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Author: Grafiati

Published: 14 March 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

De Pietro, Gabriele, Alberto Garcia de Miguel, E. Carrera, Gaetano Giunta, Salim Belouettar, and Alfonso Pagani. "Strong and weak form solutions of curved beams via Carrera’s unified formulation." Mechanics of Advanced Materials and Structures 27, no. 15 (November 5, 2018): 1342–53. http://dx.doi.org/10.1080/15376494.2018.1510066.

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12

Carrera, Erasmo, and Enrico Zappino. "Carrera Unified Formulation for Free-Vibration Analysis of Aircraft Structures." AIAA Journal 54, no. 1 (January 2016): 280–92. http://dx.doi.org/10.2514/1.j054265.

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13

Bharati, Raj B., M. Filippi, Prashanta K. Mahato, and E. Carrera. "Flutter analysis of laminated composite structures using Carrera Unified Formulation." Composite Structures 253 (December 2020): 112759. http://dx.doi.org/10.1016/j.compstruct.2020.112759.

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14

Arruda, M. R. T., L. M. S. Castro, A. J. M. Ferreira, D. Martins, and J. R. Correia. "Physically non-linear analysis of beam models using Carrera Unified Formulation." Composite Structures 195 (July 2018): 60–73. http://dx.doi.org/10.1016/j.compstruct.2018.03.107.

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15

Carrera, E., M. Filippi, and E. Zappino. "Free vibration analysis of rotating composite blades via Carrera Unified Formulation." Composite Structures 106 (December 2013): 317–25. http://dx.doi.org/10.1016/j.compstruct.2013.05.055.

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16

Carrera, Erasmo, Enrico Zappino, and Guohong Li. "Analysis of beams with piezo-patches by node-dependent kinematic finite element method models." Journal of Intelligent Material Systems and Structures 29, no. 7 (October 23, 2017): 1379–93. http://dx.doi.org/10.1177/1045389x17733332.

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This article presents a family of one-dimensional finite element method models with node-dependent kinematics for the analysis of beam structures with piezo-patches. The models proposed are built by applying Carrera unified formulation. Carrera unified formulation permits to obtain finite element method stiffness matrices through so-called fundamental nuclei whose form is independent of the assumptions made for the displacement/electrical field over the cross section of a beam. In the previous works, uniform kinematic assumptions have been applied to all the nodes within the same element. The present contribution proposes to use different kinematics on different nodes, leading to node-dependent kinematic finite element method formulations. In such an approach, non-uniform cross sections introduced by piezo-patches can be considered. With the help of layer-wise models, piezoelectric and mechanical domains each can possess individual constitutive relations. Meanwhile, node-dependent kinematics can integrate equivalent single layer models and layer-wise models to reach an optimal balance between accuracy and use of computational resources. Static governing equations for beam elements with node-dependent kinematics accounting for electromechanical effects are derived from the principle of virtual displacements. The competence of the proposed approach is validated by comparing the obtained results with solutions taken from the literature and ABAQUS three-dimensional modelling. Both extension and shear actuation mechanisms are considered.

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17

Petrolo, M., MH Nagaraj, E. Daneshkhah, R. Augello, and E. Carrera. "Static analysis of thin-walled beams accounting for nonlinearities." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236, no. 6 (October 14, 2021): 2967–80. http://dx.doi.org/10.1177/09544062211032997.

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This paper presents numerical results concerning the nonlinear analysis of thin-walled isotropic structures via 1 D structural theories built with the Carrera Unified Formulation (CUF). Both geometrical and material nonlinearities are accounted for, and square, C- and T-shaped beams are considered. The results focus on equilibrium curves, displacement, and stress distributions. Comparisons with literature and 3 D finite elements (FE) are provided to assess the formulation’s accuracy and computational efficiency. It is shown how 1 D models based on Lagrange expansions of the displacement field are comparable to 3 D FE regarding the accuracy but require considerably fewer degrees of freedom.

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18

Ribeiro, Marcelo L., Gregório F. O. Ferreira, Ricardo de Medeiros, António J. M. Ferreira, and Volnei Tita. "Experimental and numerical dynamic analysis of laminate plates via Carrera Unified Formulation." Composite Structures 202 (October 2018): 1176–85. http://dx.doi.org/10.1016/j.compstruct.2018.05.085.

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19

Yan, Yang, Erasmo Carrera, Alfonso Pagani, Ibrahim Kaleel, and Alberto Garcia de Miguel. "Isogeometric analysis of 3D straight beam-type structures by Carrera Unified Formulation." Applied Mathematical Modelling 79 (March 2020): 768–92. http://dx.doi.org/10.1016/j.apm.2019.11.003.

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20

Arruda, M. R. T., L. M. S. Castro, A. J. M. Ferreira, M. Garrido, J. Gonilha, and J. R. Correia. "Analysis of composite layered beams using Carrera unified formulation with Legendre approximation." Composites Part B: Engineering 137 (March 2018): 39–50. http://dx.doi.org/10.1016/j.compositesb.2017.10.040.

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21

Viola, Erasmo, Francesco Tornabene, and Nicholas Fantuzzi. "Stress and Strain Recovery of Laminated Composite Doubly-Curved Shells and Panels Using Higher-Order Formulations." Key Engineering Materials 624 (September 2014): 205–13. http://dx.doi.org/10.4028/www.scientific.net/kem.624.205.

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The present paper investigates the static behaviour of doubly-curved laminated composite shells and panels. A two dimensional Higher-order Equivalent Single Layer approach, based on the Carrera Unified Formulation (CUF), is proposed. The differential geometry is used for the geometric description of shells and panels. The numerical solution is calculated using the generalized differential quadrature method. The through-the-thickness strains and stresses are computed using a three dimensional stress recovery procedure based on the shell equilibrium equations. Sandwich panels are considered with soft cores. The numerical results are compared with the ones obtained with a finite element code. The proposed higher-order formulations can be used for solving elastic problems involved in the first stage of any scientific procedure of analysis and design of masonry structures.

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22

Maturi, D. A., A. J. M. Ferreira, A. M. Zenkour, and D. S. Mashat. "Analysis of Laminated Shells by Murakami’s Zig-Zag Theory and Radial Basis Functions Collocation." Journal of Applied Mathematics 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/123465.

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The static and free vibration analysis of laminated shells is performed by radial basis functions collocation, according to Murakami’s zig-zag (ZZ) function (MZZF) theory . The MZZF theory accounts for through-the-thickness deformation, by considering a ZZ evolution of the transverse displacement with the thickness coordinate. The equations of motion and the boundary conditions are obtained by Carrera’s Unified Formulation and further interpolated by collocation with radial basis functions.

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23

Kumar, S. Keshava, Dineshkumar Harursampath, Erasmo Carrera, Maria Cinefra, and Stefano Valvano. "Modal analysis of delaminated plates and shells using Carrera Unified Formulation – MITC9 shell element." Mechanics of Advanced Materials and Structures 25, no. 8 (April 27, 2017): 681–97. http://dx.doi.org/10.1080/15376494.2017.1302024.

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24

Pagani, A., and E. Carrera. "Large-deflection and post-buckling analyses of laminated composite beams by Carrera Unified Formulation." Composite Structures 170 (June 2017): 40–52. http://dx.doi.org/10.1016/j.compstruct.2017.03.008.

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25

Wu, B., A. Pagani, M. Filippi, W. Q. Chen, and E. Carrera. "Large-deflection and post-buckling analyses of isotropic rectangular plates by Carrera Unified Formulation." International Journal of Non-Linear Mechanics 116 (November 2019): 18–31. http://dx.doi.org/10.1016/j.ijnonlinmec.2019.05.004.

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26

Neves, Ana M. A., António J. M. Ferreira, Erasmo Carrera, Maria Cinefra, Carla M. C. Roque, Renato M. N. Jorge, and Cristóvăo M. M. Soares. "Buckling behaviour of cross-ply laminated plates by a higher-order shear deformation theory." Science and Engineering of Composite Materials 19, no. 2 (June 1, 2012): 119–25. http://dx.doi.org/10.1515/secm-2011-0131.

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AbstractIn this article, Carrera’s Unified Formulation (CUF) is combined with a radial basis function collocation technique. A higher-order theory that considers deformations in the thickness direction was developed under CUF to predict the buckling behaviour of laminated plates. The obtained governing equations and boundary conditions are then interpolated by collocation with radial basis functions. The accuracy and efficiency of the combination of the two techniques for buckling problems of laminated plates are demonstrated through numerical experiments.

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27

Ramos, I. A., J. L. Mantari, and A. M. Zenkour. "Laminated composite plates subject to thermal load using trigonometrical theory based on Carrera Unified Formulation." Composite Structures 143 (May 2016): 324–35. http://dx.doi.org/10.1016/j.compstruct.2016.02.020.

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28

De Miguel, A. G., M. Cinefra, M. Filippi, A. Pagani, and E. Carrera. "Validation of FEM models based on Carrera Unified Formulation for the parametric characterization of composite metamaterials." Journal of Sound and Vibration 498 (April 2021): 115979. http://dx.doi.org/10.1016/j.jsv.2021.115979.

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29

Mantari, J. L., I. A. Ramos, E. Carrera, and M. Petrolo. "Static analysis of functionally graded plates using new non-polynomial displacement fields via Carrera Unified Formulation." Composites Part B: Engineering 89 (March 2016): 127–42. http://dx.doi.org/10.1016/j.compositesb.2015.11.025.

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30

Foroutan, K., E. Carrera, A. Pagani, and H. Ahmadi. "Post-buckling and large-deflection analysis of a sandwich FG plate with FG porous core using Carrera’s Unified Formulation." Composite Structures 272 (September 2021): 114189. http://dx.doi.org/10.1016/j.compstruct.2021.114189.

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31

Carrera, E., A. Pagani, and J. R. Banerjee. "Linearized buckling analysis of isotropic and composite beam-columns by Carrera Unified Formulation and dynamic stiffness method." Mechanics of Advanced Materials and Structures 23, no. 9 (March 9, 2016): 1092–103. http://dx.doi.org/10.1080/15376494.2015.1121524.

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32

Petrolo, M. "Flutter analysis of composite lifting surfaces by the 1D Carrera Unified Formulation and the doublet lattice method." Composite Structures 95 (January 2013): 539–46. http://dx.doi.org/10.1016/j.compstruct.2012.06.021.

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33

Carrera, E., M. Petrolo, and P. Nali. "Unified Formulation Applied to Free Vibrations Finite Element Analysis of Beams with Arbitrary Section." Shock and Vibration 18, no. 3 (2011): 485–502. http://dx.doi.org/10.1155/2011/706541.

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This paper presents hierarchical finite elements on the basis of the Carrera Unified Formulation for free vibrations analysis of beam with arbitrary section geometries. The displacement components are expanded in terms of the section coordinates, (x, y), using a set of 1-D generalized displacement variables. N-order Taylor type expansions are employed. N is a free parameter of the formulation, it is supposed to be as high as 4. Linear (2 nodes), quadratic (3 nodes) and cubic (4 nodes) approximations along the beam axis, (z), are introduced to develop finite element matrices. These are obtained in terms of a few fundamental nuclei whose form is independent of both N and the number of element nodes. Natural frequencies and vibration modes are computed. Convergence and assessment with available results is first made considering different type of beam elements and expansion orders. Additional analyses consider different beam sections (square, annular and airfoil shaped) as well as boundary conditions (simply supported and cantilever beams). It has mainly been concluded that the proposed model is capable of detecting 3-D effects on the vibration modes as well as predicting shell-type vibration modes in case of thin walled beam sections.

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34

Daraei, Behnam, Saeed Shojaee, and Saleh Hamzehei-Javaran. "Analysis of stationary and axially moving beams considering functionally graded material using micropolar theory and Carrera unified formulation." Composite Structures 271 (September 2021): 114054. http://dx.doi.org/10.1016/j.compstruct.2021.114054.

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35

Naderi Beni, Nasrin. "Free vibration analysis of annular sector sandwich plates with FG-CNT reinforced composite face-sheets based on the Carrera’s Unified Formulation." Composite Structures 214 (April 2019): 269–92. http://dx.doi.org/10.1016/j.compstruct.2019.01.094.

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36

Mantari, J. L., I. A. Ramos, and A. M. Zenkour. "A Unified Formulation for Laminated Composite and Sandwich Plates Subject to Thermal Load Using Various Plate Theories." International Journal of Applied Mechanics 08, no. 08 (December 2016): 1650087. http://dx.doi.org/10.1142/s1758825116500873.

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This paper proposes several normalized and non-normalized displacement fields based on hybrid and trigonometric hyperbolic shear strain shape functions in order to solve the analytical thermoelastic problem of simply-supported laminated composite and sandwich plates using the Carrera unified formulation (CUF) as strategy. The equivalent single layer (ESL) governing equations for laminated composite plate are obtained by employing the principle of virtual displacement (PVD) and are solved using Navier’s method solution. Linear and nonlinear temperature distributions through the plate thickness are taken into account. A hybrid and trigonometric hyperbolic shear strain shape functions are introduced in normalized and non-normalized form in the mathematical model. The obtained results are compared with the classical polynomial ones for several order of expansion. Interesting approximations with 3D solution are shown for low and high order of expansion.

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37

Arruda, M. R. T., Mário Garrido, L. M. S. Castro, A. J. M. Ferreira, and J. R. Correia. "Numerical modelling of the creep behaviour of GFRP sandwich panels using the Carrera Unified Formulation and Composite Creep Modelling." Composite Structures 183 (January 2018): 103–13. http://dx.doi.org/10.1016/j.compstruct.2017.01.074.

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38

Rezaei, A. S., and A. R. Saidi. "Application of Carrera Unified Formulation to study the effect of porosity on natural frequencies of thick porous–cellular plates." Composites Part B: Engineering 91 (April 2016): 361–70. http://dx.doi.org/10.1016/j.compositesb.2015.12.050.

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39

Fallahi, Nasim, Andrea Viglietti, Erasmo Carrera, Alfonso Pagani, and Enrico Zappino. "EFFECT OF FIBER ORIENTATION PATH ON THE BUCKLING, FREE VIBRATION, AND STATIC ANALYSES OF VARIABLE ANGLE TOW PANELS." Facta Universitatis, Series: Mechanical Engineering 18, no. 2 (July 29, 2020): 165. http://dx.doi.org/10.22190/fume200615026f.

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In this work, the effect of the fiber orientation on the mechanical response of variable angle tow (VAT) panels is investigated. A computationally efficient high-order one-dimensional model, derived under the framework of the Carrera unified formulation (CUF), is used. In detail, a layerwise approach is adopted to predict the complex phenomena that may appear in VAT panels. Static, free-vibration and buckling analyses are performed, considering several material properties, geometries, and boundary conditions, and the results are assessed with those obtained using existing approaches. Considering the findings of the comparative analysis, several best design practices are suggested to improve the mechanical performances of VAT panels.

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Hanten, L., G. Giunta, S. Belouettar, and V. Salnikov. "Free Vibration Analysis of Fibre-Metal Laminated Beams via Hierarchical One-Dimensional Models." Mathematical Problems in Engineering 2018 (June 26, 2018): 1–12. http://dx.doi.org/10.1155/2018/2724781.

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This paper presents a free vibration analysis of beams made of fibre-metal laminated beans. Due to its attractive properties, this class of composites has gained more and more importance in the aeronautic field. Several higher-order displacements-based theories as well as classical models (Euler-Bernoulli’s and Timoshenko’s ones) are derived, assuming Carrera’s Unified Formulation by a priori approximating the displacement field over the cross section in a compact form. The governing differential equations and the boundary conditions are derived in a general form that corresponds to a generic term in the displacement field approximation. The resulting fundamental term, named “nucleus”, does not depend upon the approximation order N, which is a free parameter of the formulation. A Navier-type, closed form solution is used. Simply supported beams are, therefore, investigated. Slender and short beams are considered. Three- and five-layer beams are studied. Bending, shear, torsional, and axial modes and frequencies are presented. Results are assessed for three-dimensional FEM solutions obtained by a commercial finite element code using three-dimensional elements showing that the proposed approach is accurate yet computationally effective.

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Alesadi, Amirhadi, Marzieh Galehdari, and Saeed Shojaee. "Free vibration and buckling analysis of composite laminated plates using layerwise models based on isogeometric approach and Carrera unified formulation." Mechanics of Advanced Materials and Structures 25, no. 12 (October 20, 2017): 1018–32. http://dx.doi.org/10.1080/15376494.2017.1342883.

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Carrera, Erasmo, Munise Didem Demirbas, and Riccardo Augello. "Evaluation of Stress Distribution of Isotropic, Composite, and FG Beams with Different Geometries in Nonlinear Regime via Carrera-Unified Formulation and Lagrange Polynomial Expansions." Applied Sciences 11, no. 22 (November 11, 2021): 10627. http://dx.doi.org/10.3390/app112210627.

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In this study, the geometrically nonlinear behaviour caused by large displacements and rotations in the cross sections of thin-walled composite beams subjected to axial loading is investigated. Newton–Raphson scheme and an arc length method are used in the solution of nonlinear equations by finite element method to determine the mechanical effect. The Carrera-Unified formulation (CUF) is used to solve nonlinear, low or high order kinematic refined structure theories for finite beam elements. In the study, displacement area and stress distributions of composite structures with different angles and functionally graded (FG) structures are presented for Lagrange polynomial expansions. The results show the accuracy and computational efficiency of the method used and give confidence for new research.

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Naderi Beni, N., and M. Botshekanan Dehkordi. "An extension of Carrera unified formulation in polar coordinate for analysis of circular sandwich plate with FGM core using GDQ method." Composite Structures 185 (February 2018): 421–34. http://dx.doi.org/10.1016/j.compstruct.2017.11.044.

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Hu, Yi, Yong Zhao, and Haopeng Liang. "Refined Beam Theory for Geometrically Nonlinear Pre-Twisted Structures." Aerospace 9, no. 7 (July 6, 2022): 360. http://dx.doi.org/10.3390/aerospace9070360.

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This paper proposes a novel fully nonlinear refined beam element for pre-twisted structures undergoing large deformation and finite untwisting. The present model is constructed in the twisted basis to account for the effects of geometrical nonlinearity and initial twist. Cross-sectional deformation is allowed by introducing Lagrange polynomials in the framework of a Carrera unified formulation. The principle of virtual work is applied to obtain the Green–Lagrange strain tensor and second Piola–Kirchhoff stress tensor. In the nonlinear governing formulation, expressions are given for secant and tangent matrices with linear, nonlinear, and geometrically stiffening contributions. The developed beam model could detect the coupled axial, torsional, and flexure deformations, as well as the local deformations around the point of application of the force. The maximum difference between the present deformation results and those of shell/solid finite element simulations is 6%. Compared to traditional beam theories and finite element models, the proposed method significantly reduces the computational complexity and cost by implementing constant beam elements in the twisted basis.

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CARRERA, E., S. LECCA, P. NALI, and M. SOAVE. "INFLUENCE OF IN-PLANE AXIAL AND SHEAR LOADING ON THE VIBRATION OF METALLIC PLATES." International Journal of Applied Mechanics 03, no. 03 (September 2011): 447–67. http://dx.doi.org/10.1142/s175882511100107x.

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This work deals with the vibration problem of metallic plates subjected to combined axial, biaxial and shear in-plane loading. Various type of boundary conditions are considered. Results related to thin plate theories and shear deformation theories are compared to a third-order plate theory including the thickness stretching effects. The Finite Element Method (FEM) is applied on the basis of Carrera Unified Formulation kinematic assumptions. FE matrices are computed by referring to the four-node element. The mixed interpolation of tensorial components technique is used in order to contrast the shear locking for both classical and refined theories. The influence of the in-plane loading (combined axial, biaxial and shear) on plate undamped natural frequencies is illustrated and discussed. Various plate geometries and boundary conditions are considered.

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Alesadi, Amirhadi, Sarah Ghazanfari, and Saeed Shojaee. "B-spline finite element approach for the analysis of thin-walled beam structures based on 1D refined theories using Carrera unified formulation." Thin-Walled Structures 130 (September 2018): 313–20. http://dx.doi.org/10.1016/j.tws.2018.05.016.

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Zappino, Enrico, and Erasmo Carrera. "Thermo-piezo-elastic analysis of amplified piezoceramic actuators using a refined one-dimensional model." Journal of Intelligent Material Systems and Structures 29, no. 17 (August 3, 2017): 3482–94. http://dx.doi.org/10.1177/1045389x17721026.

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The thermo-piezo-elastic analysis of amplified piezoceramic actuators is presented in this article. A refined one-dimensional multi-field finite element model, based on the Carrera Unified Formulation, has been developed. Thermal and piezoelectric effects have been included in the structural model and a fully coupled thermo-piezo-elastic analysis has been performed. The finite element model has been assessed by comparing it with results from open literature The model has also been used to perform the analysis of complex amplified piezoceramic actuators. These actuators are able to amplify the displacements produced by piezoceramic material, but they suffer from high deformations when they undergo high thermal loads. An accurate thermal analysis has been performed to evaluate the strain/stress field. The results show the accuracy of the present model and its capabilities in multi-field analyses.

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Zappino, Enrico, Guohong Li, and Erasmo Carrera. "Node-dependent kinematic elements for the dynamic analysis of beams with piezo-patches." Journal of Intelligent Material Systems and Structures 29, no. 16 (September 2018): 3333–45. http://dx.doi.org/10.1177/1045389x18798942.

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This article extends the use of one-dimensional elements with node-dependent kinematics to the dynamic analysis of beam structures with piezo-patches. Node-dependent kinematics allows the kinematic assumptions to be defined individually on each finite element node, leading to finite element models with variable nodal kinematics. Derived from Carrera unified formulation, node-dependent kinematics facilitates the mathematical refinement to an arbitrary order at any desirable region on the nodal level while keeping the compactness of the formulation. As an ideal approach to simulate structures with special local features, node-dependent kinematics has been employed to model piezo-patches in static cases. In this work, the application of node-dependent beam elements in dynamic problems is demonstrated. Node-dependent kinematics is applied to increase the numerical accuracy in the areas where the piezo-patches lie in through sufficiently refined models, while lower order assumptions are used elsewhere. The dissimilar constitutive relations of neighboring components are appropriately considered with layer-wise models. Both open- and short-circuit conditions are considered. The results are compared against those from literature. The numerical study shows that the adoption of node-dependent kinematics allows accurate results to be obtained at reduced computational costs.

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Yan, Yang, Alfonso Pagani, Erasmo Carrera, and Qingwen Ren. "Exact solutions for the macro-, meso- and micro-scale analysis of composite laminates and sandwich structures." Journal of Composite Materials 52, no. 22 (March 7, 2018): 3109–24. http://dx.doi.org/10.1177/0021998318761785.

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The present work proposes a closed-form solution based on refined beam theories for the static analysis of fiber-reinforced composite and sandwich beams under simply supported boundary conditions. The higher-order beam models are developed by employing Carrera Unified Formulation, which uses Lagrange-polynomials expansions to approximate the kinematic field over the cross section. The proposed methodology allows to carry out analysis of composite structure analysis through a single formulation in global-local sense, i.e. homogenized laminates at a global scale and fiber-matrix constituents at a local scale, leading to component-wise analysis. Therefore, three-dimensional stress/displacement fields at different scales can be successfully detected by increasing the order of Lagrange polynomials opportunely. The governing equations are derived in a strong-form and solved in a Navier-type sense. Three benchmark numerical assessments are carried out on a single-layer transversely isotropic beam, a cross-ply laminate [Formula: see text] beam and a sandwich beam. The results show that accurate displacement and stress values can be obtained in different parts of the structure with lower computational cost in comparison with traditional, enhanced as well as three-dimensional finite element methods. Besides, this study may serve as benchmarks for future assessments in this field.

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Fallahi, Nasim. "GA Optimization of Variable Angle Tow Composites in Buckling and Free Vibration Analysis through Layerwise Theory." Aerospace 8, no. 12 (December 3, 2021): 376. http://dx.doi.org/10.3390/aerospace8120376.

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In the current research, variable angle tow composites are used to improve the buckling and free vibration behavior of a structure. A one-dimensional (1D) Carrera Unified Formulation (CUF) is employed to determine the buckling loads and natural frequencies in Variable Angle Tow (VAT) square plates by taking advantage of the layerwise theory (LW). Subsequently, the Genetic Algorithm (GA) optimization method is applied to maximize the first critical buckling load and first natural frequency using the definition of linear fiber orientation angles. To show the power of the genetic algorithm for the VAT structure, a surrogate model using Response Surface (RS) method was used to demonstrate the convergence of the GA approach. The results showed the cost reduction for optimized VAT performance through GA optimization in combination with the 1D CUF procedure. Additionally, a Latin hypercube sampling (LHS) method with RS was used for buckling analysis. The capability of LHS sampling confirmed that it could be employed for the next stages of research along with GA.

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