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Academic literature on the topic 'Carrera's Unified Formulation'

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Published: 14 March 2023

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Journal articles on the topic "Carrera's Unified Formulation"

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Ferreira, A. J. M., C. M. C. Roque, E. Carrera, M. Cinefra, and O. Polit. "Two higher order Zig-Zag theories for the accurate analysis of bending, vibration and buckling response of laminated plates by radial basis functions collocation and a unified formulation." Journal of Composite Materials 45, no. 24 (May 10, 2011): 2523–36. http://dx.doi.org/10.1177/0021998311401103.

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In this article, we combine the Carrera's Unified Formulation, CUF (Carrera E. Theories and Finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking. Arch. Comput. Methods Eng., 2003; 10: 215–297.) and a radial basis function collocation technique for predicting the static deformations, free vibrations and buckling behavior of thin and thick cross-ply laminated plates. We develop by the CUF two Zig-Zag theories according to Murakami's Zig-Zag function. Both theories account for through-the-thickness deformations, allowing the analysis of thick plates. The accuracy and efficiency of this collocation technique for static, vibration, and buckling problems are demonstrated through numerical examples.
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CARRERA, ERASMO, and GAETANO GIUNTA. "REFINED BEAM THEORIES BASED ON A UNIFIED FORMULATION." International Journal of Applied Mechanics 02, no. 01 (March 2010): 117–43. http://dx.doi.org/10.1142/s1758825110000500.

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This paper proposes several axiomatic refined theories for the linear static analysis of beams made of isotropic materials. A hierarchical scheme is obtained by extending plates and shells Carrera's Unified Formulation (CUF) to beam structures. An N-order approximation via Mac Laurin's polynomials is assumed on the cross-section for the displacement unknown variables. N is a free parameter of the formulation. Classical beam theories, such as Euler-Bernoulli's and Timoshenko's, are obtained as particular cases. According to CUF, the governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. The governing differential equations are solved via the Navier type, closed form solution. Rectangular and I-shaped cross-sections are accounted for. Beams undergo bending and torsional loadings. Several values of the span-to-height ratio are considered. Slender as well as deep beams are analysed. Comparisons with reference solutions and three-dimensional FEM models are given. The numerical investigation has shown that the proposed unified formulation yields the complete three-dimensional displacement and stress fields for each cross-section as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam and loading conditions.
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Carrera, E., P. Nali, S. Lecca, and M. Soave. "Effects of In-Plane Loading on Vibration of Composite Plates." Shock and Vibration 19, no. 4 (2012): 619–34. http://dx.doi.org/10.1155/2012/318931.

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This paper deals with the dynamic analysis of pre-stressed laminated composite plates. Particular emphasis is devoted to the case of in-plane mono-axial, biaxial, shear and combined loadings. Both equivalent single layer and layer-wise plate kinematic description are addressed, according to the hierarchical approach proposed by the Carrera's unified formulation. The different kinematic approaches are compared in order to identify the appropriate modeling for laminated composite plates subjected to combined loadings. The principle of virtual displacement is applied in order to obtain governing equations and the corresponding problem is solved through the finite element method. When possible, assessments/comparisons with exact solutions are proposed. Moreover, the effects of different stacking sequences, boundary conditions, geometries and materials on plate natural frequencies are illustrated.
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Alesadi, Amirhadi, Marzieh Galehdari, and Saeed Shojaee. "Free vibration and buckling analysis of cross-ply laminated composite plates using Carrera's unified formulation based on Isogeometric approach." Computers & Structures 183 (April 2017): 38–47. http://dx.doi.org/10.1016/j.compstruc.2017.01.013.

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BRISCHETTO, S. "EFFECT OF THE THROUGH-THE-THICKNESS TEMPERATURE DISTRIBUTION ON THE RESPONSE OF LAYERED AND COMPOSITE SHELLS." International Journal of Applied Mechanics 01, no. 04 (December 2009): 581–605. http://dx.doi.org/10.1142/s1758825109000393.

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This paper considers the thermal stress problem of thick and thin multilayered cylindrical and spherical shells including carbon fiber reinforced layers and/or a central soft core. The following two cases are considered: (i) the temperature distribution in thickness direction is assumed linear; (ii) the temperature distribution in thickness direction is calculated via Fourier's heat conduction equation. Carrera's Unified Formulation and the Principle of Virtual Displacements are used to obtain the governing equations in the case of shells with constant radii of curvature subjected to established temperature conditions on their upper and lower surfaces. Both Equivalent Single Layer and Layer Wise models with an order of expansion in the thickness direction from linear to fourth order are considered. The importance of refined models for a correct evaluation of displacement and stress fields in multilayered shells can be noted. Furthermore, it has been shown that results obtained assuming a linear temperature profile in the thickness direction can be meaningless.
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Cinefra, Maria, and Erasmo Carrera. "Shell Finite Elements for the Analysis of Multifield Problems in Multilayered Composite Structures." Applied Mechanics and Materials 828 (March 2016): 215–36. http://dx.doi.org/10.4028/www.scientific.net/amm.828.215.

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This paper deals with the analysis of layered structures under thermal and electro-mechanical loads. Constitutive equations for multifield are considered and the Principle of Virtual Displacements (PVD) is employed to derive the governing equations. The MITC9 shell finite element based on the Carrera's Unified Formulation (CUF) has been applied for the analysis. The models grouped in the CUF have variable through-the-thickness kinematic and they provide an accurate distribution of displacements and stresses along the thickness of the laminate. The shell element has nine nodes and the Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phenomenon. The finite element analysis of multilayered plates and shells has been addressed. Variable kinematics, as well as layer-wise and equivalent single layer descriptions, have been considered for the presented FEs, according to CUF. A few problems are analyzed to show the effectiveness of the proposed approach. Various laminations, thickness ratios and curvature ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in literature and the analytical solutions obtained using the CUF and the Navier's method.
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Giunta, G., E. Carrera, and S. Belouettar. "Free Vibration Analysis of Composite Plates via Refined Theories Accounting for Uncertainties." Shock and Vibration 18, no. 4 (2011): 537–54. http://dx.doi.org/10.1155/2011/741801.

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The free vibration analysis of composite thin and relatively thick plates accounting for uncertainty is addressed in this work. Classical and refined two-dimensional models derived via Carrera's Unified Formulation (CUF) are considered. Material properties and geometrical parameters are supposed to be random. The fundamental frequency related to the first bending eigenmode is stochastically described in terms of the mean value, the standard deviation, the related confidence intervals and the cumulative distribution function. The Monte Carlo Method is employed to account for uncertainty. Cross-ply, simply supported, orthotropic plates are accounted for. Symmetric and anti-symmetric lay-ups are investigated. Displacements based and mixed two-dimensional theories are adopted. Equivalent single layer and layer wise approaches are considered. A Navier type solution is assumed. The conducted analyses have shown that for the considered cases, the fundamental natural frequency is not very sensitive to the uncertainty in the material parameters, while uncertainty in the geometrical parameters should be accounted for. In the case of thin plates, all the considered models yield statistically matching results. For relatively thick plates, the difference in the mean value of the natural frequency is due to the different number of degrees of freedom in the model.
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Brischetto, S., and E. Carrera. "Free Vibration Analysis for Layered Shells Accounting of Variable Kinematic and Thermo-Mechanical Coupling." Shock and Vibration 19, no. 2 (2012): 155–73. http://dx.doi.org/10.1155/2012/806756.

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The free vibration analysis of one-layered and two-layered metallic cylindrical shell panels is evaluated in this work. The free frequency values are investigated for both thermo-mechanical and pure mechanical problems. Thermo-mechanical frequencies are calculated by means of a fully coupled thermo-mechanical model where both the displacement and temperature are primary variables in the considered governing equations. Pure mechanical frequencies are obtained from a mechanical model where the effect of the temperature field is not included in the stiffness matrix and the displacement is the only primary variable of the problem. The inclusion of the thermal part in the stiffness matrix gives larger frequencies. Both thermo-mechanical and pure mechanical models are developed in the framework of Carrera's Unified Formulation (CUF) in order to obtain several variable kinematic models. Both equivalent single layer and layer wise approaches are considered for multilayered shells. The use of refined two-dimensional theories for shells permits the evaluation of the effects of the thermo-mechanical coupling for lower and higher order modes, higher frequency values, multilayered configurations, thick and thin shells and several values of the radius of curvature of the shell geometry. It has mainly been concluded that the thermo-mechanical coupling is not influenced by the curvature of the shells, therefore, the main conclusions already given for the plate geometry are here confirmed: – the thermo-mechanical coupling is correctly determined if both the thermal and mechanical parts are correctly approximated; – it is small for each investigated case; – it influences the various vibration modes in different ways; – it has a limited dependence on the considered case, but this dependence vanishes if a global coupling is considered.
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BRISCHETTO, S., and E. CARRERA. "THERMOMECHANICAL EFFECT IN VIBRATION ANALYSIS OF ONE-LAYERED AND TWO-LAYERED PLATES." International Journal of Applied Mechanics 03, no. 01 (March 2011): 161–85. http://dx.doi.org/10.1142/s1758825111000920.

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The free vibration problem of one-layered and two-layered metallic plates is investigated in this work. The thermomechanical effect is evaluated using a fully coupled thermomechanical model. The free frequency values of fully coupled problems are compared to the values of the pure mechanical problems. In pure mechanical models, the displacement is the only primary variable of the problem, while in fully coupled thermomechanical models, the temperature is also considered as a primary variable and the effect of the thermomechanical stiffness is evaluated. The thermoelastic coupling usually provides higher frequencies with respect to the pure mechanical case because it acts like a thermal source, which is proportional to the strain rate, which leads to a bigger global stiffness of the structure. Both thermomechanical and mechanical models are developed in the framework of Carrera's Unified Formulation (CUF). CUF permits several refined two-dimensional theories to be obtained with orders of expansion in the thickness direction, from linear to fourth-order, for both displacements and temperature. Both equivalent single layer and layer-wise approaches are considered for the multilayered plates. The thermomechanical effect is investigated, in terms of frequencies, for thick and thin one-layered and two-layered plates, and for lower and higher modes. It has mainly been concluded that the thermomechanical coupling: (a) Is correctly determined if both the thermal and mechanical parts are correctly approximated; (b) Is small for each investigated case; (c) Influences the various vibration modes in different ways; and (d) Has a limited dependence on the considered case, but this dependence vanishes if a global coupling is considered. Only fully coupled thermomechanical models allow to analyze this type of problem. The effect of the thermomechanical coupling on higher-order modes can only be investigated using refined two-dimensional theories.
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Pagani, A., M. Petrolo, and E. Carrera. "Dynamic response of laminated and sandwich composite structures via 1D models based on Chebyshev polynomials." Journal of Sandwich Structures & Materials 21, no. 4 (July 7, 2017): 1428–44. http://dx.doi.org/10.1177/1099636217715582.

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This article presents the dynamic response of composite structures via refined beam models. The mode superposition method was used, and the Carrera Unified Formulation was exploited to create the advanced structural models. The finite element method was employed to compute the natural frequencies and modes. The main novelty of this article concerns the use of Chebyshev polynomials to define the displacement field above the cross-section of the beam. In particular, polynomials of the second kind were adopted, and the results were compared with those from analytical solutions and already established Carrera Unified Formulation-based beam models, which utilize Taylor and Lagrange polynomials to develop refined kinematics theories. Sandwich beams and laminated, thin-walled box beams were considered. Non-classical effects such as the cross-section distortion and bending/torsion coupling were evaluated. The results confirm the validity of the Carrera Unified Formulation for the implementation of refined structural models with any expansion functions and orders. In particular, the Chebyshev polynomials provide accuracies very similar to those from Taylor models. The use of high-order expansions, e.g. seventh-order, leads to results as accurate as those of Lagrange models which, from previous publications, are known as the most accurate Carrera Unified Formulation 1D models for this type of structural problems.
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Dissertations / Theses on the topic "Carrera's Unified Formulation"

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DE, PIETRO GABRIELE. "Modeling and Design of Multi-Stable Composite Structures." Doctoral thesis, Politecnico di Torino, 2019. http://hdl.handle.net/11583/2729360.

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HUI, YANCHUAN. "Multi-scale Modelling and Design of Composite Structures." Doctoral thesis, Politecnico di Torino, 2019. http://hdl.handle.net/11583/2739922.

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FALLAHI, NASIM. "Analysis and Optimization of Variable Angle Tow Composites Through Unified Formulation." Doctoral thesis, Politecnico di Torino, 2021. http://hdl.handle.net/11583/2875739.

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Wenzel, Christian. "Local FEM Analysis of Composite Beams and Plates : free-Edge effect and Incompatible Kinematics Coupling." Thesis, Paris 10, 2014. http://www.theses.fr/2014PA100107/document.

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Cette thèse traite des problèmes des concentrations de contraintes locales, en particularité des effets des bords libres dans des structures stratifiés. À l'interface entre deux couches avec des propriétés élastiques différentes, les contraintes ont un comportement singulier dans le voisinage du bord libre en supposant un comportement de matériau élastique linéaire. Par conséquent, ils sont essentiels pour promouvoir le délaminage. Via Formulation unifiée de la Carrera (CUF) différents modèles cinématiques sont testés dans le but de capter les concentrations de contraintes. Dans la première partie de ce travail, les approches de modélisation dimensionnelle réduits sont comparées. Deux classe principale sont présentés: la couche équivalent (ESL) et l'approche par couche, LW. Par la suite leurs capacités à capter les singularités sont comparées. En utilisant une fonction a priori singulière, via une expression exponentielle, une mesure des contraintes singulières est introduite. Seulement deux paramètres décrivent pleinement les composantes des contraintes singulières au voisinage du bord libre. Sur la base des paramètres obtenus les modèles sont comparés et aussi les effets sous des charges d'extension et de flexion et pour différents stratifiés. Les résultats montrent une nécessité des modèles complexes dans le voisinage du bord libre. Cependant loin des bords libres, dans le centre de plaques composite, aucune différence significative ne peut être noté pour les modèles plutôt simples. La deuxième partie de ce travail est donc dédiée au couplage de modèles cinématique incompatibles. Modèles complexes et coûteux sont utilisés seulement dans des domaines locaux d'intérêt, tandis que les modèles économiques simples seront modéliser le domaine global. La eXtended Variational Formulation (XVF) est utilisé pour coupler les modèles de dimensionnalité homogènes mais de cinématique hétérogènes. Ici pas de recouvrement de domaine est présent. En outre, le XVF offre la possibilité d'adapter les conditions imposées à l'interface en utilisant un paramètre scalaire unique. On montre que, pour le problème de dimensionnalité homogène, que deux conditions différentes peuvent être imposées par ce paramètre. Un correspondant à des conditions fortes des Multi Point Constraints (MPC) et un second fournir des conditions faibles. La dernière offre la possibilité de réduire extrêmement le domaine qui utilise le modèle cinématique complexe, sans perte de précision locale. Comme il s'agit de la première application de la XVF vers les structures composites, le besoin d'un nouvel opérateur de couplage a été identifié. Un nouveau formulaire est proposé, testé et sa robustesse sera évaluée
This work considers local stress concentrations, especially the free-Edge effects of multilayered structures. At the interface of two adjacent layers with different elastic properties, the stresses can become singular in the intermediate vicinity of the free edge. This is valid while assuming a linear elastic material behaviour. As a consequence this zones are an essential delamination trigger. Via the Carrera Unified Formulation (CUF), different kinematical models are testes in order to obtain the correct local stress concentration. In the first part of this work, the reduced dimensional modelling approaches are compared. Two main class are presented: Equivalent Single Layer (ESL) models treating the layered structure like one homogenous plate of equal mechanical proper- ties, and the Layer Wise approach, treating each layer independently. Subsequently their capabilities to capture the appearing singularities are compared. In order to have a comparable measurement of those singularities, the obtained stress distributions will be expressed via a power law function, which has a priori a singular behaviour. Only two parameters fully describe therefore the singular stress components in the vicinity of the free edge. With the help of these two parameters not only the different models capabilities will be compared, but also the free edge effect itself will be measured and compared for different symmetrical laminates and the case of extensional and uniform bending load. The results for all laminates under both load cases confirm the before stated need for rather complex models in the vicinity of the free edge. However far from the free edges, in the composite plates centre, no significant difference can be noted for rather simple models. The second part of this work is therefore dedicated to the coupling of kinematically incompatible models. The use of costly expensive complex models is restricted to local domains of interest, while economic simple models will model the global do- main. The Extended Variational Formulation (XVF) is identified as the most suitable way to couple the kinematically heterogenous but dimensional homogenous models. As it uses a configuration with one common interface without domain overlap, the additional efforts for establishing the coupling are limited. Further the XVF offers the possibility to adapt the conditions imposed at the interface using a single scalar parameter. It will be shown that for the homogenous dimensional problem under consideration only two different conditions can be imposed by this parameter. One matching the strong conditions imposed by the classical Multi Point Constrains (MPC) and a second one providing a weak condition. The last one is shown to provide the possibility to reduce further the domain using the complex kinematical model, without the loss of local precision. As this is the first application of the XVF towards composite structures, the need for a new coupling operator was identified. A new form is proposed, tested and its robustness will be evaluated
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REHAN, REHAN. "One-dimensional Advanced Beam Models for Marine Structural Applications." Doctoral thesis, Politecnico di Torino, 2017. http://hdl.handle.net/11583/2680980.

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At preliminary design stage, the global mechanical behavior of large marine vessels such as container ships has previously been analyzed idealizing them as a classical beam. These structures are complex and a classical beam idealization significantly compromises important structural behavior associated with cross section warping or in-plane displacements. On the other hand, 3D Finite Element (FE) models have been utilized which are accurate in capturing these details but pose high computational cost. In present work, structural analyses of marine vessels with realistic boundary conditions have been presented using well-known Carrera Unified Formulation (CUF). Using CUF, higher order theories can be implemented without the need of ad-hoc formulations. The finite element arrays are written in terms of fundamental nuclei for 1D beam elements that are independent of problem characteristics and the approximation order. Thus, refined models can be developed in an automatic manner. In the present work, the beam cross sections are discretized using elements with Lagrange polynomials and the FE model is regarded as Component-Wise (CW), allowing one to model complex 3D features, such as inclined hull walls, floors and girders in the form of components. The work is mainly divided in two parts: Hull in vacuo (in absence of water) and Hull with Hydrostatic Stiffness (in presence of water). The former involves static and dynamic structural analyses of hulls with realistic geometries without the effect of water. The later involves static and dynamic analyses of realistic hull geometries that are supported by buoyancy springs. The stiffness of buoyancy springs is made part of the fundamental nuclei and the corresponding FEM matrices for hydrostatic and hydrodynamic loads are obtained. The hydrodynamic loads have been considered in the form of Radiation Wave loads which include damping and added mass effects. Utilization of Component-Wise (CW) model under hydrodynamic loads has afforded an ease in modelling the complex geometrical configurations such as realistic boat shapes and the dynamic response analyses of aircraft carrier due to moving aircraft. All the analyses have been validated with published literature and their computational efficacy is established through their comparison with the results from commercial code.
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ZAPPINO, ENRICO. "Variable kinematic 1D, 2D and 3D Models for the Analysis of Aerospace Structures." Doctoral thesis, Politecnico di Torino, 2014. http://hdl.handle.net/11583/2573739.

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The aerospace structure design is one of the most challenging field in the mechanical engineering. The advanced structural configurations, introduced to satisfy the weight and strength requirements, require advanced analysis techniques able to predict complex physical phenomena. Finite Element Method, FEM, is one of the most used approach to perform analyses of complex structures. The use of FEM method allows the classical structural models to be used to investigate complex structures where a close form solution is not available. The FEM formulation can be easily implemented in automatic calculation routines therefore this approach can take advantage of the improvements of computers. In the last fifty years many commercial codes, base on FEM, has been developed and commercialized, as examples it is possible to refer to Nastran R by MSC or Abaqus R by Dassault Systémes. All the commercial codes are based on classical structural models. The beam model are based on Euler-Bernoulli or Timoshenko theories while two-dimensional models deal with Kirchhoff or Mindlin theories. The limitations introduced by the kinematic assumptions of such theories make the FEM elements based oh these models inef- fective in the analysis of advanced structures. The physical phenomena introduced by composite and smart materials, multi-field application and unconventional loads configurations can not be investigated using the classical FEM models, where the only solution improvement can be reached by refining the mesh and increasing the number of degrees of freedom. This scenario makes the development of advanced structural models very attractive in the structural engineering. With the development of new materials and structural solutions, a number of new structural models have been introduced in order to perform an accurate design of advanced structures. Classical structural model have been im- proved introducing more refined kinematics formulation. One- and two- dimensional models are widely used in aerospace structure design, the limitations introduced by the classical models have been overcame by introducing refined kinematic formulations able to deal with the complexities of the problems. On the other hand, while in the classical models each point is characterized by 3 translations and 3 rotations, the use of advanced models with complex kinematic introduces a number of complication in the analysis of complex geometries, in fact is much more difficult to combine models with different kinematics. The aim of this thesis is to develop new approaches that allow different kinematic models to be used in the same structural analysis. The advanced models used in the present thesis have been derived using the Carrera Unified Formulations, CUF. The CUF allows any structural model do be derived by means of a general formulation independent from the kinematics assumed by the theory. One-, two- and three- dimensional models are derived using the same approach. These models are therefore combined together using different techniques in order to perform structural analysis of complex structures. The results show the capabilities of the present approach to deal with the analysis of typical complex aerospace structure. The performances of variable kinematics models have been investigated and many assessment have been proposed. This walled structure, reinforced structure and composite and sandwich material have been con- sidered. The advanced models introduced in this thesis have been used to perform static, dynamic and aeroelastic analysis in order to highlight the capabilities of the approach in different field. The results show that the present models are able to provide accurate results with a strong reduction in the computational cost with respect classical approaches.
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MAIARU', MARIANNA. "Multiscale approaches for the failure analysis of fiber-reinforced composite structures using the 1D CUF." Doctoral thesis, Politecnico di Torino, 2014. http://hdl.handle.net/11583/2571353.

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Composites provide significant advantages in performance, efficiency and costs; thanks to these features, their application is increasing in many engineering fields, such as aerospace, naval and mechanical engineering. Although the adoption of composites is rising, there are still open issues to be investigated, in particular, understanding their failure mechanism has a prominent role in enhancing component designs. Numerous methodologies are available to compute accurate stress/strain fields for laminated structures, multi-scale approaches are required when micro- and macro-scales are accounted for. Despite the increasing development in computer hardware, the computational effort of these methods is still prohibitive for extensive applications, especially when a high number of layers is considered. Then, the reduction of the computational time and cost required to perform failure analysis is still a challenging task. This work proposes two multiscale approaches for the failure analysis of fiber-reinforced composites. A concurrent multiscale approach ("Component-Wise") and a hierarchical method are developed based on the 1D Carrera Unified Formulation (CUF). 1D higher order elements are very powerful tools for multiscale analysis since they provide accurate stress and strain fields with very low computational costs.
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KALEEL, IBRAHIM. "Computationally-efficient multiscale models for progressive failure and damage analysis of composites." Doctoral thesis, Politecnico di Torino, 2019. http://hdl.handle.net/11583/2729362.

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LI, GUOHONG. "Variable Kinematic Finite Element Formulations Applied to Multi-layered Structures and Multi-field Problems." Doctoral thesis, Politecnico di Torino, 2019. http://hdl.handle.net/11583/2729361.

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AUGELLO, RICCARDO. "Advanced FEs for the micropolar and geometrical nonlinear analyses of composite structures." Doctoral thesis, Politecnico di Torino, 2021. http://hdl.handle.net/11583/2872330.

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Book chapters on the topic "Carrera's Unified Formulation"

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Hui, Y., G. Giunta, S. Belouettar, H. Hu, and E. Carrera. "Multiscale Nonlinear Analysis of Beam Structures by Means of the Carrera Unified Formulation." In Advances in Predictive Models and Methodologies for Numerically Efficient Linear and Nonlinear Analysis of Composites, 47–63. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11969-0_4.

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"Carrera Unified Formulation (CUF)." In Encyclopedia of Continuum Mechanics, 257. Berlin, Heidelberg: Springer Berlin Heidelberg, 2020. http://dx.doi.org/10.1007/978-3-662-55771-6_300076.

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"Carrera Unified Formulation and Refined Beam Theories." In Beam Structures, 45–63. Chichester, UK: John Wiley & Sons, Ltd, 2011. http://dx.doi.org/10.1002/9781119978565.ch5.

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Conference papers on the topic "Carrera's Unified Formulation"

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Carrera, E., A. Pagani, B. Wu, and M. Filippi. "Large-Deformation Analysis of Elastomeric Structures by Carrera Unified Formulation." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-11364.

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Abstract Based on the well-known nonlinear hyperelasticity theory and by using the Carrera Unified Formulation (CUF) as well as a total Lagrangian approach, the unified theory of slightly compressible elastomeric structures including geometrical and physical nonlinearities is developed in this work. By exploiting CUF, the principle of virtual work and a finite element approximation, nonlinear governing equations corresponding to the slightly compressible elastomeric structures are straightforwardly formulated in terms of the fundamental nuclei, which are independent of the theory approximation order. Accordingly, the explicit forms of the secant and tangent stiffness matrices of the unified 1D beam and 2D plate elements are derived by using the three-dimensional Cauchy-Green deformation tensor and the nonlinear constitutive equation for slightly incompressible hyperelastic materials. Several numerical assessments are conducted, including uniaxial tension nonlinear response of rectangular elastomeric beams. Our numerical findings demonstrate the capabilities of the CUF model to calculate the large-deformation equilibrium curves as well as the stress distributions with high accuracy.
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Sartorato, Murilo, Ricardo De Medeiros, Antonio Ferreira, Volnei Tita, and Marcelo Leite Ribeiro. "Dynamic analysis of laminate plates via Carrera Unified Formulation." In 24th ABCM International Congress of Mechanical Engineering. ABCM, 2017. http://dx.doi.org/10.26678/abcm.cobem2017.cob17-0168.

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Zappino, Enrico, and Erasmo Carrera. "Mixed One-/Two-Dimensional Models With Node Dependent Kinematic Capabilities for the Analysis of Metallic and Composite Structures." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87490.

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The present paper presents an innovative approach to connect one-/two-dimensional models using a unified formulation with node-dependent kinematic capabilities. These models can use a different kinematics approximation at each node of the element. Carrera Unified Formulation has been used to derive the governing equations in a compact and general form. The possibility to connect one- and two-dimensional elements, and eventually to refine the kinematic model locally, has lead to a general reduction of the computational costs guaranteeing the same numerical accuracy.
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Nicassio, Francesco, Maria Cinefra, Gennaro Scarselli, Matteo Filippi, Alfonso Pagani, and Erasmo Carrera. "Carrera unified formulation (CUF) for the analysis of disbonds in single lap joints (SLJ)." In Nondestructive Characterization and Monitoring of Advanced Materials, Aerospace, Civil Infrastructure, and Transportation XVI, edited by Peter J. Shull, Tzuyang Yu, Andrew L. Gyekenyesi, and H. Felix Wu. SPIE, 2022. http://dx.doi.org/10.1117/12.2616542.

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Filippi, Matteo, and Erasmo Carrera. "Advanced Zig-Zag Beam Theories for Sandwich Structures Analyses." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86783.

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This work aims at evaluating the capabilities of several higher-order beam formulations for stress and dynamic analyses of layered sandwich structures. The structural models are conceived within the framework of the Carrera Unified Formulation (CUF) that allows one to generate (and compare) an infinite number of displacement fields. The number and the type of functions that are selected to generate the kinematic expansions are input parameters of the problem. Besides the well-known Taylor- and Lagrange-type expansions, great attention is paid to a new class of advanced higher-order zig-zag theories, which are written as combinations of continuous piecewise polynomial functions. Numerical simulations are performed on laminated and sandwich beams with very low length-to-depth ratio values. Also, structures with soft layers made of viscoelastic materials are considered to investigate the different dissipation mechanisms.
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Carrera, Erasmo, Matteo Filippi, and Enrico Zappino. "Free Vibration Analysis of Rotating Structures by One-Dimensional, Variable Kinematic Theories." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-63183.

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In this paper, Carrera’s Unified Formulation (CUF) is extended to perform free-vibrational analyses of rotating structures. CUF is a hierarchical formulation which offers a procedure to obtain refined structural theories that account for variable kinematic description. These theories are obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor’s polynomials of N-order, in which N is a free parameter. The linear case (N = 1) permits us to obtain classical beam theories while higher order expansions could lead to three-dimensional description of dynamic response of both rotors and centrifugally stiffened beams. The Finite Element method is used to derive the weak form of the three-dimensional differential equations of motion in term of fundamental nuclei, whose forms do not depend on the approximation used (N). The present formulations include gyroscopic effects and stiffening due to centrifugal stresses. In order to verify the accuracy of the new theories, several analyses are carried out and the results are compared with solutions presented in the literature in graphical and numerical form. The advantages of the variable kinematic models are evident especially when shafts with deformable discs and thin-walled rotating beams made up with composite materials are studied.
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Pagani, Alfonso, Riccardo Augello, and Erasmo Carrera. "Evaluation of In-Plane and Out-of-Plane Stresses in Composite Structures Subjected to Large Displacements/Rotations." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86671.

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In many engineering applications, such as civil, mechanical and aerospace, large displacements and rotations may occur within the working composite structures, due to the extreme loading conditions that may occur during service. This afflicts the equilibrium states of the structures and could change them, eventually, in a catastrophic manner. Therefore, it may be necessary to predict the nonlinear stress conditions of the laminated structures through numerical simulation, in order to prevent the failure of the entire system. To take into account these conditions, a geometrical nonlinear analysis has to be performed. The nonlinear framework proposed in this work is based on the Carrera Unified Formulation (CUF). CUF is a hierarchical formulation that considers the order of the structural model as an input of the analysis, so that no specific formulations are needed to obtain any refined model. The possibility to generate high-order structural elements makes possible to analyze any loading cases, including the post-buckling situation. Furthermore, this methodology allows to evaulate of the full three-dimensional stress tensor in laminated structures. In fact, as CUF is able to calculate the stiffness matrix in an automatic manner, there is no need to include any simplification to evaluate the out-of-plane components of the stress tensor.
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Carrera, Erasmo, Alberto García de Miguel, Alfonso Pagani, and Enrico Zappino. "Reissner’s Mixed Variational Theorem for Layer-Wise Refined Beam Models Based on the Unified Formulation." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-71612.

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The present paper proposes the application of the Reissners Mixed Variational Theorem (RMVT) for the accurate stress analysis of general multi-layered beam problems. Laminated materials usually differ from homogeneous materials in that they exhibit much higher transverse shear and transverse normal deformabilities. These characteristics, and others such as the Transverse Anisotropy (TA) and the Interlaminar Continuity of transverse stresses (IC), make Classical Laminated Theories (CLT) inappropriate for the analysis of multi-layered structures. The Carrera Unified Formulation (CUF) sets a framework in which classical-to-refined beam models can be generated by expanding the unknown variables over the cross-sectional domain by means of arbitrary functions. A LW expansion is adopted for both displacements and transverse stresses over the cross-section section domain. In this manner, the ZZ condition is automatically satisfied through the use of independent kinematics for each layer in a LW sense, with no need of introducing ad-hoc ZZ functions.
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Kaleel, Ibrahim, Marco Petrolo, Erasmo Carrera, and Anthony M. Waas. "Micromechanical Progressive Failure Analysis of Fiber-Reinforced Composite Using Refined Beam Models." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-71304.

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An efficient and novel micromechanical computational platform for progressive failure analysis of fiber reinforced composites is presented. The numerical framework is based on a class of refined beam models called Carrera Unified Formulation (CUF), a generalized hierarchical formulation which yields a refined structural theory via variable kinematic description. The crack band theory is implemented in the framework to capture the damage propagation within the constituents of composite materials. A representative volume element (RVE) containing randomly distributed fibers is modeled using the Component-Wise approach (CW), an extension of CUF beam model based on Lagrange type polynomials. The efficiency of the proposed numerical framework is achieved through the ability of the CUF models to provide accurate three-dimensional displacement and stress fields at a reduced computational cost.
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Carrera, Erasmo, and Enrico Zappino. "Analysis of Complex Structures Coupling Variable Kinematics One-Dimensional Models." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37961.

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One-dimensional models are widely used in mechanical design. Classical models, Euler-Bernoulli or Timoshenko, ensure a low computational cost but are limited by their assumptions, many refined models were proposed to overcome these limitations and extend one-dimensional models at the analysis of complex geometries or advanced materials. In this work a new approach is proposed to couple different kinematic models. A new finite element is introduced in order to connect one-dimensional elements with different displacement fields. The model is derived in the frameworks of the Carrera Unified Formulation (CUF), therefore the formulation can be written in terms of fundamental nuclei. The results show that the use variable kinematic models allows the computational costs to be reduced without reduce the accuracy, moreover, refined-one dimensional models can be used in the analysis of complex structures.
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