Dynamic reduction strategies to extend modal analysis approach at higher frequencies

Modal analysis on huge finite element models requires a numerical simplification in terms of total number of degrees of freedom (d.o.f.'s). The above aim is generally achieved by choosing some master d.o.f.'s and condensing the structure matrices on those d.o.f.'s. Static condensation (i.e. stiffness matrix reduction) is theoretically an errorless operation; on the other hand, mass condensation can only be approximate in dynamic applications. In order to accomplish matrix condensation, the technique mainly used is the so-called Guyan reduction. The present paper outlines the limitations of the technique, introducing some significant improvements. These are related to the inertia conservation properties of the reduced mass matrix and the condensed mass matrix assembly by means of fictitious and appropriate stiffness connections that are different from those obtained by the stiffness model. The effectiveness of the modified approach is demonstrated with respect to the modal analysis results obtained by Guyan approach, through three different test cases. (c) 2007 Elsevier B.V. All rights reserved

Intraplate transtensional tectonics in the East Antarctic Craton: insight from buried subglacial bedrock in the Lake Vostok – Dome C region

""This study presents the results of forward numerical models of a series of sections of the Aurora Trench (East Antarctica). derived from radio echo-sounding data that allowed to reconstruct the 3D shape of the Aurora Fault, a crustal listric. normal fault characterized by a length exceeding 100 km. A similar extensional fault setting allows to replicate the. asymmetric buried morphology of the magnetic basement at the Lake Vostok depression derived by the available gravity. and magnetic profiles. Both the Aurora and Vostok listric fault reach their basal decollment at 34 km depth, possibly. the base of the crust in this intracratonic environment. Integration of these results with the existing geologic interpretations. of the tectonic origin of the Concordia Trench by normal faulting allowed to frame the Concordia, Aurora and. Vostok normal faults within an intraplate transtensional corridor with a left-lateral movement component. The westward. projection of the proposed strike-slip deformation belt may develop in correspondence of an older tectonic lineament. stretching from the Eastern flanks of the Gamburtsev Subglacial Mts to the Lambert rift and characterized by a. poly-phased complex tectonic history. The possible Cenozoic reactivation of these structures is discussed in the paper."

analytical stiffness matrix for curved metal wires

Abstract The paper presents an analytic stiffness matrix for curved thin metal wires, derived by the application of the second Castigliano's Theorem. The matrix accounts both bending and axial stiffness contributions in plane. The beam geometry is described by a cubic polynomial function of the curvature radius with a monotonical attitude angle as the independent variable. The solution proposed if fully analytical although a consistent number of adding factors appear. Some test cases are discussed and compared with Finite Element solutions, formed by a plentiful assembly of straight beams

Influence of coil contact on static behavior of helical compression springs

Large deformations of helical springs are affected by coil contact, but most available spring modelling techniques only account for nonlinear vertical motion, and Finite Elements (FE) nonlinear analysis that considers contact between coils can be very expensive. A 2D model based on equivalent beam and penalty-based contact algorithm is developed for efficient yet realistic prediction of non-uniform spring deflection. The proposed model is tested versus FE, where the helical wire is modelled using beam elements. Two scenarios are taken into account: a cylindrical spring in compression/bending and a progressive conical spring under simple compression. It is shown that the proposed model matches FE at a very low computational cost

Optimal uniform strength design of frame and lattice structures

This paper provides a procedure to obtain the uniform strength of frame and lattice structures. Uniform strength condition is achieved by performing the shape optimization of all beam elements of the structure. The beam shape which guarantees uniform strength is analytically deduced from the one-dimensional Timoshenko model. The optimization problem presents itself as the search for the zeros of the objective-functions vector, which is a non-linear system of equations representing the kinematic-congruence and forces balance at every node of the structure. The analytical formulation of the optimization problem allows to construct the objective-functions vector without the use of external structural computation, i.e. not recurring to any Finite Element Analysis to accomplish iterations. This latter feature entails a great advantage in terms of computing time required to perform optimization. The proposed analytical formulation allows to directly insert the uniform strength condition into the objective-functions vector, transforming the optimization into an unconstrained problem. Some examples are shown in which the performance of the optimization procedure is discussed in terms of robustness and rate of computational complexity while increasing the degrees of freedom of the structure. The reliability and the quality of the optimization are verified through Finite Element Analysis

Modello coesivo per l’avanzamento di fratture mediante rilascio nodale di strutture discretizzate con elementi finiti

La simulazione numerica della propagazione di una frattura in MODO I, viaggiante ad elevatavelocità in un acciaio a comportamento duttile è realizzata attraverso un modello coesivo che governa ladistribuzione delle forze di rilascio nodale. Come noto, la ricerca di un valore di tensione all’apice non ha alcunsenso nel caso elastico; infatti, la tensione può essere valutata solo mediante fattori di campo. Nel caso elasto-plastico, incrudimento e softening di origine geometrica o legato al progressivo danneggiamento influisconodecisamente sull’andamento esponenziale del campo tensionale. È possibile comunque individuare un valore diriferimento, di entità finita, mediante estrapolazione delle tensioni elasto-plastiche nella zona di inizio softeningdella frattura. Tale grandezza può essere presa come fattore di riferimento per il calcolo delle forze di rilasciocoesive e quindi dell’energia dissipata. Nel lavoro viene discusso come determinare, dal campo di tensioneelasto-plastico locale, il valore che governa la zona coesiva al variare del T-stress

Elevation modelling and palaeo-environmental interpretation in the Siwa area (Egypt): Application of SAR interferometry and radargrammetry to COSMO-SkyMed imagery

PublishedJournal Article© 2015 Elsevier B.V. Digital elevation models produced from COSMO-SkyMed imagery were used to delineate palaeo-drainage in a wide area surrounding the Siwa and Al-Jaghbub oases of the western Sahara Desert (Egypt and Libya).This new generation of synthetic aperture radar imagery is suitable for this purpose because of its high spatial resolution and capacity to penetrate dry surface sediments. Different techniques such as radar interferometry and radargrammetry were used to produce digital elevation models. These were assessed for accuracy and then combined to produce a single elevation model of the area. The resulting elevation model was used to support the geological study and palaeo-environmental interpretation of the area. It revealed buried features of the landscape, including inactive palaeo-drainage systems. Drainage features were extracted from the elevation model using geographical information systems; results were combined and assessed with respect to geological field data, as well as data from the literature. Previous studies in the area suggest that a wide river, probably the old Nile River, flowed into the Libyan palaeo-Sirte before the Late Messinian drawdown of the Mediterranean Sea. During the Late Messinian lowering of the sea the fluvial system changed shape and carved deep canyons throughout north-eastern Africa. The reported findings on the key Siwa area were used to precisely delineate the physiography of the modern drainage network and to confirm findings from our previous geological research in the area.We gratefully acknowledge Ruggero Matteucci and Johannes Pignatti (La Sapienza, University of Rome), Francesco Checchi (ENI S.p.A., IOEC), Filippo Bonciani and Debora Graziosi (University of Siena) for their collaboration. Research was supported by the ASI (Id 2262) in the framework of the COSMO-SkyMed Announcement of Opportunity project “Application of COSMO-SkyMed data for geological researches in Egypt and Libya”

An RBF Meshless Approach to Evaluate Strain Due to Large Displacements in Flexible Printed Circuit Boards

Thin plates are very often employed in a context of large displacements and rotations, for example, whenever the extreme flexibility of a body can replace the use of complicated kinematic pairs. This is the case of the flexible Printed Circuit Boards (PCBs) used, for example, within last-generation foldable laptops and consumer electronics products. In these applications, the range of motion is generally known in advance, and a simple strategy of stress assessment leaving out nonlinear numerical calculations appears feasible other than desirable. In this paper, Radial Basis Functions (RBFs) are used to represent a generic transformation of a bi-dimensional plate, with all the derivate fields being analytically achieved without the need for a numerical grid for large-displacement applications. Strains due to bending are easily retrieved with this method and satisfactorily compared to analytical and shell-based Finite Element Method (FEM) benchmarks. On the other hand, the computational costs of the juxtaposed methods appear far different; with the machine being equal, the orders of magnitude of the time elapsed in computation are seconds for the RBF-based strategy versus minutes for the FEM approach