Free vibration analysis of a sandwich cylindrical shell with an FG core based on the CUF

Habib Ahmadi,Kamran Foroutan,Erasmo Carrera 국제구조공학회 2022 Smart Structures and Systems, An International Jou Vol.30 No.2

An analytical approach for the free vibration behavior of a sandwich cylindrical shell with a functionally graded (FG) core is presented. It is considered that the FG distribution is in the direction of thickness. The material properties are temperature-dependent. The sandwich cylindrical shell with a FG core is considered with two cases. In the first model, i.e., Ceramic-FGM-Metal (CFM), the interior layer of the cylindrical shell is rich metal while the exterior layer is rich ceramic and the FG material is located between two layers and for the second model i.e., Metal-FGM-Ceramic (MFC), the material distribution is in reverse order. This study develops Carrera's Unified Formulation (CUF) to analyze sandwich cylindrical shell with an FG core for the first time. Considering the Principle of Virtual Displacements (PVDs) according to the CUF, the dependent boundary conditions and governing equations are obtained. The coupled governing equations are derived using Galerkin's method. In order to validate the present results, comparisons are made with the available solutions in the previous researches. The effects of different geometrical and material parameters on the free vibration behavior of a sandwich cylindrical shell with an FG core are examined.

Analysis of Stokes flows by Carrera unified formulation

Varello, Alberto,Pagani, Alfonso,Guarnera, Daniele,Carrera, Erasmo Techno-Press 2018 Advances in aircraft and spacecraft science Vol.5 No.3

One-dimensional (1D) models of incompressible flows, can be of interest for many applications in which fast resolution times are demanded, such as fluid-structure interaction of flows in compliant pipes and hemodynamics. This work proposes a higher-order 1D theory for the flow-field analysis of incompressible, laminar, and viscous fluids in rigid pipes. This methodology is developed in the domain of the Carrera Unified Formulation (CUF), which was first employed in structural mechanics. In the framework of 1D modelling, CUF allows to express the primary variables (i.e., velocity and pressure fields in the case of incompressible flows) as arbitrary expansions of the generalized unknowns, which are functions of the 1D computational domain coordinate. As a consequence, the governing equations can be expressed in terms of fundamental nuclei, which are invariant of the theory approximation order. Several numerical examples are considered for validating this novel methodology, including simple Poiseuille flows in circular pipes and more complex velocity/pressure profiles of Stokes fluids into non-conventional computational domains. The attention is mainly focused on the use of hierarchical McLaurin polynomials as well as piece-wise nonlocal Lagrange expansions of the generalized unknowns across the pipe section. The preliminary results show the great advantages in terms of computational costs of the proposed method. Furthermore, they provide enough confidence for future extensions to more complex fluid-dynamics problems and fluid-structure interaction analysis.

Free vibration analysis of damaged beams via refined models

Petrolo, Marco,Carrera, Erasmo,Alawami, Ali Saeghier Ali Saeed Techno-Press 2016 Advances in aircraft and spacecraft science Vol.3 No.1

This paper presents the free vibration analysis of damaged beams by means of 1D (beam) advanced finite element models. The present 1D formulation stems from the Carrera Unified Formulation (CUF), and it leads to a Component-Wise (CW) modelling. By means of the CUF, any order 2D and 1D structural models can be developed in a unified and hierarchical manner, and they provide extremely accurate results with very low computational costs. The computational cost reduction in terms of total amount of DOFs ranges from 10 to 100 times less than shell and solid models, respectively. The CW provides a detailed physical description of the real structure since each component can be modelled with its material characteristics, that is, no homogenization techniques are required. Furthermore, although 1D models are exploited, the problem unknown variables can be placed on the physical surfaces of the real 3D model. No artificial surfaces or lines have to be defined to build the structural model. Global and local damages are introduced by decreasing the stiffness properties of the material in the damaged regions. The results show that the proposed 1D models can deal with damaged structures as accurately as a shell or a solid model, but with far lower computational costs. Furthermore, it is shown how the presence of damages can lead to shell-like modal shapes and torsional/bending coupling.

Accurate Free Vibration Analysis of Launcher Structures Using Refined 1D Models

Carrera, Erasmo,Zappino, Enrico,Cavallo, Tommaso The Korean Society for Aeronautical and Space Scie 2015 International Journal of Aeronautical and Space Sc Vol.16 No.2

This work uses different finite element approaches to the free vibration analysis of reinforced shell structures, and a simplified model of a typical launcher with two boosters is used as an example. The results obtained using a refined one-dimensional (1D) beam model are compared to those obtained with commercial finite element software. The 1D models that are used in the present work are based on the Carrera Unified Formulation (CUF), which assumes a variable kinematic displacement field over the cross-sections of the beam. Two different sets of polynomials that correspond to Taylor (TE) or Lagrange (LE) expansions were used. The analyses focused on three reinforced structures: a stiffened panel, a reinforced cylinder and the complete structure of the launcher. The frequencies and natural modes obtained using one-dimensional models are compared to those obtained from classical finite element analysis. The classical FE models were built using a beam-shell or solid elements, and the results indicate that the refined beam models can in fact be used to investigate the behavior of very complex reinforced structures. These models can predict the shell-like modes that are typical of thin-walled structures that cannot be detected using classical beam models. The refined 1D models used in the present work provide results that are as accurate as those from solid FE models, but the 1D models have a much lower computational cost.

Accurate Free Vibration Analysis of Launcher Structures Using Refined 1D Models

Erasmo Carrera,Enrico Zappino,Tommaso Cavallo 한국항공우주학회 2015 International Journal of Aeronautical and Space Sc Vol.16 No.2

This work uses different finite element approaches to the free vibration analysis of reinforced shell structures, and a simplified model of a typical launcher with two boosters is used as an example. The results obtained using a refined one-dimensional (1D) beam model are compared to those obtained with commercial finite element software. The 1D models that are used in the present work are based on the Carrera Unified Formulation (CUF), which assumes a variable kinematic displacement field over the cross-sections of the beam. Two different sets of polynomials that correspond to Taylor (TE) or Lagrange (LE) expansions were used. The analyses focused on three reinforced structures: a stiffened panel, a reinforced cylinder and the complete structure of the launcher. The frequencies and natural modes obtained using one-dimensional models are compared to those obtained from classical finite element analysis. The classical FE models were built using a beam-shell or solid elements, and the results indicate that the refined beam models can in fact be used to investigate the behavior of very complex reinforced structures. These models can predict the shell-like modes that are typical of thin-walled structures that cannot be detected using classical beam models. The refined 1D models used in the present work provide results that are as accurate as those from solid FE models, but the 1D models have a much lower computational cost.

Capabilities of 1D CUF-based models to analyse metallic/composite rotors

Filippi, Matteo,Carrera, Erasmo Techno-Press 2016 Advances in aircraft and spacecraft science Vol.3 No.1

The Carrera Unified Formulation (CUF) is here extended to perform free-vibrational analyses of rotating structures. CUF is a hierarchical formulation, which enables one to obtain refined structural theories by writing the unknown displacement variables using generic functions of the cross-section coordinates (x, z). In this work, Taylor-like expansions are used. The increase of the theory order leads to three-dimensional solutions while, the classical beam models can be obtained as particular cases of the linear theory. The Finite Element technique is used to solve the weak form of the three-dimensional differential equations of motion in terms of "fundamental nuclei", whose forms do not depend on the adopted approximation. Including both gyroscopic and stiffening contributions, structures rotating about either transversal or longitudinal axis can be considered. In particular, the dynamic characteristics of thin-walled cylinders and composite blades are investigated to predict the frequency variations with the rotational speed. The results reveal that the present one-dimensional approach combines a significant accuracy with a very low computational cost compared with 2D and 3D solutions. The advantages are especially evident when deformable and composite structures are analyzed.

Static Aeroelastic Response of Wing-Structures Accounting for In-Plane Cross-Section Deformation

Varello, Alberto,Lamberti, Alessandro,Carrera, Erasmo The Korean Society for Aeronautical and Space Scie 2013 International Journal of Aeronautical and Space Sc Vol.14 No.4

In this paper, the aeroelastic static response of flexible wings with arbitrary cross-section geometry via a coupled CUF-XFLR5 approach is presented. Refined structural one-dimensional (1D) models, with a variable order of expansion for the displacement field, are developed on the basis of the Carrera Unified Formulation (CUF), taking into account cross-sectional deformability. A three-dimensional (3D) Panel Method is employed for the aerodynamic analysis, providing more accuracy with respect to the Vortex Lattice Method (VLM). A straight wing with an airfoil cross-section is modeled as a clamped beam, by means of the finite element method (FEM). Numerical results present the variation of wing aerodynamic parameters, and the equilibrium aeroelastic response is evaluated in terms of displacements and in-plane cross-section deformation. Aeroelastic coupled analyses are based on an iterative procedure, as well as a linear coupling approach for different free stream velocities. A convergent trend of displacements and aerodynamic coefficients is achieved as the structural model accuracy increases. Comparisons with 3D finite element solutions prove that an accurate description of the in-plane cross-section deformation is provided by the proposed 1D CUF model, through a significant reduction in computational cost.

Static Aeroelastic Response of Wing-Structures Accounting for In-Plane Cross-Section Deformation

Alberto Varello,Alessandro Lamberti,Erasmo Carrera 한국항공우주학회 2013 International Journal of Aeronautical and Space Sc Vol.14 No.4

In this paper, the aeroelastic static response of flexible wings with arbitrary cross-section geometry via a coupled CUFXFLR5 approach is presented. Refined structural one-dimensional (1D) models, with a variable order of expansion for the displacement field, are developed on the basis of the Carrera Unified Formulation (CUF), taking into account cross-sectional deformability. A three-dimensional (3D) Panel Method is employed for the aerodynamic analysis, providing more accuracy with respect to the Vortex Lattice Method (VLM). A straight wing with an airfoil cross-section is modeled as a clamped beam, by means of the finite element method (FEM). Numerical results present the variation of wing aerodynamic parameters, and the equilibrium aeroelastic response is evaluated in terms of displacements and in-plane cross-section deformation. Aeroelastic coupled analyses are based on an iterative procedure, as well as a linear coupling approach for different free stream velocities. A convergent trend of displacements and aerodynamic coefficients is achieved as the structural model accuracy increases. Comparisons with 3D finite element solutions prove that an accurate description of the in-plane crosssection deformation is provided by the proposed 1D CUF model, through a significant reduction in computational cost.

Full composites hydrogen fuel cells unmanned aerial vehicle with telescopic boom

Carrera, E.,Verrastro, M.,Boretti, Alberto Techno-Press 2022 Advances in aircraft and spacecraft science Vol.9 No.1

This paper discusses an improved unmanned aerial vehicle, UAV, configuration characterized by telescopic booms to optimize the flight mechanics and fuel consumption of the aircraft at various loading/flight conditions.The starting point consists of a full-composite smaller UAV which was derived by a general aviation ultralight motorized aircraft ULM. The present design, named ToBoFlex, extends the two-booms configuration to a three tons aircraft. To adapt the design to needs relevant to different applications, new solutions were proposed in aerodynamic fields and materials and structural areas. Different structural solutions were reported. To optimize aircraft endurance, the innovative concept of Telescopic Tail Boom was considered along with two different tails architecture. A new structural configuration of the fuselage was proposed. Further consideration of hydrogen fuel cell electric propulsion is now being studied in collaboration between the Polytechnic of Turin and Prince Mohammad Bin Fahd University which could be the starting point of future investigations.

Full composites hydrogen fuel cells unmanned aerial vehicle with telescopic boom

Carrera, E.,Verrastro, M.,Boretti, Alberto Techno-Press 2022 Advances in aircraft and spacecraft science Vol.9 No.1

This paper discusses an improved unmanned aerial vehicle, UAV, configuration characterized by telescopic booms to optimize the flight mechanics and fuel consumption of the aircraft at various loading/flight conditions.The starting point consists of a full-composite smaller UAV which was derived by a general aviation ultralight motorized aircraft ULM. The present design, named ToBoFlex, extends the two-booms configuration to a three tons aircraft. To adapt the design to needs relevant to different applications, new solutions were proposed in aerodynamic fields and materials and structural areas. Different structural solutions were reported. To optimize aircraft endurance, the innovative concept of Telescopic Tail Boom was considered along with two different tails architecture. A new structural configuration of the fuselage was proposed. Further consideration of hydrogen fuel cell electric propulsion is now being studied in collaboration between the Polytechnic of Turin and Prince Mohammad Bin Fahd University which could be the starting point of future investigations.