1,721,147 research outputs found
Mixed finite elements for nonlocal elastic multilayered composite plate refined theories
Full text linkA novel mixed finite element formulation for the layerwise analysis of nonlocal multilayered composite plates is
presented. The finite elements are formulated starting from the weak form of a set of governing equations for the
laminate layers that were deduced via the Reissner Mixed Variational Theorem. The primary variables, namely
displacements and out-of-plane stresses, are expressed at layer level as through-the-thickness expansions of suitable
selected functions with coefficients approximated by the finite element scheme. The through-the-thickness expansion
order is considered as a free parameter. This way, finite elements for different refined higher order plate
theories can be systematically developed by assembling the layers contributions associated with the variable expansion
terms. These contributions are called fundamental nuclei and their definition is formally unique whatever
the considered expansion order. The obtained finite elements inherently ensure stresses and displacements continuity
at the layer interfaces and they allow to associate different values of the nonlocal parameter to the laminate
layers. Standard 9-node and 16-node isoparametric, quadrilateral finite elements have been implemented to verify
the viability of the proposed formulation. The obtained results compare favourably with literature solutions and
highlight the characteristics of the approach. Original results are proposed also to serve as benchmarking data
Discontinuous Galerkin models for composite multilayered shells with higher order kinematics
No full textComposite multilayered shells are widely employed in aerospace, automotive and civil engineering as weight-saving structural components. In multilayered shells, despite its versatility, the interplay between the curved geometry and the properties of the composite layers induces a complex distribution of the mechanical fields, which must be accurately resolved to safely employ generally curved composite shells as load-bearing structures.
The problem can be addressed through the two-dimensional shell theories, which are based on suitable assumptions on the behavior of the mechanical fields throughout the thickness of the considered structures and are a viable strategy for reducing the computational complexity with respect to 3D models. After the wide investigation on the CLT and FSDT shell theories, motivated by the need of accurate models, researchers have introduced the so-called higher-order theories for plate and shells. These can be classified into Equivalent-Single-Layer (ESL) theories, whereby the layers are replaced by a single layer with equivalent mechanical properties, Layer-Wise (LW) theories, whereby each layer is treated independently, and sub-laminate theories, whereby groups of layers are replaced by groups of equivalent layers. A unified description of these approaches has been introduced by the Carrera Unified Formulation (CUF) [1], which provides a framework able to determine the best 2D theory in terms of computational efficiency versus solution accuracy for a given structural problem. In most cases, numerical models based on these theories are solved using the Finite Element Method [2]. Among the available numerical strategies alternative to FEM for solving problems governed by systems of partial differential equations, the discontinuous Galerkin (dG) method has been recognized as powerful in enabling the seamless use of high-order elements and hierarchical meshes with tunable hp-refinement. The dG approach has been successfully used for general plate theories described via the CUF [3,4].
In this work, for the first time, Equivalent-Single-Layer dG formulations for generally curved multilayered shells are proposed. To account for complex structures, the shell geometry is described by using NURBS whereas different order theories are obtained via a CUF-based description of the shell kinematic model. An Interior Penalty dG scheme, which allows for a high-order numerical solution of the governing equations throughout the shell modeling domain. The dG scheme is also coupled with the implicitly defined mesh technique, which allows to resolve curved boundaries with high-order accuracy by combining an easy-to-generate background grid and the implicit representation of the domain of analysis. Results are presented to show the accuracy and potentiality of the proposed approach.
References
[1] E. Carrera. Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Archives of Computational Methods in Engineering, 10(3):215{296, 2003.
[2] M. F. Caliri, A. J.M. Ferreira, V. Tita. A review on plate and shell theories for laminated and sandwich structures highlighting the Finite Element Method. Composite Structures, 156: 63-77, 2016.
[3] V. Gulizzi, I. Benedetti, and A. Milazzo. An implicit mesh discontinuous Galerkin formulation for higher-order plate theories. Mechanics of Advanced Materials and Structures, 27(17):1494-1508, 2020.
[4] V. Gulizzi, I. Benedetti, and A. Milazzo. A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates. Composite Structures, 242:112137, 2020
Accurate Multilayered Shell Buckling Analysis via the Implicit-Mesh Discontinuous Galerkin Method
Full text linkA novel formulation for the linear buckling analysis of multilayered shells is presented. High-order equivalent single-layer shell theories based on the through-the-thickness expansion of the covariant components of the displace ment field are employed. The novelty of the formulation regards the governing equations solution via implicit-mesh
discontinuous Galerkin method. It is a high-order accurate numerical technique based on a discontinuous
representation of the solution among the mesh elements and on the use of suitably defined boundary integrals to
enforce the continuity of the solution at the inter-element interfaces as well as the boundary conditions. Owing to its
discontinuous nature, it can be naturally employed with nonconventional meshes. In this work, it is combined with the
implicitly defined mesh technique, whereby the mesh of the shell modeling domain is constructed by intersecting an
easy-to-generate background grid and a level set function implicitly representing the cutouts. Several numerical
examples are considered for the buckling loads of plates and shells modeled by different theories and characterized by
various materials, geometry, boundary conditions, and cutouts. The obtained results are compared with literature
and finite-element solutions, and they demonstrate the accuracy and the robustness of the proposed approac
A single-domain Ritz approach for buckling and post-buckling analysis of cracked plates
No full textA Ritz approach for the analysis of buckling and post-buckling of plates with through-the-thickness cracks is presented. The plate behavior is described by the first order shear deformation theory and von Kar- man’s geometric nonlinearity. The admissible functions used in the displacements approximation are se- ries of regular orthogonal polynomial supplemented with special functions able to decribe the diconti- nuity across the crack and the singularity at the crack tips; boundary functions are used to fullfill the homogeneous essential boundary conditions. Convergence studies and analysis results are presented for buckling and post-buckling of plates with a central through-the-thickness crack evidencing differences in the structural response between pre- and post-buckling regimes, which can substantially affect the plate residual strength. The performed analyses show the efficiency and potential of the method, which pro- vides accurate results in conjunction with a reduced number of degrees of freedom and simplified data preparation
A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates
Full text linkIn this work, a novel high-resolution formulation for multilayered composite plates is presented. The formulations
is referred to as high-resolution since it combines (i) Layer-Wise plate theories, which are based on a perlayer,
high-order expansion of the primary variables throughout the plate’s thickness, providing a detailed layerlevel
description of the sought solution; (ii) The discontinuous Galerkin method, a numerical approach based on
a discontinuous representation of the unknown fields over the mesh elements and on the introduction of
boundary integral operators enforcing inter-element continuity, which allow the natural treatment of high-order
mesh elements and provide high-resolution on the representation of the primary variables and their derivatives;
(iii) The implicitly-defined mesh technique, a meshing strategy based on an implicit representation of the plate
domain, which allows resolving the presence of curved boundaries with high-order accuracy.
Numerical tests are provided to investigate the effect of the penalty parameter and to show the optimal
convergence of the proposed formulation, which is subsequently employed in combination with an implicitlydefined
hierarchical quad-tree mesh to resolve the stress distribution in a rectangular plate and in a plate with a
circular hol
A hybrid virtual–boundary element formulation for heterogeneous materials
Full text linkIn this work, a hybrid formulation based on the conjoined use of the recently developed virtual element method (VEM) and the boundary element method (BEM) is proposed for the effective computational analysis of multi-region domains, representative of heterogeneous materials. VEM has been recently developed as a generalisation of the finite element method (FEM) and it allows the straightforward employment of elements of general polygonal shape, maintaining a high level of accuracy. For its inherent features, it allows the use of meshes of general topology, including non-convex elements. On the other hand, BEM is an effective technique for the numerical solution of sets of boundary integral equations, employed as the original model of the represented physical problem. For several classes of problems, BEM offers some advantages over more popular techniques, namely the reduction of the dimensionality of the problem, with associated computational savings. In this study, the inherent advantages of VEM and BEM are simultaneously employed for the study of heterogeneous material microstructures.
The method has been applied to i) the elastic analysis and ii) computational homogenization of fibre-reinforced composite materials and to iii) the analysis of composite unit cells exhibiting matrix isotropic damage. The discussed results show how the hybrid technique inherits the generality of VEM and the modelling simplification and accuracy of BEM, ensuring high accuracy and fast convergence and providing a versatile tool for the analysis of multiphase materials, also including non-linear behaviour such as material degradation. Further directions of research are identified and discussed after commenting on the presented results
X-Ritz Solution for Nonlinear Free Vibrations of Plates with Embedded Cracks
No full textThe analysis of large amplitude vibrations of cracked plates is considered in this study. The problem is addressed via a Ritz
approach based on the first-order shear deformation theory and von Kármán’s geometric nonlinearity assumptions. The
trial functions are built as series of regular orthogonal polynomial products supplemented with special functions able to
represent the crack behaviour (which motivates why the method is dubbed as eXtended Ritz); boundary functions are used
to guarantee the fulfillment of the kinematic boundary conditions along the plate edges. Convergence and accuracy are
assessed to validate the approach and show its efficiency and potential. Original results are then presented, which illustrate
the influence of cracks on the stiffening effect of large amplitude vibrations. These results can also serve as benchmark for
future solutions of the problem
Virtual Element Method: Micro-Mechanics Applications
No full textIn this contribution we present an application of the lowest order Virtual Element Method (VEM) to the problem of material computational homogenization. Material homogenization allows retrieving material properties through suitable volume averaging procedures, starting from a detailed representation of the micro-constituents of the considered material. The representation of such microstructure constitutes a remarkable effort in terms of data/mesh preparation, especially when there is not evident microstructural regularity. For such a reason, computational micromechanics may represent a challenging benchmark for showing the potential of VEM. In this contribution, polycrystalline materials are considered as an application. The proposed technique constitutes a first step towards modelling of damage processes in micro-structured materials
Post-Buckling Analysis of Damaged Multilayered Composite Stiffened Plates by Rayleigh-Ritz Method
No full textA Rayleigh-Ritz approach for the analysis of buckling and post-buckling behavior of
cracked composite stiffened plates is presented. The structure is modeled as the assembly of plate
elements modeled by the first order shear deformation theory and taking geometric nonlinearities
into account through the von Karman’s theory assumptions. Continuity along the plate elements
connected edges and the enforcement of rigid and elastic restraints of the plate boundaries are
obtained by using penalty techniques, which also allow to straightforwardly implement efficient
crack modeling strategies. General symmetric and unsymmetric stacking sequences are considered
and numerical procedures have been developed and used to validate the present solution by
comparison with FEA results. Original results are presented for post-buckling solution of
multilayered stiffened plates with through-the-thickness cracks, showing the effects of large
displacements on the cracked plate post-buckling behavior
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
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