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Francesco Tornabene - One of the best experts on this subject based on the ideXlab platform.
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a posteriori stress and strain Recovery Procedure for the static analysis of laminated shells resting on nonlinear elastic foundation
Composites Part B-engineering, 2017Co-Authors: Francesco Tornabene, Nicholas Fantuzzi, Michele Bacciocchi, J N ReddyAbstract:Abstract The numerical analysis of laminated composite plates and shells resting on nonlinear elastic foundation is the main topic of the paper. The generalized differential quadrature (GDQ) technique and the Newton-Raphson iteration are employed to obtain the solution of the static problems under consideration. The nonlinear elastic foundation is modeled using the Winkler-Pasternak model embedded with quadratic and cubic nonlinearities in order to a have a more complete description of the interaction. The structural behavior is modeled by means of higher-order displacement fields developed in the framework of a unified formulation. Several lamination schemes are studied. The class of sandwich structures with an inner soft-core is also taken into account with the help of the Murakami’s function, which correctly captures the so-called zig-zag effect. The presented approach can deal with doubly-curved surfaces characterized by two radii of curvature that can vary in each point of the reference domain, whereas most of the examples available in the literature considers only shells with constant curvature, such as spherical and cylindrical shells. Solutions are presented in terms of through-the-thickness variations of strains, stresses, and displacements. For these purposes, a posteriori Recovery Procedure based on the GDQ method is introduced. The accuracy and effectiveness of the proposed approach are proven by means of the comparison with the numerical results obtained by a three-dimensional finite element model.
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generalized stress strain Recovery formulation applied to functionally graded spherical shells and panels under static loading
Composite Structures, 2016Co-Authors: Erasmo Viola, Nicholas Fantuzzi, Luigi Rossetti, Francesco TornabeneAbstract:Abstract The present investigation concludes the triad of papers by the first three authors concerning the 2D-unconstrained third order shear deformation theory for shell-like structures. Here, the static behavior of functionally graded spherical shells and panels subjected to uniform loadings at the extreme surfaces is studied. The material properties are graded in the thickness direction according to a four parameter power law. The structural model involves the a posteriori stress and strain Recovery Procedure. The obtained governing equations are solved by means of the GDQ numerical technique. An extensive numerical investigation is carried out to characterize the effect of material parameters on the stress, strain and displacement profiles along the thickness direction. The second order equilibrium operators, of the fundamental system of equations for functionally graded spherical shells and panels, are reported in the extended form.
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Inter-laminar stress Recovery Procedure for doubly-curved, singly-curved, revolution shells with variable radii of curvature and plates using generalized higher-order theories and the local GDQ method
Mechanics of Advanced Materials and Structures, 2016Co-Authors: Francesco Tornabene, Nicholas Francesco, Erasmo ViolaAbstract:ABSTRACTThe stress and strain Recovery Procedure already applied for solving doubly-curved structures with variable radii of curvature has been considered in this article using an equivalent single layer approach based on a general higher-order formulation, in which the thickness functions of the in-plane displacement parameters are defined independently from the ones through the shell thickness. The theoretical model considers composite structures in such a way that employs the differential geometry for the description of doubly-curved, singly-curved, revolution with variable radii of curvature and degenerate shells. Furthermore, the structures at hand can be laminated composites made of a general stacking sequence of orthotropic generically oriented plies. The governing static equilibrium equations are solved in their strong form using the local generalized differential quadrature (GDQ) method. Moreover the generalized integral quadrature (GIQ) is exploited for the evaluation of the stress resultants of...
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static analysis of doubly curved anisotropic shells and panels using cuf approach differential geometry and differential quadrature method
Composite Structures, 2014Co-Authors: Francesco Tornabene, Nicholas Fantuzzi, Erasmo Viola, Erasmo CarreraAbstract:The present paper investigates the static behavior of doubly-curved laminated composite shells and panels. A two dimensional General Higher-order Equivalent Single Layer (GHESL) approach, based on the Carrera Unified Formulation (CUF), is proposed. The geometry description of the middle surface of shells and panels is computed by means of differential geometry tools. All structures have been solved through the generalized differential quadrature numerical methodology. A three dimensional stress Recovery Procedure based on the shell equilibrium equations is used to calculate through-the-thickness quantities, such as displacements components and the strain and stress tensors. Several lamination schemes, loadings and boundary conditions are considered in the worked out applications. The numerical results are compared with the ones obtained with commercial finite element codes. New profiles, concerning displacements, strains and stresses, for doubly-curved multi-layered shell structures are presented for the first time by the authors.
Francesco Ubertini - One of the best experts on this subject based on the ideXlab platform.
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Patch based Recovery in finite element elastoplastic analysis
Computational Mechanics, 2013Co-Authors: Federica Daghia, Stefano De Miranda, Francesco UbertiniAbstract:A new patch based stress Recovery Procedure for elastoplastic analysis is presented in this paper. The formulation derives from the extension to the elastic-perfectly plastic case of the Recovery by Compatibility in Patches Procedure recently proposed by the authors. The present Procedure is designed to simultaneously reconstruct both a new stress field and a new plastic strain field, so to ensure that elastoplastic consistency is satisfied. The numerical results on two common benchmark problems show the effectiveness of the new Procedure.
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On the analysis of thin walled members in the framework of the Generalized Beam Theory
2013Co-Authors: Alejandro Gutierrez, Stefano De Miranda, Rosario Miletta, Francesco UbertiniAbstract:The analysis of thin walled members in the framework of the Generalized Beam Theory (GBT) is critically revised. Firstly, the classic form of the GBT is briefly explained along with its main advantages and problems. Subsequently, a new formulation that coherently accounts for shear deformation is presented along with a unique modal decomposition, the Cross Section analysis, that allows to recover classical shear deformable beam theories exactly. Furthermore, a stress Recovery Procedure for the finite element analysis of GBT beams is proposed as an improvement on the traditional elasto-kinematic approach. Performance is shown in numerical tests.
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Patch based stress Recovery for plate structures
Computational Mechanics, 2011Co-Authors: G. Castellazzi, S. Miranda, Francesco UbertiniAbstract:In this paper we address the application of Recovery Procedures in advanced problems in structural mechanics. The attention is focused on the Recovery by compatibility in patches Procedure (RCP) and shear deformable plate structures. The formulation of RCP Procedure is extended to shear deformable plate problems (Reissner–Mindlin theory) and is applied to recover stresses from mixed and hybrid stress finite elements. These elements offer new possibilities, for Recovery Procedures in general, which deserve to be discussed. A comprehensive investigation on which finite element solution can be used as input for the Recovery Procedures is given through standard benchmark problems, obtained for several values of the thickness on structured and unstructured meshes. The numerical results confirm the effectiveness of the Recovery Procedure extended to plates problems.
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A posteriori error estimation based on the superconvergent Recovery by Compatibility in Patches
International Journal for Numerical Methods in Engineering, 2006Co-Authors: Angela Benedetti, Stefano De Miranda, Francesco UbertiniAbstract:The present work deals with an a posteriori error estimator for linear finite element analysis, based on a stress Recovery Procedure called Recovery by Compatibility in Patches. The key idea of this Procedure is to recover improved stresses by minimizing the complementary energy over patches of elements. Displacements computed by the finite element analysis are prescribed on the boundary of the patch. Here, a new form of this Recovery Procedure is presented. Adopting a different patch configuration, centred upon an element instead of a node, allows to drastically simplify the Recovery process, thus improving efficiency and making the implementation in finite element codes much easier. The robustness tests demonstrate that the error estimator associated to the new form of the Recovery Procedure retains the very good properties of the original one, such as superconvergence. The numerical results on two common benchmark problems confirm the effectiveness of the proposed error estimator, which appears to be competitive with those currently available. Copyright © 2006 John Wiley & Sons, Ltd.
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Patch Recovery based on complementary energy
International Journal for Numerical Methods in Engineering, 2004Co-Authors: Francesco UbertiniAbstract:In this paper a new stress Recovery Procedure is presented. The formulation is very simple and based on improving stresses by enforcing compatibility over local patches of elements. This is obtained by minimizing the complementary energy, properly defined for the patch thought as a separate system, among an assumed set of equilibrated stress fields. The resultant implementation is simple, cost effective and numerically stable. Several numerical tests evidence an excellent performance which promises a wide applicability of the new Procedure. Copyright © 2004 John Wiley & Sons, Ltd.
Gabriel Di Lemos Santiago Lima - One of the best experts on this subject based on the ideXlab platform.
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Harada-Tsutsui Gauge Recovery Procedure: From Abelian Gauge Anomalies to the Stueckelberg Mechanism
Annals of Physics, 2014Co-Authors: Gabriel Di Lemos Santiago LimaAbstract:Abstract Revisiting a path-integral Procedure developed by Harada and Tsutsui for recovering gauge invariance from anomalous effective actions, it is shown that there are two ways to achieve gauge symmetry: one already presented by the authors, which is shown to preserve the anomaly in the sense of standard current conservation law, and another one which is anomaly-free, preserving current conservation. It is also shown that the application of the Harada–Tsutsui technique to other models which are not anomalous but do not exhibit gauge invariance allows the identification of the gauge invariant formulation of the Proca model, also done by the referred authors, with the Stueckelberg model, leading to the interpretation of the gauge invariant map as a generalization of the Stueckelberg mechanism.
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harada tsutsui gauge Recovery Procedure from abelian gauge anomalies to the stueckelberg mechanism
arXiv: General Physics, 2013Co-Authors: Gabriel Di Lemos Santiago LimaAbstract:Revisiting a path-integral Procedure of recovering gauge invariance from anomalous effective actions developed by Harada and Tsutsui, it is shown that there are two ways to achieve gauge symmetry: one already presented by the authors, which is shown to preserve the anomaly in the sense of standard conservation law, and another one which is anomaly-free, preserving current conservation. It is also shown that the aplication of Harada-Tsutsui technique to other models which are not anomalous but do not exhibit gauge invariance allows the identification of the gauge invariant formulation of the Proca model, also done by the referred authors, with the Stueckelberg model, leading to the interpretation of the gauge invariant map as a generalization of the Stueckelberg mechanism.
Nicholas Fantuzzi - One of the best experts on this subject based on the ideXlab platform.
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a posteriori stress and strain Recovery Procedure for the static analysis of laminated shells resting on nonlinear elastic foundation
Composites Part B-engineering, 2017Co-Authors: Francesco Tornabene, Nicholas Fantuzzi, Michele Bacciocchi, J N ReddyAbstract:Abstract The numerical analysis of laminated composite plates and shells resting on nonlinear elastic foundation is the main topic of the paper. The generalized differential quadrature (GDQ) technique and the Newton-Raphson iteration are employed to obtain the solution of the static problems under consideration. The nonlinear elastic foundation is modeled using the Winkler-Pasternak model embedded with quadratic and cubic nonlinearities in order to a have a more complete description of the interaction. The structural behavior is modeled by means of higher-order displacement fields developed in the framework of a unified formulation. Several lamination schemes are studied. The class of sandwich structures with an inner soft-core is also taken into account with the help of the Murakami’s function, which correctly captures the so-called zig-zag effect. The presented approach can deal with doubly-curved surfaces characterized by two radii of curvature that can vary in each point of the reference domain, whereas most of the examples available in the literature considers only shells with constant curvature, such as spherical and cylindrical shells. Solutions are presented in terms of through-the-thickness variations of strains, stresses, and displacements. For these purposes, a posteriori Recovery Procedure based on the GDQ method is introduced. The accuracy and effectiveness of the proposed approach are proven by means of the comparison with the numerical results obtained by a three-dimensional finite element model.
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generalized stress strain Recovery formulation applied to functionally graded spherical shells and panels under static loading
Composite Structures, 2016Co-Authors: Erasmo Viola, Nicholas Fantuzzi, Luigi Rossetti, Francesco TornabeneAbstract:Abstract The present investigation concludes the triad of papers by the first three authors concerning the 2D-unconstrained third order shear deformation theory for shell-like structures. Here, the static behavior of functionally graded spherical shells and panels subjected to uniform loadings at the extreme surfaces is studied. The material properties are graded in the thickness direction according to a four parameter power law. The structural model involves the a posteriori stress and strain Recovery Procedure. The obtained governing equations are solved by means of the GDQ numerical technique. An extensive numerical investigation is carried out to characterize the effect of material parameters on the stress, strain and displacement profiles along the thickness direction. The second order equilibrium operators, of the fundamental system of equations for functionally graded spherical shells and panels, are reported in the extended form.
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static analysis of doubly curved anisotropic shells and panels using cuf approach differential geometry and differential quadrature method
Composite Structures, 2014Co-Authors: Francesco Tornabene, Nicholas Fantuzzi, Erasmo Viola, Erasmo CarreraAbstract:The present paper investigates the static behavior of doubly-curved laminated composite shells and panels. A two dimensional General Higher-order Equivalent Single Layer (GHESL) approach, based on the Carrera Unified Formulation (CUF), is proposed. The geometry description of the middle surface of shells and panels is computed by means of differential geometry tools. All structures have been solved through the generalized differential quadrature numerical methodology. A three dimensional stress Recovery Procedure based on the shell equilibrium equations is used to calculate through-the-thickness quantities, such as displacements components and the strain and stress tensors. Several lamination schemes, loadings and boundary conditions are considered in the worked out applications. The numerical results are compared with the ones obtained with commercial finite element codes. New profiles, concerning displacements, strains and stresses, for doubly-curved multi-layered shell structures are presented for the first time by the authors.
Erasmo Viola - One of the best experts on this subject based on the ideXlab platform.
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generalized stress strain Recovery formulation applied to functionally graded spherical shells and panels under static loading
Composite Structures, 2016Co-Authors: Erasmo Viola, Nicholas Fantuzzi, Luigi Rossetti, Francesco TornabeneAbstract:Abstract The present investigation concludes the triad of papers by the first three authors concerning the 2D-unconstrained third order shear deformation theory for shell-like structures. Here, the static behavior of functionally graded spherical shells and panels subjected to uniform loadings at the extreme surfaces is studied. The material properties are graded in the thickness direction according to a four parameter power law. The structural model involves the a posteriori stress and strain Recovery Procedure. The obtained governing equations are solved by means of the GDQ numerical technique. An extensive numerical investigation is carried out to characterize the effect of material parameters on the stress, strain and displacement profiles along the thickness direction. The second order equilibrium operators, of the fundamental system of equations for functionally graded spherical shells and panels, are reported in the extended form.
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Inter-laminar stress Recovery Procedure for doubly-curved, singly-curved, revolution shells with variable radii of curvature and plates using generalized higher-order theories and the local GDQ method
Mechanics of Advanced Materials and Structures, 2016Co-Authors: Francesco Tornabene, Nicholas Francesco, Erasmo ViolaAbstract:ABSTRACTThe stress and strain Recovery Procedure already applied for solving doubly-curved structures with variable radii of curvature has been considered in this article using an equivalent single layer approach based on a general higher-order formulation, in which the thickness functions of the in-plane displacement parameters are defined independently from the ones through the shell thickness. The theoretical model considers composite structures in such a way that employs the differential geometry for the description of doubly-curved, singly-curved, revolution with variable radii of curvature and degenerate shells. Furthermore, the structures at hand can be laminated composites made of a general stacking sequence of orthotropic generically oriented plies. The governing static equilibrium equations are solved in their strong form using the local generalized differential quadrature (GDQ) method. Moreover the generalized integral quadrature (GIQ) is exploited for the evaluation of the stress resultants of...
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static analysis of doubly curved anisotropic shells and panels using cuf approach differential geometry and differential quadrature method
Composite Structures, 2014Co-Authors: Francesco Tornabene, Nicholas Fantuzzi, Erasmo Viola, Erasmo CarreraAbstract:The present paper investigates the static behavior of doubly-curved laminated composite shells and panels. A two dimensional General Higher-order Equivalent Single Layer (GHESL) approach, based on the Carrera Unified Formulation (CUF), is proposed. The geometry description of the middle surface of shells and panels is computed by means of differential geometry tools. All structures have been solved through the generalized differential quadrature numerical methodology. A three dimensional stress Recovery Procedure based on the shell equilibrium equations is used to calculate through-the-thickness quantities, such as displacements components and the strain and stress tensors. Several lamination schemes, loadings and boundary conditions are considered in the worked out applications. The numerical results are compared with the ones obtained with commercial finite element codes. New profiles, concerning displacements, strains and stresses, for doubly-curved multi-layered shell structures are presented for the first time by the authors.
