Papers by Francesco Tornabene
Applied Sciences
This work studies the buckling and free vibration behavior of Shape Memory Alloy Hybrid Composite... more This work studies the buckling and free vibration behavior of Shape Memory Alloy Hybrid Composite (SMAHC) sandwich beams under a thermal environment. The sandwich beams consist of layers reinforced with SMAs and a FGM core, and they are simply supported at both ends. The higher order theory is combined with the Minimum Potential Energy principle or Hamilton principle to derive the governing equations of the thermal buckling and thermal vibration problems, respectively. The material properties of the beam are assumed as temperature-independent (TID) or temperature-dependent (TD). In the last case, two different types of thermal distribution are considered, namely a uniform and a linear distribution. The results based on the proposed formulation are verified against the reference literature, with a very good matching. A parametric study checks for the influence of different effective parameters such as thickness-to-length ratios, volume fraction powers, initial strain, volume fraction...
Nanomaterials
The increased requirements in design and manufacturing nanotechnology have favored the developmen... more The increased requirements in design and manufacturing nanotechnology have favored the development of enhanced composite materials with tailored properties, such as functionally graded (FG) and carbon-based materials, primarily carbon nanotubes (CNTs), and graphene sheets or nanoplatelets, because of their remarkable mechanical properties, electrical conductivity, and high permeability [...]
Applied Sciences
The large use of composite materials and shell structural members with complex geometries in tech... more The large use of composite materials and shell structural members with complex geometries in technologies related to various branches of engineering, has gained increased attention from scientists and engineers for the development of even more refined approaches, to investigate their mechanical behavior [...]
Applied Sciences
The advancement in manufacturing technology and scientific research have improved the development... more The advancement in manufacturing technology and scientific research have improved the development of enhanced composite materials with tailored properties depending on their design requirements in many engineering fields, as well as in thermal and energy management [...]
Applied Sciences
The present work studies an axisymmetric rotating truncated cone made of functionally graded (FG)... more The present work studies an axisymmetric rotating truncated cone made of functionally graded (FG) porous materials reinforced by graphene platelets (GPLs) under a thermal loading. The problem is tackled theoretically based on a classical linear thermoelasticity approach. The truncated cone consists of a layered material with a uniform or non-uniform dispersion of GPLs in a metal matrix with open-cell internal pores, whose effective properties are determined according to the extended rule of mixture and modified Halpin–Tsai model. A graded finite element method (FEM) based on Rayleigh–Ritz energy formulation and Crank–Nicolson algorithm is here applied to solve the problem both in time and space domain. The thermo-mechanical response is checked for different porosity distributions (uniform and functionally graded), together with different types of GPL patterns across the cone thickness. A parametric study is performed to analyze the effect of porosity coefficients, weight fractions o...
Applied Sciences
This work deals with the wave propagation analysis in functionally graded carbon nanotubes (CNTs)... more This work deals with the wave propagation analysis in functionally graded carbon nanotubes (CNTs)-reinforced composite beams lying on an elastic medium. Despite the large amount of experimental and theoretical studies in the literature on the mechanical behavior of composite structures strengthened with CNTs, limited attention has been paid to the effect of an axial graduation of the reinforcing phase on the mechanical response of CNTs-reinforced composite beams. In this paper, CNT fibers are graded across the beam length, according to a power-law function, which expresses a general variation from a linear to parabolic pattern. An Euler-Bernoulli beam theory is considered herein to model the CNTs-reinforced composite structure resting on a Winkler–Pasternak foundation, whose governing equations are derived from the Hamiltonian principle. The theoretical solution of the problem checks for the sensitivity of the mechanical response to different parameters, i.e., the wave number, power...
This work focuses on the static analysis of functionally graded (FGM) and laminated doubly-curved... more This work focuses on the static analysis of functionally graded (FGM) and laminated doubly-curved shells and panels resting on nonlinear and linear elastic foundations using the Generalized Differential Quadrature (GDQ) method. The First-order Shear Deformation Theory (FSDT) for the aforementioned moderately thick structural elements is considered. The solutions are given in terms of generalized displacement components of points lying on the middle surface of the shell. Several types of shell structures such as doubly-curved shells (elliptic and hyperbolic hyperboloids), singly-curved (spherical, cylindrical and conical shells), and degenerate panels
A comparative SFEMand IGA-based numerical prediction of the stress concentration factor in plates... more A comparative SFEMand IGA-based numerical prediction of the stress concentration factor in plates with discontinuities / Dimitri, Rossana; Fantuzzi, Nicholas; Tornabene, Francesco; Zavarise, Giorgio. ELETTRONICO. (2016), pp. 34-35. ((Intervento presentato al convegno XXI Convegno Italiano di Meccanica Computazionale e VIII Riunione del Gruppo Materiali AIMETA, tenutosi a Lucca, Italia nel 27-29 Giugno 2016. Original A comparative SFEMand IGA-based numerical prediction of the stress concentration factor in plates with discontinuities
Journal of Composites Science, 2021
The present work analyzes the free vibration response of functionally graded (FG) plates made of ... more The present work analyzes the free vibration response of functionally graded (FG) plates made of Aluminum (Al) and Alumina (Al2O3) with different porosity distributions, as usually induced by a manufacturing process. The problem is tackled theoretically based on a higher-order shear deformation plate theory, while proposing a Navier-type approximation to solve the governing equations for simply-supported plates with different porosity distributions in the thickness direction. The reliability of the proposed theory is checked successfully by comparing the present results with predictions available from literature based on further first-order or higher-order theories. A large parametric study is performed systematically to evaluate the effect of different mechanical properties, such as the material indexes, porosity volume fractions, porosity distributions, and length-to-thickness ratios, on the free vibration response of FG plates, as useful for the design purposes of most engineered...
A collocation model based on a Generalized Differential Quadrature Method (GDQM) is proposed for ... more A collocation model based on a Generalized Differential Quadrature Method (GDQM) is proposed for the dynamic analysis of anisotropic curved laminated structures with a central lattice core and different external constraints. The theory is based on the Equivalent Single Layer (ESL) approach, together with higher-order kinematic assumptions. The reliability of the proposed method is checked with respect to classical 3D FEM-based solutions, for different shell geometries, lamination schemes and unit cell configurations. Based on the numerical investigation, the proposed formulation reveals to be computationally performing even for complicated shapes and structural members, compared to more expensive commercial finite-element-based packages.
Symmetry, 2020
In this paper, we focus on the bending behavior of isotropic doubly-curved nanoshells based on a ... more In this paper, we focus on the bending behavior of isotropic doubly-curved nanoshells based on a high-order shear deformation theory, whose shape functions are selected as an accurate combination of exponential and trigonometric functions instead of the classical polynomial functions. The small-scale effect of the nanostructure is modeled according to the differential law consequent, but is not equivalent to the strain-driven nonlocal integral theory of elasticity equipped with Helmholtz’s averaging kernel. The governing equations of the problem are obtained from the Hamilton’s principle, whereas the Navier’s series are proposed for a closed form solution of the structural problem involving simply-supported nanostructures. The work provides a unified framework for the bending study of both thin and thick symmetric doubly-curved shallow and deep nanoshells, while investigating spherical and cylindrical panels subjected to a point or a sinusoidal loading condition. The effect of sever...
Nanomaterials, 2018
This study aims at investigating the wave propagation of porous nanoshells. The Bi-Helmholtz non-... more This study aims at investigating the wave propagation of porous nanoshells. The Bi-Helmholtz non-local strain gradient theory is employed in conjunction with a higher-order shear deformation shell theory, in order to include the size-dependent effects. The nanoshells are made of a porous functionally graded material (P-FGM), whose properties vary continuously along the thickness direction. A variational approach is here applied to handle the governing equations of the problem, which are solved analytically to compute the wave frequencies and phase velocities as function of the wave numbers. The sensitivity of the wave response is analyzed for a varying porosity volume fraction, material properties, non-local parameters, strain gradient length scales, temperature, humidity, and wave numbers. Based on the results, it is verified that the size-dependence of the response is almost the same to the one of plates, beams and tubes.
Composites Part B: Engineering, 2018
The present work shows a systematic comparison between different shell models in the case of stat... more The present work shows a systematic comparison between different shell models in the case of static analysis of multilayered composite and sandwich plates and spherical shells. Transverse shear loads are applied on these structures. The behavior through the thickness direction is analyzed in terms of the three displacement components and the six stress components. Such evaluations allow to remark the typical zigzag effect of displacements and the interlaminar continuity conditions in terms of congruence and equilibrium equations in the multilayered plates and shells. The boundary load conditions at the external surfaces are also verified. The proposed 3D models are closed form solutions of 3D shell theories developed in the framework of analytical and semi-analytical approaches for differential equations in z. The 2D numerical shell models are classical and refined models developed in both equivalent single layer and layer wise viewpoints. 2D numerical theories are solved by means of the Generalized Differential Quadrature Model (GDQM), which allows general solutions for different boundary conditions, load applications, lamination schemes and geometries. The advantages of this methodology are also clearly shown and discussed for complicated geometries such as doublecurved shells.
Thin-Walled Structures, 2018
POLITECNICO DI TORINO Repository ISTITUZIONALE 3D capability of refined GDQ models for the bendin... more POLITECNICO DI TORINO Repository ISTITUZIONALE 3D capability of refined GDQ models for the bending analysis of composite and sandwich plates, spherical and doublycurved shells / Tornabene, Francesco; Brischetto, Salvatore.-In: THIN-WALLED STRUCTURES.
Composite Structures, 2016
Original 2D and 3D shell models for the free vibration investigation of functionally graded cylin... more Original 2D and 3D shell models for the free vibration investigation of functionally graded cylindrical and spherical panels Publisher:
Applied Sciences, 2017
The main aim of the present paper is to solve numerically the free vibration problem of sandwich ... more The main aim of the present paper is to solve numerically the free vibration problem of sandwich shell structures with variable thickness and made of Functionally Graded Materials (FGMs). Several Higher-order Shear Deformation Theories (HSDTs), defined by a unified formulation, are employed in the study. The FGM structures are characterized by variable mechanical properties due to the through-the-thickness variation of the volume fraction distribution of the two constituents and the arbitrary thickness profile. A four-parameter power law expression is introduced to describe the FGMs, whereas general relations are used to define the thickness variation, which can affect both the principal coordinates of the shell reference domain. A local scheme of the Generalized Differential Quadrature (GDQ) method is employed as numerical tool. The natural frequencies are obtained varying the exponent of the volume fraction distributions using higher-order theories based on a unified formulation. The structural models considered are two-dimensional and require less degrees of freedom when compared to the corresponding three-dimensional finite element (FE) models, which require a huge number of elements to describe the same geometries accurately. A comparison of the present results with the FE solutions is carried out for the isotropic cases only, whereas the numerical results available in the literature are used to prove the validity as well as accuracy of the current approach in dealing with FGM structures characterized by a variable thickness profile.
Applied Sciences, 2016
The main purpose of the paper is to present an innovative higher-order structural theory to accur... more The main purpose of the paper is to present an innovative higher-order structural theory to accurately evaluate the natural frequencies of laminated composite shells. A new kinematic model is developed starting from the theoretical framework given by a unified formulation. The kinematic expansion is taken as a free parameter, and the three-dimensional displacement field is described by using alternatively the Legendre or Lagrange polynomials, following the key points of the most typical Layer-wise (LW) approaches. The structure is considered as a unique body and all the geometric and mechanical properties are evaluated on the shell middle surface, following the idea of the well-known Equivalent Single Layer (ESL) models. For this purpose, the name Equivalent Layer-Wise (ELW) is introduced to define the present approach. The governing equations are solved numerically by means of the Generalized Differential Quadrature (GDQ) method and the solutions are compared with the results available in the literature or obtained through a commercial finite element program. Due to the generality of the current method, several boundary conditions and various mechanical and geometric configurations are considered. Finally, it should be underlined that different doubly-curved surfaces may be considered following the mathematical framework given by the differential geometry.
Mechanics of Advanced Materials and Structures, 2016
Structural and Computational Mechanics Book Series, 2016
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Papers by Francesco Tornabene