Multilayered Shell Structure Research Articles

Baseline-free damage localization in multilayer metallic spherical shell structures using guided wave tomography

Multi-layer metal spherical shell structure is widely used as the core component of pressure-bearing equipment, deep-sea exploration equipment and other critical areas due to its plane stress uniformity and high specific strength. Its long-term service in complex and harsh environments will inevitably produce a variety of defects and damages, which will affect the safety of the equipment in service. Ultrasonic guided wave inspection is a potential non-destructive testing method, but the multilayer metal bonding structure between the metal and non-metal bonding layer impedance difference is large, resulting in defects located in the internal reflection signal is difficult to propagate to the outer layer with a sensor, the multilayer spherical shell structure itself leads to the complexity of the guided wave propagation characteristics, it is difficult to extract the individual modes of the time information for the defects of the detection and localization. Therefore, in this paper, we propose a probabilistic damage existence imaging method for spherical shell structures and combine it with the virtual time reversal technique to detect and localize the defects on the inner and outer surfaces of multilayered metallic spherical shell structures without benchmarks. The results show that the newly proposed method can realize the accurate localization imaging of internal/external defects of multilayer metal spherical shell structures.

A convergence criterion for sound transmission of single-, double-, and triple-walled cylindrical shell based on Love's, Donnell's, and Flügge's shell theories

Different sound transmission loss (STL) analytical methods based on Love's, Donnell's and Flügge's cylindrical thin-shell theories have been widely used. However, there are no available convergence criterion and formulas of sound transmission losses for multi-layer cylindrical shell structures. The current convergence determination approach is to select several typical frequencies (low, middle, and high frequencies) for convergence analysis, and then estimate the convergence of all other frequencies. This typically results in sound transmission loss jumps, leading to inaccurate sound transmission loss results in the high-frequency region. In this study, a novel convergence criterion and formulas are developed for calculating sound transmission loss mode numbers in the complete convergence zones of single-, double-, and triple-walled cylindrical shells based on Love's, Donnell's, and Flügge's thin shell theories, which can be used to directly determine the truncation iterations for sound transmission losses in all frequency ranges.

Study of impact resistance of a novel bio-inspired ceramic-composite structure using finite element simulations

The multi-layer armor shell structure of the scaly-foot snail has been proven to be resistant to penetration and perforation. Inspired by the special structure, a novel ceramic-composite impact-resistant structure was proposed. We developed a user-defined subroutine (VUMAT) of the finite element software ABQUS to analyze the progressive damage process and energy dissipation mechanism under impact. It is found that the novel structure features rigid-flexible coupling, both soft and hard layers play a key role in the impact resistance process. Compared with the traditional sandwich structure, the novel structure has better impact resistance under the impact energy of 20 J–80 J.

Generalized differential quadrature element solution, swarm, and GA optimization technique to obtain the optimum frequency of the laminated rotary nanostructure

Optimization of the fiber angle in the laminated composite material to achieve the highest strength or stability has great importance in structural design. In the present study, we aim to utilize genetic algorithm (GA) and particle swarm optimization (PSO) together to find the best angle of composite layers in a multilayer cylindrical shell structure. To this aim, a detailed formulation of the composite cylindrical structure is presented using nonlocal strain gradient theory (NSGT), zigzag theory, and Hamilton's principle for a shear deformable shell displacement field. The modal equations of motion are further solved using the general differential quadrature element method (GDQEM). Having the route of obtaining the resonance frequency of the cylindrical composite structure, GA-PSO is engaged to obtain the optimal angle of the laminate composite to achieve the highest frequency. It is revealed that angle θ = 37.5° provides the highest frequency for a single-layer cylindrical shell. Using this angle, stacking sequences for 3, 5, and 7 layers’ composite are optimized to have the highest frequency. In the end, a detailed parametric study is presented using optimum condition shell composite. The results show that after 30 composite layers, changing the number of layers seems to be not effective on the resonance frequency of the cylinder for both simply supported and clamped boundary conditions.

Isogeometric analysis of multilayer composite shell structures: Plasticity, damage, delamination and impact modeling

A comprehensive Isogeometric Analysis framework for damage modeling of laminated composite structures is presented. The formulation is based on a multilayer approach that employs Kirchhoff–Love shell theory coupled with anisotropic elastoplastic damage to model the mechanical behavior of the individual plies. The plies are connected at their interfaces through a mixed-mode cohesive damage model that is used to represent delamination. The ply no-interpenetration condition is enforced using a penalty formulation. The formulation ensures a smooth transition from the opening mode, which is governed by the cohesive damage law, to the closing mode, which is governed by the penalty approach, and results in a significantly more stable numerical methodology overall. The resulting framework is deployed on a series of simulation cases with increasing complexity of the geometry and mechanical phenomena modeled. In all cases, experimental data is used for model validation purposes and for demonstrating the superior robustness and predictive capabilities of the formulation presented.

Cavitation bubble interaction with compliant structures on a microscale: A contribution to the understanding of bacterial cell lysis by cavitation treatment

Numerous studies have already shown that the process of cavitation can be successfully used for water treatment and eradication of bacteria. However, most of the relevant studies are being conducted on a macro scale, so the understanding of the processes at a fundamental level remains poor. In attempt to further elucidate the process of cavitation-assisted water treatment on a scale of a single bubble, the present paper numerically addresses interaction between a collapsing microbubble and a nearby compliant structure, that mechanically and structurally resembles a bacterial cell. A fluid–structure interaction methodology is employed, where compressible multiphase flow is considered and the bacterial cell wall is modeled as a multi-layered shell structure. Simulations are performed for two selected model structures, each resembling the main structural features of Gram-negative and Gram-positive bacterial cell envelopes. The contribution of two independent dimensionless geometric parameters is investigated, namely the bubble-cell distance δ and their size ratio ς. Three characteristic modes of bubble collapse dynamics and four modes of spatiotemporal occurrence of peak local stresses in the bacterial cell membrane are identified throughout the parameter space considered. The former range from the development of a weak and thin jet away from the cell to spherical bubble collapses. The results show that local stresses arising from bubble-induced loads can exceed poration thresholds of cell membranes and that bacterial cell damage could be explained solely by mechanical effects in absence of thermal and chemical ones. Based on this, the damage potential of a single microbubble for bacteria eradication is estimated, showing a higher resistance of the Gram-positive model organism to the nearby bubble collapse. Microstreaming is identified as the primary mechanical mechanism of bacterial cell damage, which in certain cases may be enhanced by the occurrence of shock waves during bubble collapse. The results are also discussed in the scope of bacteria eradication by cavitation treatment on a macro scale, where processes of hydrodynamic and ultrasonic cavitation are being employed.

A two-dimensional model to analyze the static and dynamic mechanical behavior of multilayered shell structures

A new exact two-dimensional model is derived to analyze the mechanical behavior of multilayered shells in this work. Particularly, this model is used to investigate the static and transient responses of doubly-curved cross-ply laminated shells. The new laminate constitutive equations (LCE) used in this model was developed through the use of Kirchhoff-Love(K-L) based kinematic equations. This LCE accounts extensional-twisting-shear, extensional-Gauss bending-shearing, Gauss bending-shearing mechanical couplings which do not exist in some other models available in literature. The proposed exact model is more general than those used in several papers. Shear stresses across the thickness are also computed. Our model has been used to develop analytical solutions of simply supported, cross-ply laminated shells based on the Navier’s approach using Hamilton’s principle. This model could also be used without major conceptual modifications to handle stiffened multilayered shells which in fact cannot be considered uniformly as shallow shell. Several examples were carried out to validate and prove the accuracy and efficiency of the present model while taking into account different lamination scheme and some ratios. We showed that the above mechanical couplings influence the static and dynamic mechanical behavior of anisotropic shells when the thickness ratio χ=h2R becomes greater. The current work improves some General anisotropic doubly-curved shell theories proposed and studied in some recent work in literature by introducing a novel LCE.

An alternative three-node triangular composite shell element in terms of Reddy-type higher-order theory

Composite curved shells are widely utilized as structural components in aerospace engineering. To inspire the potentiality of such structure, it is very necessary to well understand mechanical behaviors of composite curved shells. Compared to the composite plates, it is more difficult to predict accurately interlaminar stresses of composite curved shells. Therefore, this paper attempts to propose an alternative triangular composite shell element in terms of the Reddy-type global–local higher-order theory. In the present model, the continuity conditions of transverse shear stresses are enforced in advance to fulfill compatibility of transverse shear stresses at adjacent layers, which can improve precision of interlaminar stresses. In order to evaluate performance of the proposed shell element, several typical examples have been analyzed. Moreover, the results acquired from the present model are compared with the three-dimensional elasticity solutions and other published results. At the same time, a compression experiment of the thin-walled cylindrical grid structure is carried out to further verify the capability of the present model. These examples show that the proposed composite shell element can be used as an alternative method for static analysis of multi-layer thin and thick shell structures.

РЕЗЕРВ АНАЛИТИЧЕСКИХ ПОВЕРХНОСТЕЙ ДЛЯ АРХИТЕКТУРЫ И СТРОИТЕЛЬСТВА

After a period of relative calm in the construction and design of thin-walled large-span shells and network multilayer shell structures, which, according to the world's leading architects, began in the 1980 s, the time has come for the expanded use of spatial structures in the architecture of public and industrial buildings. Less commonly, shells are used in small-sized housing construction: ecological villages, noospheric and bionic architecture. The entire 20th century did not stop research on the development of analytical and numerical methods for analyzing shells for strength and stability, for the creation of new building materials. Geometers have created and studied more than 600 analytical surfaces that can be mistaken for the mid-surfaces of civil and mechanical engineering shells. As a result, by the beginning of the 21st century, architects and engineers had all the necessary tools to continue the traditions of the "golden age of shells". The analysis of problems with the use of new forms in parametric architecture, carried out in the article, showed that more than ten classes of surfaces from their classification have not yet found application in architecture and mechanical engineering. It is assumed that the number of applied classes of surfaces will not expand, and new ideas for the shaping of shells will be based on the use of already well-known surfaces, namely, surfaces of revolution, transfer, umbrella, minimal, ruled and wavy surfaces. Mainly, shell structures will be designed taking into account environmental, energy-saving requirements and transforming structures.

Numerical modeling of a double-walled spherical reservoir

Extensive and important class of multilayer shell structures is three-layer structures. In a three-layer structure, a rigid filler plays an important role, due to which the bearing layers are spaced that gives the layer stack high rigidity and durability with a relatively low weight. By combining the thicknesses of the bearing layers and the filler, the desired properties of a three-layer shell structure can be achieved. Compared with traditional single-walled, three-layer construction has increased rigidity and durability, which allows reducing the thickness and weight of the shells.
 In order to reduce the metal content of the spherical reservoir for storing liquefied gases, this work considers the design of a double-walled reservoir, in which the inter-wall space is filled with reinforced polyurethane. Numerical modeling made it possible to determine the parameters of the stress-strain state of the structure with an error of no more than 5 %. It has been established on the example of a reservoir with a volume of 4000 m3 that the spatial structure of the spherical reservoir wall can reduce the metal content up to 19 %. Field of application for the research results is the assessment of the stress-strain state of spherical reservoirs at their designing.
 Method for building the structure of a double-walled spherical reservoir in the SCAD software has been developed, which allows calculating the stress-strain state (SSS) by the finite element method.
 Numerical model of a double-walled spherical reservoir has been developed. It was found that to obtain calculation results with an error of P ≤ 5 % the size of the final element should not exceed 300×300×δ mm.
 Design of a double-walled spherical reservoir was investigated. Design parameters have been established to ensure the operational reliability of the structure with a decrease in metal content in comparison with a single-wall reservoir by 19 %.

Interlaminar stress analysis of composite shell structures using a geometrically nonlinear layer-wise shell finite element

This work aims to calculate interlaminar stress distribution through the thickness of multilayered composite shell structures by employing a novel nonlinear layer-wise shell finite element formulation. Adapting the Mindlin– Reissner theory in each layer, the shear-deformable layer-wise shell element presents the interlaminar shear stress distributions by increasing the number of layers. The interlaminar normal stress distribution is then determined using the finite difference solution of the general form of equilibrium equation in the non-orthogonal curvilinear grid along the Gaussian points. Two boundary conditions at the bottom and the top surfaces are satisfied by adopting the linear Lagrange interpolation function. The developed formulation is assessed through some illustrative problems solved using a proprietary finite element computer program. The results compare very well with those available in the literature and those obtained by simulations with the commercial finite element software Ansys.

Three-dimensional numerical modelling of multi-layered shell structures using two-dimensional plane mesh

The article presents a full three-dimensional (3D) numerical analysis of curved laminated shell structures using only a two-dimensional (2D) planar finite element mesh. The applied numerical method is called FEM23, which stands for the 2D finite element method for a full 3D analysis. FEM23 makes it possible to perform a numerical analysis of a multi-layered shell, utilising a numerical model based on a 2D finite element mesh. FEM23 ensures exact shell geometry since a pure mathematical description of a geometry is applied in the numerical model. Examples provided in the following paper prove FEM23 to be accurate and flexible. They involve the analysis of a special laminated structure - laminated glass, which comprises of glass panes bonded by thin polymer films. A full 3D description is provided for the glass panes as well as polymer films, even though the film thickness is over ten times smaller than the glass layers. The results are verified by the analytical solution and those obtained by standard 3D FEM. A unique post-processing procedure developed specially for FEM23 enables visualisation of the full 3D results.

Coupled thermo-mechanical finite element models with node-dependent kinematics for multi-layered shell structures

Node-dependent Kinematic (NDK) shell finite element (FE) formulations are presented for the steady-state thermo-mechanical analysis of laminated structures. The displacements and temperature change are treated as primary variables in the FE models and are directly solved through the coupled thermo-mechanical models. The enforcement of distributed temperature boundary conditions on the top or the bottom surface of hierarchical shell elements is conducted through the Linear Least Squares. The effectiveness of the proposed FE approaches is verified by comparing the results against those from the literature. The application of adaptive refinement approach based on the hierarchical elements and NDK to build FE models with optimal efficiency is demonstrated through numerical examples.

Microcapsules of multilayered shell structure synthesized via one-part strategy and their application in self-healing coatings

Abstract The microcapsules of multilayered shells structure loaded with dicyclopentadiene (DCPD) were prepared via one-part strategy in Pickering emulsions stabilized by hydrolyzed poly(glycidyl methacrylate) (PGMA) nanoparticle. The target microcapsules had polyurethane (PU) inner shell layer, phenol-formaldehyde (PF) outer shell layer, and PGMA outermost layer. Meanwhile, in order to compare with the target microcapsules, the microcapsules of double layered shells (Sample 1) were both acquired. Size distribution, morphology, chemical structure and reaction heat of the capsules were studied by particle size analysis, scanning electron microscopy (SEM), fourier transform infrared spectra (FTIR), nuclear magnetic resonance (NMR), and differential scanning calorimetry (DSC). It was found that the ingredients of PF, PU and PGMA were contained in the target microcapsules of multilayered shells, and the encapsulated core materials still kept high chemical reactivity. The resistant properties against thermal and solvent were evaluated by thermogravimetric analysis (TGA) and the solvent immersion test. When the IPDI content was suitable, the multilayered shells microcapsules (Sample 2, 3) possessed excellent thermal and solvent resistances comparing with Sample 1. In addition, the coatings embedded Sample 3 have displayed good self-healing performance by SEM, electrochemical impedance spectroscopy (EIS), salt immersion test and the tensile analysis of tapered double cantilever beam (TDCB) fracture specimens.

An adaptable refinement approach for shell finite element models based on node-dependent kinematics

Towards improving the numerical efficiency in the analysis of multi-layered shell structures with the finite element (FE) method, an adaptable two-level mathematical refinement approach is proposed for refined curvilinear shell elements. Based on Carrera Unified Formulation (CUF), the approximation of displacement functions of shell elements can be improved by refining the through-the-thickness assumptions and enriching the shape functions. By using the hierarchical Legendre polynomial expansions (HLE) as shape functions, the element capabilities can be enhanced conveniently without re-meshing. To further increase the numerical efficiency of shell FE models, Node-Dependent Kinematics (NDK) is utilized to implement local kinematic refinements on the selected FE nodes within the domain of interest. The conjunction of NDK with the two-level refinements of the shell FE models leads to an adaptable refinement approach in the analysis of shell structures, which can be used to build FE models with optimal efficiency and high fidelity. The competence of the proposed approach is investigated through numerical studies on laminated shells.

Dynamic stability of doubly-curved multilayered shells subjected to arbitrarily oriented angular velocities: Numerical evaluation of the critical speed

The paper is focused on the evaluation of the critical speed of rotating doubly-curved multilayered shell structures. The theoretical framework developed to this aim is based on a general formulation capable to define several Higher-order Shear Deformation Theories (HSDTs) in a unified manner. The current approach can deal easily with angular velocities applied about a generic axis of the structure. This aspect represents a clear advancement with respect to the formulations available in the literature, which are developed mainly to investigate the dynamic behavior of rotating shells of revolution (disks, circular cylinders and conical shells), in which the angular velocity is applied about their revolution axis. It is important to underline that the effects of both Coriolis and centripetal accelerations on the dynamic response of shell structures, characterized by various geometric shapes, are included in the model. The quadratic eigenvalue problem that lies behind the free vibration analysis in hand is solved numerically by means of the well-known Generalized Differential Quadrature (GDQ) method. The critical speed is obtained as a result of many parametric investigations, which are defined for increasing values of the applied angular velocities. Finally, it should be mentioned that the current research falls within the aim of the study of the dynamic stability of rotating structures. For this purpose, several considerations concerning the flutter and divergence phenomena are presented.

Analysis of laminated composite structures with embedded piezoelectric sheets by variable kinematic shell elements

In this article, the static analysis of multilayered shell structure embedding piezoelectric layers is performed using some advanced theories, obtained by expanding the unknown variables along the thickness direction using equivalent single-layer models, layer-wise models, and variable kinematic models. The variable kinematic models permit to reduce the computational cost of the analyses by grouping some layers of the multilayered structure with equivalent single-layer models and keeping the layer-wise models in other zones of the multilayer. This model is here extended to the static analysis of electro-mechanical problems. The used refined models are grouped in the Carrera Unified Formulation, and they accurately describe the displacement field, the stress distributions, and the electric potential along the thickness of the multilayered shell. The shell element has nine nodes, and the mixed interpolation of tensorial components method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the principle of virtual displacement, and the finite element method is employed to solve them. Cross-ply plates and shells, with piezoelectric skins and simply supported edges, subjected to bi-sinusoidal mechanical or electrical load are analyzed. Various aspect ratios and radius-to-thickness ratios are considered. The results, obtained with different theories within Carrera Unified Formulation context, are compared with the elasticity solutions given in the literature. From the results, it is possible to conclude that the shell element based on Carrera Unified Formulation is very efficient in the study of electro-mechanical problems of composite structures. The variable kinematic models combining the equivalent single-layer with the layer-wise models permit to have a reduction of the computational costs, with respect to the full layer-wise theories, preserving the accuracy of the results in localized layers.

The symmetry and coupling properties of solutions in general anisotropic multilayer waveguides.

Multilayered plate and shell structures play an important role in many engineering settings where, for instance, coated pipes are commonplace such as in the petrochemical, aerospace, and power generation industries. There are numerous demands, and indeed requirements, on nondestructive evaluation (NDE) to detect defects or to measure material properties using guided waves; to choose the most suitable inspection approach, it is essential to know the properties of the guided wave solutions for any given multilayered system and this requires dispersion curves computed reliably, robustly, and accurately. Here, the circumstances are elucidated, and possible layer combinations, under which guided wave solutions, in multilayered systems composed of generally anisotropic layers in flat and cylindrical geometries, have specific properties of coupling and parity; the partial wave decomposition of the wave field is utilised to unravel the behaviour. A classification into five families is introduced and the authors claim that this is the fundamental way to approach generally anisotropic waveguides. This coupling and parity provides information to be used in the design of more efficient and robust dispersion curve tracing algorithms. A critical benefit is that the analysis enables the separation of solutions into categories for which dispersion curves do not cross; this allows the curves to be calculated simply and without ambiguity.

A variable kinematic shell formulation applied to thermal stress of laminated structures

ABSTRACTIn this article, the thermoelastic static analysis of multilayered shell structure is performed using some advanced theories, obtained by expanding the unknown displacement variables along the thickness direction using equivalent-single-layer (ESL) models, layer-wise (LW) models, and variable-kinematic models. The variable-kinematic models permit to reduce the computational cost of the analyses grouping some layers of the multilayered structure with ESL models and keeping the LW models in other zones of the multilayer. This model is here extended for the static analysis of uncoupled thermomechanical problems. The results obtained with the classical assumed linear temperature profile along the thickness of the shell are compared with those achieved with the calculated temperature profile solving the Fourier heat conduction equation. The used refined models are grouped in the Carrera’s unified formulation (CUF), and they accurately describe the displacement field and the stress distributions along the thickness of the multilayered shell. The shell element has nine nodes, and the mixed interpolation of tensorial components method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the principle of virtual displacement, and the finite element method is used to solve them. Cross-ply plates and shells with simply supported edges, subjected to bisinusoidal thermal load are analyzed. Various aspect ratios and radius to thickness ratios are considered. The results, obtained with different theories within CUF context, are compared with the elasticity solutions given in the literature. From the results, it is possible to conclude that the shell element based on the CUF is very efficient in the study of thermomechanical problems of composite structures. The variable-kinematic models combining the ESL with the LW models permit to have a reduction of the computational costs, with respect with the full LW models, preserving the accuracy of the results in localized layers.

Preparation of a Fe3O4-Au-GO nanocomposite for simultaneous treatment of oil/water separation and dye decomposition.

A nanocomposite capable of simultaneously controlling multiple water pollutants (soluble organic dye and insoluble chemical solvent) has been obtained. The Au and Fe3O4 nanoparticles (NPs) were modified on a graphene oxide (GO) surface via light reduction and covalent attachment. The obtained Fe3O4-Au-GO nanocomposite has magnetic driving ability and catalytic applications. The nanocomposite can form emulsions after wrapping an insoluble and volatile organic solvent inside; moreover, the multi-layer graphene shell structure may delay volatilization of the solvent, ensuring that the oil droplets are collected efficiently and completely by the Fe3O4-Au-GO nanocomposite. At the same time, the Au NPs on the surface of the composite can effectively catalyze the decomposition of an organic dye in water and the recovery of the nanocomposite catalyst can also be realized using an external magnetic field. The simultaneous treatment of non-soluble oil (organic solvents) and organic dyes in water can be realized by the Fe3O4-Au-GO nanocomposite. Therefore, based on surface modification of GO, one material with two types of water pollution treatment functions was realized. This provides a new way for the simultaneous treatment of oil separation and dye decomposition, and the assembled structure may result in emulsions to give new applications in fuel cells and other fields.