323,123 research outputs found
A variable kinematic doubly-curved MITC9 shell element for the analysis of laminated composites
No full textThe present article considers the linear static analysis of composite shell structures with double-curvature geometry by means of a shell finite element with variable through-the-thickness kinematic. The refined models used are grouped in the Unified Formulation by Carrera (CUF) and they permit the distribution of displacements and stresses along the thickness of the multilayered shell to be accurately described. 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 governing equations are derived from the principle of virtual displacement (PVD) and the finite element method (FEM) is employed to solve them. Cross-ply spherical shells with simply-supported edges and subjected to bi-sinusoidal pressure are analyzed. 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 the literature and the analytical solutions obtained using the CUF and the Navier's method. From the analysis, one can conclude that the shell element based on the CUF is very efficient and its use is mandatory with respect to the classical models in the study of composite structures. Finally, shells with different lamination, boundary conditions, and loads are also analyzed using high-order layer-wise theories in order to provide FEM benchmark solution
Nonlocal analytical solution for multilayered composite shells
No full textAbstract In this work, an advanced nonlocal analytical formulation for the static analysis of composite
shell structures is proposed. The governing equations are derived from the Principle of Virtual
Displacement (PVD) [1] and are solved by the use of the Navier solution [2]. Layer-Wise models
related to linear up to fourth order variations of the unknown variables in the thickness direction are
treated. The modelization of multilayered structure materials takes into account the composite material
properties and the nonlocal behavior based on the work of Eringen [3]. In order to take into account
the nonlocality of the material, the Eringen’s stress-gradient model is employed [4]. The novelty and
innovation of this work is related to the development of an advanced nonlocal analytical formulation
for static analysis of composite shells structures by the use of stress-gradient model combined with
Layer-Wise kinematics. The accuracy of the present analytical formulation is validate through various
assessments. Isotropic, cross-ply composite and simply-supported shell structures are considered.
Different lamination sequences and different shell aspect ratios are taken into account to generalize
the obtained results. References [1] J.N. Reddy, An evaluation of equivalent-single-layer and layerwise
theories of composite laminates, Composite Structures, 25 (1993) 21–35. [2] A. Alaimo, C. Orlando,
S. Valvano, Analytical frequency response solution for composite plates embedding viscoelastic layers,
Aerospace Science and Technology 92 (2019) 429–445. [3] A.C. Eringen, D.G.B. Edelen, On nonlocal
elasticity, International Journal of Engineering Science, 10 (1972) 233–248. [4] J.N. Reddy, Nonlocal
theories for bending, buckling and vibration of beams, International Journal of Engineering Science, 45
(2007) 288–307
Variable kinematic shell elements for the analysis of electro-mechanical problems
No full textThe present article considers the linear static analysis of both composite plate and shell structures embedding piezoelectric layers by means of a shell finite element with variable through-the-thickness kinematic. The refined models used are grouped in the Unified Formulation by Carrera (CUF) and they permit to accurately describe the distribution of displacements and stresses along the thickness of the multilayered shell. The shell element has nine nodes and the mixed interpolation of tensorial components (MITC) method is employed to contrast the membrane and shear locking phenomenon. The governing equations are derived from the principle of virtual displacement (PVD) and the finite element method (FEM) is employed to solve them. Cross-ply multilayered plates and cylindrical shells embedding piezoelectric layers are analyzed with simply-supported boundary conditions and subjected to sensor and actuator configurations. Various thickness 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 Naviers method. From the analysis, one can conclude that the shell element based on the CUF is very efficient and its use is mandatory with respect to the classical models in the study of multilayered structures embedding piezo-layers. © 201
Thermal Stress Analysis of laminated structures by a variable kinematic MITC9 shell element
No full textA linear static thermal stress analysis of composite shell structures is carried out by means of a shell nite element with variable through-the-thickness kinematic. The re- ned models used are both Equivalent Single Layer (ESL) and Layer Wise (LW) and they are grouped in the Unied Formulation by Carrera (CUF). These models permit the distribution of displacements, stresses and temperature along the thickness of the multi- layered shell to be accurately described. The Principle of Virtual Displacement (PVD) is employed to derive the governing equations. The Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phe- nomenon for a nine-node shell element. Cross-ply plate, cylindrical and spherical shells with simply-supported edges and subjected to bi-sinusoidal thermal load are analyzed and various thickness ratios are considered. The results, obtained with dierent theories con- tained in the CUF, are compared with both the elasticity solutions given in the literature and the analytical solutions obtained using higher-order models and the Navier's method. From the analysis, one can conclude that the shell element based on the CUF is very ef- cient, and its use leads to reach higher accuracy than classical models in the study of layered structure
Electro-mechanical analysis of composite and sandwich multilayered structures by shell elements with node-dependent kinematics
No full textIn this work, a new class of finite elements for the analysis of composite and sandwich shells embedding piezoelectric skins and patches is proposed. The main idea of models coupling is developed by presenting the concept of nodal dependent kinematics where the same finite element can present at each node a different approximation of the main unknowns by setting a node-wise through-the-thickness approximation base. In a global/local approach scenario, the computational costs can be reduced drastically by assuming refined theories only in those zones/nodes of the structural domain where the resulting strain and stress states, and their electro-mechanical coupling present a complex distribution. Several numerical investigations are carried out to validate the accuracy and efficiency of the present shell element. An accurate representation of mechanical stresses and electric displacements in localized zones is possible with reduction of the computational costs if an accurate distribution of the higher-order kinematic capabilities is performed. On the contrary, the accuracy of the solution in terms of mechanical displacements and electric potential values depends on the global approximation over the whole structure. The efficacy of the present node-dependent variable kinematic models, thus, depends on the characteristics of the problem under consideration as well as on the required analysis type
Heat conduction and thermal stress analysis of laminated composites by a variable kinematic MITC9 shell element
No full textThe present paper considers the linear static
thermal stress analysis of composite structures by means
of a shell finite element with variable through-thethickness
kinematic. The temperature profile along the
thickness direction is calculated by solving the Fourier
heat conduction equation. The refined models considered
are both Equivalent Single Layer (ESL) and Layer
Wise (LW) and are grouped in the Unified Formulation
by Carrera (CUF). These permit the distribution of displacements,
stresses along the thickness of the multilayered
shell to be accurately described. 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 governing
equations are derived from the Principle of Virtual Displacement
(PVD). Cross-ply plate, cylindrical and spherical
shells with simply-supported edges and subjected to
bi-sinusoidal thermal load are analyzed.Various 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 the
literature and the analytical solutions obtained using the
CUF and the Navier’s method. Finally, plates and shells
with different lamination and boundary conditions are analyzed
using high-order theories in order to provide FEM
benchmark solutions
A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches
No full textThe present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic. The refined models used are derived from Carrera’s Unified Formulation (CUF) and they permit the vibration modes along the thickness to be accurately described. The finite-element method is employed and the plate element implemented has nine nodes, and the mixed interpolation of tensorial component (MITC) method is used to contrast the membrane and shear locking phenomenon. The related governing equations are derived from the principle of virtual displacement, extended to the analysis of electromechanical problems. An isotropic plate with piezoelectric patches is analyzed, with clamped-free boundary conditions and subjected to open- and short-circuit configurations. The results, obtained with different theories, are compared with the higher-order type solutions given in the literature. The conclusion is reached that the plate element based on the CUF is more suitable and efficient compared to the classical models in the study of multilayered structures embedding piezo-patches
Classical, higher-order, zig-zag and variable kinematic shell elements for the analysis of composite multilayered structures
No full textIn the present work, a shell finite element with a variable kinematic field based on a new zig-zag power function
is proposed for the analysis of laminated shell structures. The kinematic field is written by using an arbitrary
number of continuous piecewise polynomial functions. The polynomial expansion order of a generic subdomain
is a combination of zig-zag power functions depending on the shell thickness coordinate. As in the classical layerwise approach, the shell thickness can be divided into a variable number of mathematical subdomains. The
expansion order of each subdomain is an input parameter of the analysis. This feature enables the solution to be
locally refined over generic regions of the shell thickness by enriching the kinematic field. The advanced finite
shell elements with variable kinematics are formulated in the framework of the Carrera Unified Formulation.
The finite element arrays are formulated in terms of fundamental nuclei, which are invariants of the theory
approximation order and the modelling technique (Equivalent-Single-Layer, Layer-Wise). In this work, the attention is focused on linear static stress analyses of composite laminated shell structures. The governing equations are obtained by applying the Principle of Virtual Displacements, and they are solved using the Finite
Element method. Furthermore, the Mixed Interpolated Tensorial Components (MITC) method is employed to
contrast the shear locking phenomenon. Several numerical investigations are carried out to validate and demonstrate the accuracy and efficiency of the present shell element
Analysis of multilayered structures embedding viscoelastic layers by higher-order, and zig-zag plate elements
No full textA variable kinematic shell formulation applied to thermal stress of laminated structures
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