497 research outputs found
Computational Shell Mechanics by Helicoidal Modeling, II: Shell Element
No full textThe virtual work of stresses developed in Part I for the helicoidal shell model and then reduced to the material surface is taken as one term of a variational principle stated on a two-dimensional domain. The other terms related to the external loads and to the boundary constraints are added here and include a weak-form treatment of the constraints, which becomes necessary in the context of helicoidal modeling. All terms are cast in incremental form and yield a linearized variational principle of the virtual work type for two-dimensional continua, endowed with an internal constraint conjugate to an extra stress field that is able to control the drilling degree of freedom. The virtual functional and the virtual tangent functional are approximated by the finite element method, using helicoidal interpolation for the kinematic field (which ensures objectivity and path independence) and a uniform representation for the extra stress field. A low-order four-node shell element is obtained, with 6 degrees of freedom per node and a unique stress-vector discrete unknown per element. Several test cases demonstrate the performance of the element and its outstanding locking-free behavior
Marco Cavallo's archipelago
No full textBasaglia Park is the symbol of borders and collapsing walls. Architecture is a way to tell stories and the story we wanted to tell is that of falling walls: Basaglia Park becomes the meeting point of 11 cities that, through 11 "madmen" (G. Deleuze, H. Bosch, F. Pessoa, W. Benjamin, J. Joyce, Rembrandt, F. Kafka, S. Freud, P. Pažic, Homer, R. Gary), becomes a city and of this last city, Marco Cavallo takes fragments to form a tower on legs ("walking archipelago") for a journey that – we hope - takes him beyond certain boundaries – human, social, political... Marco Cavallo's archipelago is a manifesto for Europe
L'arcipelago di Marco Cavallo
No full textIl Parco Basaglia è il simbolo dei confini e dei muri che cadono. L'architettura è un modo per raccontare storie e la storia che abbiamo voluto raccontare è quella di muri che cadono: il Parco Basaglia diventa il punto di incontro di 11 città che, tramite 11 "pazzi" (G. Deleuze, H. Bosch, F. Pessoa, W. Benjamin, J. Joyce, Rembrandt, F. Kafka, S. Freud, P. Pažic, Omero, R. Gary), diventa una città e di quest'ultima città, Marco Cavallo prende dei frammenti per formare una torre su zampe ("walking arcipelago") per un viaggio che – lo speriamo – lo porta oltre certi confini – umani, sociali, politici...
L'arcipelago di Marco Cavallo è un manifesto per l'Europa
Computational Shell Mechanics by Helicoidal Modeling, I: Theory
No full textStarting from recently formulated helicoidal modeling in three-dimensional continua, a low-order kinematical model of a solid shell is established. It relies on both the six degrees of freedom (DOFs) on the reference surface, including the drilling DOF, and a dual director - six additional DOFs - that controls the relative rototranslation of the material particles within the thickness. Since the formulation pertains to the framework of the micropolar mechanics, the solid shell mechanical model includes a workless stress variable - the axial vector of the Biot stress tensor, referred to as the Biot-axial - that allows us to handle nonpolar materials. The local Biot-axial is approximated with a linear field across the thickness and relies on two vector parameters. On the reference surface, the dual director is condensed locally together with one Biot-axial parameter, leaving the surface strains and the other Biot - axial parameter as the basic variables governing the two-dimensional internal work functional. The continuum-based shell mechanics are cast in weak incremental form from the beginning. They yield the two-dimensional nonlinear constitutive law of the shell in incremental form, built dynamically along the solution process. Poisson thickness locking, related to the low-order kinematical model, is prevented by a dynamical adaptation of the local constitutive law. No hypotheses are introduced that restrict the amplitudes of displacements, rotations, and strains, so the formulation is suitable for computations with strong geometrical and material nonlinearities, as shown in Part II
The Helicoidal Modeling in Computational Finite Elasticity. Part I: Variational Formulation
No full textThe finite elasticity mechanics of continua capable of a polar description is formulated by an alternative modeling to keeping position and orientation as uncoupled fields. The rototranslation between two material particles can be described by a single, complex tensorial quantity, which is recognized to be orthogonal. Its linearization gives the characteristic curvature and differential vectors underlying the helicoidal modeling in both the sense of the body geometric description and the evolution of a deforming body. After due introduction to dual tensors and rototranslations, the polar description of the continuum is addressed, with particular care to mixed differentiations of the rototranslation field. Then, a thorough variational framework is established for the most general polar continuum under hyperelasticity hypothesis, and the three-field, two-field and one-field principles are drawn and linearized. The proposed modeling is expected to be profitably exploited in non-linear finite element analyses of solids undergoing finite displacements, rotations and strain
Consistency Issues in Shell Elements for Geometrically Nonlinear Problems
No full textSome singular concepts and non-standard practices in the FEM solution of geometrically nonlinear shell problems are highlighted and discussed. In particular, four issues are addressed. (i) The question of the drilling rotation: a shell is essentially a non-polar medium in its tangent plane, so the drilling rotation is a redundant d.o.f. to be defined by an extra stress field, and the latter ought to hold as a primary unknown field of the surface mechanics. It is shown that a proper constitutive characterization and a sound variational formulation lead to a full micropolar setting of the shell mechanics with a true three-parametric rotation tensor. (ii) The interpolation of the orientation field on the shell surface. It is shown that an interpolation scheme firmly abiding by the rules of the SO(3) group leads naturally to frame-invariant and path-independent finite elements. (iii) The linearization of the virtual functional. Again, an approach fully complying with the special orthogonal group allows an easy and correct resolution of the mixed virtual-incremental variation variables that issue in nonlinear variational formulations involving finite rotations. (iv) The question of a good discrete representation of curved surface geometries. It is shown that a pole-based kinematics built on an integral orthogonal oriento-position field leads to a fair approximation of curved geometries and allows to build low-order finite elements that are naturally locking-free
Erratum: The helicoidal modeling in computational finite elasticity. Part II: Multiplicative interpolation (vol 41, pg 5383, 2004)
No full textOn Successive Differentiations of the Rotation Tensor: an Application to Nonlinear Beam Elements
No full textSuccessive differentiations of the rotation tensor are characterized by successive differential rotation vectors. Useful expressions of the differential rotation vectors for differentiations up to third order are derived. In the context of the exponential parameterization, explicit expressions for the differential maps (the maps providing the differential rotation vectors from the differentials of the parameters chosen) are obtained by resorting to an original infinite family of recursive subexponential maps. Useful properties of the mapping tensors are discussed. The formulation is appropriate for nonlinear problems of computational solid mechanics, when spatial, incremental, and virtual variations of particle orientations must be dealt with together. As an application, the classical problem of modeling space-curved slender beams by finite elements is considered. The variational formulation and the nonlinear interpolation of the orientations, together with the relevant linearizations, consistently exploit the proposed differentiations and lead to an objective beam element. Two test cases are discussed
Il "rumore di fondo" è una cosa seria
No full textThe balance between the monumentality of grand designs and the ordinariness of the urban fabric that marks the tradition of the European city seems to have partially undergone a crisis. At the same time, the welfare state has difficulties in ensuring diffusion and high-level of public services, due to critical economic conditions. Because of the lack of urban quality and of the difficulty in responding to the needs of daily life it is necessary to focus on the construction and ‘care’ of the ordinary city, intended as chains of common places and services, a hyper-familiar space, with no exceptional elements. How to intervene in the ordinary city is the question and it needs to be investigated, both in projects of physical modification and in policies of urban management, usually thought separately. The article starts to question and explore this field of research - which needs to be regenerated in planning but also in architecture and public policies
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