305,167 research outputs found
Vibration of Thin-Walled Tubes in Thermal Environment
No full textVibrations induced by fast varying thermal gradients were first investigated by Boley in the Fifties with respect to the case of beams operating in extra-atmospheric microgravity environment. Indeed, spacecrafts and orbiting satellites crossing from the Earth’s shadow into sunlight experience rapid changes in the thermal loading due to the solar radiation. Such loading is responsible of time dependent bending moments and transverse shear forces on appendages and booms. Those are typically lightweight structures having high flexibility with low frequency and damping characteristic. The thermally-induced bending moment produces a sudden deflection of such flexible structures, accompanied by a change of sunlight incidence angle. These two set up the onset of vibrations with fluctuating moment that could not be correctly analyzed if the inertia effect and the coupling between temperature and strain fields are not taken into account. A correct comprehension of the phenomenon is of interest since thermally-induced vibrations may interfere with system operations of booms, often carrying a payload for measurement. In the worst cases thermal flutter, a self-excited vibration of increasing amplitudes, may lead to the failure of the structural member. In problems in which thermal effect induces deflections and vibrations of a slender body, thermal conductivity, material stiffness and mass density play an important role. If correctly selected these properties could improve the material robustness against deflection and oscillation. Hence, the question is if indeed does exist a certain combination of those material properties which can help to lower deflections and damp oscillations. In the proposed contribution a cantilever beam with a circular hollow cross-section is considered and the possibility to protect the beam from thermal effects by optimizing the structure of the cross-sectional wall is investigated. Some preliminary results seem encouraging and may pave the way for passive control of deflection and thermal flutter effects
Dynamics of an axially functionally graded beam under axial load
No full textThis paper considers the dynamics of a simply supported
beam under axial time–dependent load. The beam is made of an axially
functionally graded material. The motion equations are deduced
from the equilibrium in deformed configuration and no restriction is
made on the amplitude of the transversal displacement, but that naturally
imposed by the inextensibility assumption that is adopted in the
present study. The transversal motion equation, that is a partial differential
equation, is approximated by its Taylor expansion until third
order and then discretized through the Galerkin procedure
Comparing Numerical solution for propagation of brittle fractures based on lacal energy minimization with classical fractures mechanical results
No full textThe Complex Architecture of the Vault System of an Early Medieval Church
No full textThe present work focuses on the solid modeling of the church of Santa Sofia in Benevento,
Italy, and is related to a multidisciplinary research project that involved methods typical to both the
humanities and mathematical engineering. Starting from the history of the church and its current
configuration, a twofold objective is pursued: to give a brief account of the methodology used to
analyze and virtualize the main phases of Santa Sofia and to report on the problem of modeling the
church vault complex. Indeed, the 3D modeling of the church presented different levels of difficulty
with some parts very easy to draw and others calling for specific geometrical analysis. In particular, to
reconstruct the complex system of vaults of the church, a home-made code based on remapping Coons
patches was written. The resulting 3D models of the different archeological and architectural phases
of Santa Sofia are an example of virtual heritage and, being a digital content, allow for immediate
sharing both to the scientific community and to a general and nonexpert audience, keeping in mind
that knowledge is the means used to ensure the enhancement and preservation of cultural heritage
Newton vs. Euler–Lagrange approach, or how and when beam equations are variational
Full text linkThere is a clear and compelling need to correctly write the equations of motion of structures in order to adequately describe their dynamics. Two routes, indeed very different from a philosophical standpoint, can be used in classical mechanics to derive such equations, namely the Newton vectorial approach (i.e., roughly, sum of forces equal to mass times acceleration) or the Euler–Lagrange variational formulation (i.e., roughly, stationarity of a certain functional). However, it is desirable that whichever derivation strategy is chosen, the equations are the same. Since many structures of interest often consist of slender and highly flexible beams operating in regimes of large displacement and large rotation, we restrict our attention to the Euler-Bernoulli assumptions with a generic initial configuration. In this setting, the question that arises is: What conditions must the constitutive assumptions satisfy in order for the equations of motion obtained by Newton’s approach to be identical to the Euler–Lagrange equations derived from an appropriate Lagrangian, natural or virtual, for any arbitrary initial configuration? The aim of this paper is to try to answer this basic question, which indeed does not have an immediate and simple answer, in particular as a consequence of the fact that bending moment could be related to two different notions of flexural curvature
Numerical applications of free discontinuity problems to folding and fracture
No full textThe aim of the thesis is the application of new numerical methods based on the theory of free discontinuities of E. De Giorgi to challenging fields of relevant practical interest in engineering, such as folding of thin walled tubes and propagation of fracture in brittle solids. Both the mathematical models to describe folding and fracture are based on the minimization of two competing energy forms: a volume and a surface energy. The variational formulation leads to the minimization (under displacement boundary conditions) of a functional F(K;u), where K is the set of discontinuous points of u. In order to perform the numerical search for the minimum of F, a powerful open code (developed by K. Brakke) named Surface Evolver has been adapted according to the purposes of the research at hand. Since the energy is non-convex the solution obtained through the algorithm is strongly dependent on the initial point. Starting from an initial faceted surface, the numerical code evolves the surface towards minimum energy through the nonlinear conjiugate gradient method
Virtualization for Knowledge and Protection: The Case of an Early Medieval Church
No full textThepresentpaperbelongstoaresearchfocusingontheearlymedievalchurchofSantaSofia,locatedinBenevento,southernItaly.Thework,ingeneral,involvedmethodstypicalofboththehumanitiesandmathematicalengineering.Thiscontributiongivessomedetailsaboutthechurchandthemethodologyusedtoanalyzeandvirtualizeitsmainphases.Then,attentionisgiventodiscussingtheapproachusedtorecon-structthecomplexvaultingsystemofthechurch.UsingCoonspatchesthatarebasedonHermitecubics,aremappingstrategywasconsideredtomaintaincontrolofalltermsappearingintheapproximation.Theobtainedsurfaceswereinsertedinthevirtualsolidmodelsofthechurch.Itmustbeemphasizedthatsolidmodelingofartifactsofarcheologicalinterestrequiresthatinformationfromdifferentsources,i.e.,geomet-ricandarchitecturaldatawitharcheologicalandarchivalfindings,aremergedtogether.Itisindeedmandatorytoadoptanarcheologicallymeaningfulmethodologytoassessthereliabilityofthevirtualrecon-structions
Minimizzazione con discontinuità libere: applicazioni al folding di tubi in parete sottile
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