–based approach for the optimal design of seismically excited reinforced concrete frames
No full textrational approach is presented for minimizing the dynamic response of reinforced concrete framed structures forced by a seismic base acceleration. Reference is made to EC8 regulations, but the presented approach may in principle be applied to structures ruled by any regulation code. Governing equations are set in the frequency domain (and not in the periods domain as usual) so as to enable the adoption of sound approaches for analysis and design of dynamic structures that are typical of automatics. Among these, a novel usage of the H∞‐norm concept is proposed that determines a rational design approach capable to minimize the structural response with reference to any quantity of engineering interest, eg, the overall compliance and the displacement of a specific point or the interstorey drift. A numerical investigation on a 6‐storey 3‐bay frame is performed, and relevant analysis and design results are presented in much detail to validate the theoretical framewor
FREQUENCY-ANALYSIS IN STOCHASTIC LINEARIZATION
No full textFrequancy analysis in stochastic equivalent linearizatio
Reinforced concrete seismically-excited frame design with a new mixed H2/H∞ optimization approach
No full textA new approach is proposed for the optimal design of seismically excited reinforced concrete frames. Unlike most existing methods that do not exploit the input/output relationship between the base acceleration and the structural response, the main feature of the presented approach is to directly shape the input/output transfer function so as to reduce the dynamic amplification factors that govern the structural response. The approach is general with respect to distinctive issues: on the one side the structural output may encompass different quantities of engineering interest such as the overall compliance, the lateral displacement of a representative point (typically the averaged top-storey displacement) and the interstorey drift vector, on the other two system norms may be considered (or a combination thereof) as to the transfer-function amplitude to be minimized, namely the (Formula presented.)-norm and the (Formula presented.)-norm. The former allows to reduce the peak-gain response whereas the latter the squared power energy of the response. By cleverly combining the two, typically by means of a convex combination, one may end up with significant peak gain as well as power response reduction. A numerical investigation on a 2D frame is conducted to validate the theoretical framework that is modeled following Eurocode 8 (CEN in Eurocode 8: design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings. European Standard EN 1998-1, Brussels (2004)) in medium ductility class (DCM) but the method applies to any regulations including modern displacement based codes such as the fib Model Code 2010 (Bulletins Nos. 65/66, Federation Internationale du Beton, Lausanne 2012
Analysis and Damage Identification of a Moderately Thick Cracked Beam Using an Interdependent Locking-Free Element
No full textThe Timoshenko interdependent interpolation element, based on the assumption of cubic interpolation for the transverse displacement and quadratic interpolation for the rotation, is developed for both the static and the dynamic problems. Next, the different behavior of a beam due to the presence of a damaged zone is investigated and the problem of identifying diffused crack affecting a portion of the beam using natural frequencies is studied. The damaged zone can be completely taken into account by introducing only three parameters, and for the inverse problem, numerical optimization is applied to define their values
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