1,720,982 research outputs found
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
Homogenization of random porous materials with low-order virtual elements
Full text linkA fast statistical homogenization procedure (FSHP) based on virtual element method (VEM) - previously developed by the authors has been successfully adopted for the homogenization of particulate random composites, via the definition of the representative volume element (RVE), and of the related equivalent elastic moduli. In particular, the adoption of virtual elements of degree one for modeling the inclusions provided reliable results for materials with low contrast, defined as the ratio between mechanical properties of inclusions and matrix. Porous media are then here described as bimaterial systems in which soft circular inclusions, with a very low value of material contrast, are randomly distributed in a continuous stiffer matrix. Several simulations have been performed by varying the level of porosity, highlighting the effectiveness of FSHP in conjunction with virtual elements of degree one
Analysis and damage identification of a moderately thick cracked beam using an interdependent locking-free element
No full textAnalysis 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
A virtual element approach for micropolar continua
Full text linkIn this work we propose a novel virtual element approach for solving boundary value problems in 2D linear isotropic micropolar elasticity. Following the basic idea of the Virtual Element Method (VEM), the degrees of freedom of each material point, i.e. the displacement and rotation fields, are decomposed into both a polynomial space, either linear or quadratic, and a remaining space that is kept virtual in the formulation. Generalized consistency and stabilization terms are consistently derived. Different patch tests, properly conceived for micropolar continua, are proposed and compared to reference solutions present in literature. The obtained results are in good agreement with these solutions, confirming the capability of the proposed elements in the modelling of the expected responses. The expected applications of this methodology concern the mechanical study of microstructured materials, inherently characterized by nonlocal response, which has been widely proven to be effectively represented by micropolar continua
Optimal sensors placement in dynamic damage detection of beams using a statistical approach
Full text linkStructural monitoring plays a central role in civil engineering; in particular, optimal sensor positioning is essential for correct monitoring both in terms of usable data and for optimizing the cost of the setup sensors. In this context, we focus our attention on the identification of the dynamic response of beam-like structures with uncertain damages. In particular, the non-localized damage is described using a Gaussian distributed random damage parameter. Furthermore, a procedure for selecting an optimal number of sensor placements has been presented based on the comparison among the probability of damage occurrence and the probability to detect the damage, where the former can be evaluated from the known distribution of the random parameter, whereas the latter is evaluated exploiting the closed-form asymptotic solution provided by a perturbation approach. The presented case study shows the capability and reliability of the proposed procedure for detecting the minimum number of sensors such that the monitoring accuracy (estimated by an error function measuring the differences among the two probabilities) is not greater than a control small value
A fast approach to analysis and optimization of viscoelastic beams
No full textA new truly-mixed finite element for the analysis of viscoelastic beams is presented that is based on the additive decomposition of the bending moment in a viscoelastic and a purely elastic contribution. Bending moments are the primary variables that belong to H2(0,l) whereas the kinematic variables (that are the velocities and not the displacements as usual) are globally discontinuous and elementwise linear. As for the peculiarities of the proposed finite element, results from relaxation and creep numerical tests are presented in much detail and a quadratic convergence assessed for all the variables involved. In the second part of the paper, a fast approach to structural (sizing) optimization, set as a topology optimization problem, of such viscoelastic beams is presented in the presence of time-dependent objective functions. Within a gradient-based minimization scheme that is solved via the method of moving asymptotes (Svanberg, 1987), a dual sensitivity analysis approach is derived and representative numerical results presented and discussed in much detail
Micromodels for the in-plane failure analysis of masonry walls with friction: Limit analysis and dem-fem/dem approaches
Full text linkDespite its complexity, the accurate structural modelling of masonry still represents an active field of research, due to several practical applications in civil engineering, with special reference to the preservation and restoration of cultural heritage. In this work a comparison of different models and techniques for the assessment of the mechanical behaviour of two-dimensional block masonry walls subjected to the static action of in-plane loads is presented. Panels are characterized by different height-to-width ratio as well as various masonry textures. Brick-block masonry, perceived as a jointed assembly of prismatic particles in dry contact, is modelled as a discrete system of rigid blocks interacting through contact surfaces unable to carry tension and resistant to sliding by friction, modelled as zero thickness elasto-plastic Mohr-Coulomb interfaces. Different approaches and numerical models are considered: Limit Analysis (LA), Discrete Element Model (DEM) and Finite Ele-ments/Discrete Element Model (FEM/DEM). Limit Analysis is able to provide fast and reliable results in term of collapse multiplier and relative kinematism. Here a standard Limit Analysis is adopted via an own made procedure based on Linear Mathematical Programming, taking into account friction at interfaces
Statistical homogenization of random porous media
Full text linkIn recent times, the scientific community paid great attention to the influence of inherent uncertainties on system behavior and recognize the importance of stochastic and statistical approaches to engineering problems [21]. In particular, statistical computational methods may be useful to the constitutive characterization of complex materials, such as composite materials characterized by non-periodic internal micro-structure. Random porous media exhibit a microstructure made of randomly distributed pores embedded into a continuous matrix. They can be modelled as a bi-material system in which circular soft inclusions (pores) with random distribution and variable diameters are dispersed in a stiffer matrix. A key aspect, recently investigated by many researchers, is the evaluation of appropriate mechanical properties to be adopted for the study of their behaviour. Differently from classical homogenization approaches, in the case of materials with random microstructure it is not possible to 'a-priori' define a Representative Volume Element (RVE), this being an unknown of the problem. Statistical homogenization procedures may be adopted for the definition of equivalent moduli able to take into account at the macroscale the material properties emerging from the internal microstructure with random distribution [26]. Here, a Fast Statistical Homogenization Procedure (FSHP) based on Virtual Element Method (VEM) approach for the numerical solution-previously developed by some of the authors [13] has been adopted for the definition of the Representative Volume Element (RVE) and of the related equivalent elastic moduli of random porous media with different volume fraction, defined as the ratio between mechanical properties of inclusions and matrix. In particular, FSHP with virtual Elements of degree 1 [2] for modelling the inclusions provides reliable results for materials with low contrast
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