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Refined zigzag models for the response of general multilayered composite and sandwich structures: numerical and experimental investigations
Full text linkL'abstract è presente nell'allegato / the abstract is in the attachmen
Dynamic analysis of sandwich beams with adhesive layers using the mixed Refined Zigzag Theory
Full text linkIn this paper, a dynamic analysis of the free vibration of sandwich beams is performed using the mixed Refined Zigzag Theory (RZT(m)). This recently developed theory has been demonstrated to be very accurate in predicting transverse displacements, fundamental frequencies, buckling loads, and local through-the-thickness quantities such as in-plane displacements and stresses. The beam is modelled using the quadrilateral finite element formulated by Refined Zigzag Theory for plates and the Reissner’s Mixed Variational Theorem in order to evaluate both flexural and torsional modes. Results of numerical models are compared with high-fidelity finite elements and those obtained with an experimental hammer test on sandwich beam specimens. It is concluded that the effect of the adhesive layers is crucial to assess the dynamic behavior of multilayered sandwich structures correctly
Robust TRIA3 and QUAD4 finite elements based on the en-RZT Kinematics for the analysis of general anisotropic multilayered composite plates
No full textA new set of robust finite elements for the analysis of general anisotropic multilayered composite plates was
presented. Recently, the enhanced-refined zigzag theory (en-RZT) has shown its accuracy in predicting the
structural response of laminated plates exhibiting a high transverse anisotropy. Moreover, the en-RZT requires
only C0 -continuous shape functions to formulate accurate and efficient finite elements. The formulation of
three-node triangular (TRIA3) and four-node quadrilateral (QUAD4) flat finite elements based on the en-RZT
kinematics was focused. In order to eliminate the shear-locking effect that affects low-order C0 -based elements,
the constrained anisoparametric interpolation strategy and an appropriate element shear correction (ESC)
factor were implemented at the element level. Then, the variational consistent triangular (enRZT-T3c) and
quadrilateral (enRZT-Q4c) elements were obtained and numerically assessed. A detailed analysis has been
performed to evaluate the convergence behavior of the newly formulated elements for bending and free-vibration
problems. The influence of the mesh distortion, load configurations, and boundary conditions were finely
addressed. The results provided and comparisons with 3D models demonstrate the accuracy and robustness of
enRZT-T3c and enRZT-Q4c elements for a wide variety of problems and laminate configurations, including
ultra-thin arbitrarily oriented multilayered plates
An experimental and numerical dynamic study of thick sandwich beams using a mixed {3,2}-RZT formulation
Full text linkThis work presents some numerical and experimental validations of the free-vibration behaviour of thick sandwich beams using the mixed {3,2}-Refined Zigzag Theory. The formulation enhances the Timoshenko’s kinematics with a piece-wise zigzag cubic distribution of the axial displacement, and a smoothed parabolic variation for the transverse deflection. Simultaneously, an a-priori assumption is made for the transverse normal stress and the transverse shear one: the former is assumed to be a third-order power series expansion of the thickness coordinate, the latter is derived through the integration of the Cauchy’s equations. The equations of motions and consistent boundary conditions for the free-vibration problem are derived through the Hellinger-Reissner (HR) theorem. Taking advantage of the C0-continuity requirement in the mixed governing functional, a simple two-node beam finite element (FE) is formulated. The analytical and FE performances of the proposed model are first addressed by means of a comparison with high-fidelity 3D FE models. Subsequently, an experimental campaign is conducted using LASER Doppler Vibrometry (LVD) to evaluate the modal parameters of a series of thick sandwich beams made of aluminium alloy face-sheets and Rohacell WF110 core. The experimental results concerning the natural frequencies and modal shapes of the thick sandwich beam specimens under free-free boundary conditions are compared with those given by the proposed model and high-fidelity 3D FE models. The numerical-experimental assessment highlights the effect of core and face-sheet thickness on frequency estimations, as well as the complexity of reproducing in the numerical model the real boundary conditions. In general, the element formulation demonstrates its accuracy and computational advantages in the dynamic analysis of thick sandwich beams
Bending, free vibration and buckling of functionally graded carbon nanotube-reinforced sandwich plates, using the extended Refined Zigzag Theory
Full text linkThe paper presents an application of the extended Refined Zigzag Theory (eRZT) in conjunction with the Ritz method to the analysis of bending, free vibration and buckling of functionally graded carbon nanotube-reinforced (FG-CNTR) sandwich plates. Two stacking sequences are taken into consideration: sandwich panels with a homogeneous core and functionally graded face-sheets and sandwich panels with homogeneous face-sheets and a functionally graded core.
After validating the convergence characteristics and the numerical accuracy of the developed approach using orthogonal and non-orthogonal admissible functions, a detailed parametric numerical investigation is carried out. Bending under bi-sinusoidal and uniform transverse pressure, free vibration and buckling loads under uniform in-plane uniaxial, biaxial and shearing loadings of FG-CNTR sandwich plates are studied. Numerical results for square and rectangular FG-CNTR sandwich plates under various combinations of geometry (core-to-face sheet thickness ratio and side to thickness ratio), different set of boundary conditions, CNTs volume fraction and grading laws are presented and discussed in detail. It is concluded that the eRZT predicts the response for static, stability and free vibration problems more accurately than first-order (FSDT) and third-order (TSDT) shear deformation theories, also for FG-CNTR sandwich plates
Bending and free vibration analysis of functionally graded sandwich plates: An assessment of the Refined Zigzag Theory
Full text linkThe paper presents a numerical assessment of the performance of the Refined Zigzag Theory (RZT) to the analysis of bending (deflection and stress distributions) and free vibration of functionally graded materials (FGM) plates, monolayer and sandwich, under a set of different boundary conditions. The numerical assessment is performed comparing results from RZT using Ritz method with those from 3-D, quasi 3-D and 2-D theories and finite element method (FEM). In the framework of 2D theories, equivalent single layer theories (ESL) of different order (sinusoidal, hyperbolic, inverse- hyperbolic, third-order (TSDT), first-order (FSDT) and classical (CPT)) have been used to investigate deformation, stresses, and free vibration and compared with results from the RZT.
After validating the convergence characteristics and the numerical accuracy of the developed approach using orthogonal admissible functions, a detailed parametric numerical investigation is carried out. Bending under transverse pressure and free vibration of FGM square and rectangular plates of different aspect ratio under various combinations of geometry (core-to-face sheet thickness ratio and plate to thickness ratio), boundary conditions and law of variation of volume fraction constituent in the thickness direction (power-law (P-FGM), exponential law (E-FGM) and sigmoidal-law (S-FGM)) is studied. Monolayer and sandwich plates with homogeneous core and functionally graded face-sheets are considered for the assessment. It is concluded that the RZT generally predicts the global (deflection and frequencies) and local (displacement and stress distributions) response of FGM sandwich plates, more accurately than first-order (FSDT) and third-order (TSDT) shear deformation theories, while retaining its simplicity
Free vibration analysis of angle-ply laminated and sandwich plates using enhanced Refined Zigzag Theory
Full text linkThe paper presents a numerical assessment of the free vibration of angle-ply laminated and sandwich plates using the enhanced Refined Zigzag Theory (en-RZT). It has been observed that standard RZT cannot predict the coupling effect of in-plane displacements for anisotropic multilayered structures, such as angle-ply laminates. The recent enhancement introduces two more zigzag functions in the local displacement field that overcome this drawback. According to the partially enforcement of transverse shear stress continuity at the interfaces, the zigzag functions are characterized. The equations of motion and consistent boundary conditions are derived through the D’Alembert principle and specialized for the linear free vibration analysis. Furthermore, the Ritz method in conjunction with the Gram-Schmidt orthogonal polynomials is used to assess the model’s performances when applied to the free-vibration analysis of plates with different types of boundary conditions. The numerical assessment investigates the influence of various design parameters, such as plate aspect ratios, boundary conditions and ply orientations
Development of a locking-free quadrilateral element for laminated composite and sandwich plates based on refined zigzag theory
No full textExperimental shape sensing of a wing structure using SSB-iFEM: Static assessment and dynamic wind tunnel test
Full text linkReconstructing the displacement field from discrete strain measurements, commonly known as shape sensing, plays a crucial role in the development of advanced Structural Health Monitoring (SHM) frameworks. Monitoring displacements throughout a structure’s operational life provides valuable data for predictive maintenance strategies and supports the implementation of digital twin technologies. Among the various shape-sensing techniques, the inverse Finite Element Method (iFEM) has emerged as a prominent solution. However, despite its demonstrated effectiveness, the practical application of iFEM remains limited by the requirement for back-to-back strain sensor configurations, i.e., sensors installed on both surfaces of a thin-walled structure. To overcome this limitation, a new variant called Single Sensor Based iFEM (SSB-iFEM) has recently been proposed. In this work, SSB-iFEM is employed to perform, for the first time, shape sensing on an entire aerospace structure: the half-wing of a commercial hotliner. The test setup reflects the complexity and constraints of real industrial conditions, as only limited structural information is available due to the commercial nature of the test article. Furthermore, the structure is instrumented exclusively on the accessible external surface and tested under simulated operating conditions in a wind tunnel. The experimental results demonstrate the high versatility and accuracy of SSB-iFEM, even when using a reduced set of strain sensors. This study proves that the proposed formulation successfully overcomes the main limitations of standard iFEM and significantly extends the applicability of shape sensing approaches to real-world aerospace structures
New Accomplishments on the Equivalence of the First-Order Displacement-Based Zigzag Theories through a Unified Formulation
Full text linkThe paper presents a critical review and new accomplishments on the equivalence of the first-order displacement-based zigzag theories for laminated composite and sandwich structures. Zigzag theories (ZZTs) have widely spread among researchers over the last few decades thanks to their accuracy in predicting the response of multilayered composite and sandwich structures while
retaining the simplicity of their underlying equivalent single-layer (ESL) theory. The displacement field consists of two main contributions: the global one, able to describe the overall structural behaviour, and the local layer-wise one that considers the transverse shear continuity at the layer interfaces that describe the "zigzag" displacement pattern typical of multilayered structures. In
the framework of displacement-based linear ZZTs, various assumptions have been made on the local contribution, and different theories have been deduced. This paper aims to provide a unified formulation for first-order ZZTs, highlighting some common aspects and underlying equivalencies with existing formulations. The mathematical demonstrations and the numerical examples prove the
equivalence of the approaches to characterising local zigzag enrichment. Finally, it is demonstrated that the kinematic assumptions are the discriminants of the ZZTs' accuracy
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