Single-layer Shell Research Articles

Mechanical analysis of al/foam composite sandwich panels under elastic and elastoplastic states

This study performs mechanical analysis for Al/Foam composite sandwich panels under 3-point bending using numerically and experimentally. The flexural rigidity, elastic deflections, and normal, shear stresses are obtained by analytical calculations of the Timoshenko beam equation and compared finite element (FE) models for 3-point bending loading conditions. The FE models are constructed using 2D single-layer shell and 3D solid discrete-layer models. The validity of FE models at the analysis is evaluated for Al/PVC Foam sandwich composites for the elastic state. The experimental bending results of Al/XPS Foam sandwich composites are compared with numerical models at elastic and elastoplastic states. The elastic results indicate that the out-of-plane deflection results agree well across numerical and analytical models. Normal stresses at the core are higher in 3D discrete-layer solid models compared to laminated shell theory-based models for thick plates, due to the more accurate characteristics of the discrete-layer solid models. The Timoshenko beam theory-based analytical bending results show a good correlation with the results from laminated shell theory-based finite element method (FEM) analyses. Elastoplastic FEM analysis indicates that discrete-layer-based 3D solid FEM models effectively predict local effects dependent on indentation failure.

Shock Response of Water-Protected Spherical Explosion Containment Vessels

Abstract Explosion containment vessels (ECVs) are important equipment used for underwater explosion experiment research. In this paper, a method is proposed to improve the blast resistance of the ECV by placing it in the water medium. The shock response caused by the underwater explosion in a spherical ECV is studied. The single-layer thin-walled spherical vessel shell submerged in an infinite domain water medium is deduced and simplified as a single-degree-of-freedom elastic vibration system with viscous damping. The underwater explosion shock wave is simplified to an exponential shock loading, and the analytical solutions of the radial shock vibration of the spherical shell are obtained using Duhamel's integrals. Compared with the numerical simulation results, the accuracy of the theoretical model is verified. The study results show that the water medium radiates out vibration energy and plays an important role in eliminating vibration through damping. It is found that the vibration damping ratio can be controlled by adjusting the vessel radius and thickness, so that the vibration of the shell can be controlled within three periods and the impact fatigue can be reduced. In addition, the radiation damping of the water medium greatly reduces the maximum radial displacement of the spherical shell, which significantly improves the blast resistance of the spherical shell.

Dispersion in bilaminated cylindrical shells: Incidence angle and thickness impacts

Under oblique incidence acoustic wave, we investigate theoretically and numerically the dispersion curves of bilaminated cylindrical shell which composed of copper and stainless steel, immersed in water and filled with air. The investigation delves into the influence of the incidence angle on the phase and group velocities of guided waves. As the incidence angle increases, circumferential and helical guided waves are initiated parallel to the axis of the cylindrical shell. This initiation transpires at an incident angle denoted as αl=sin−1(C1/Cl) (where C1 represents the wave velocity in water and Cl signifies the phase velocity of the lth guided wave). Beyond this angle, the respective guided wave undergoes a transition to a “cut off” state, adopting an evanescent character. This investigation also unveils that at a particular angle of incidence, resonance trajectories of certain guided waves manifest at cut-off frequencies, and these frequencies escalate with the angle of incidence. Concurrently, we examine how varying thicknesses impact the dispersion curves of waves in both the outer layer (copper) and inner layer (stainless steel) of the bilaminated shell. Notably, we observe a sensitivity in the phase and group velocities concerning changes in these thicknesses. Furthermore, the dispersion curves of the bilaminated cylindrical shell presents a tendency to shift towards low frequencies as either the outer or inner layer progressively thickens. This trend brings the dispersion curves closer to those of a single-layered cylindrical shell composed of the material with the greater thickness in the bilaminated shell. The obtained results demonstrate a commendable agreement with the existing experimental findings on copper and stainless steel single-layered cylindrical shells.

A Study on the Critical Saturation Response Characteristics of Simple and Sandwich Cylindrical Shells under Long-Duration Blast Loading.

Experimental research and numerical simulations of the structural response to shock waves with pulse durations of hundreds of milliseconds, or even seconds, are extremely challenging. This paper takes typical single-layer and sandwich cylindrical shells as the research objects. The response rules of cylindrical shells under long-duration blast loadings were studied. The results show that when the pulse duration is greater than or equal to 4~5 times the first-order period of the structure, the maximum response of the structure tends to be consistent, that is, the maximum response of the cylindrical shells with different vibration shapes shows a saturation effect as the pulse duration increases. This study established the relationship between the saturation loading time and the inherent characteristics of the structure. It was found that the saturation effect was applicable under the following conditions, including different load waveforms, elastic-plastic deformation of the structure, and the loading object being a sandwich shell. This will help transform the long-duration explosion wave problem into a finite pulse-duration shock wave problem that can be realized by both experiments and numerical simulations.

Combination of Chemical and Physical Cancer Therapeutics Developed with Microcapsules Made of κ-Casein and Gold Nanoparticles in the Presence of Drug-Loaded Phase Change Materials.

Tumor heterogeneity requires development of an anticancer system equipped with both chemical and physical therapeutics to eradicate cancer exhibiting drug resistance and clonal evolution into diverse tumor cells. Assortment of various toxic components into one platform without compromising their individual toxic activity remains a formidable task. Herein, a novel drug delivery system (DDS) exerting potent cytotoxicity toward cancer cells was fabricated with gold nanoparticles (AuNPs) coated with an innocuous self-assembly protein of κ-casein (κC). Pickering emulsions of the κC-AuNP conjugates in the presence of chloroform inside led to the κC-AuNP microcapsules being stabilized via robust β-sheet formation between κC molecules located on the single-layered shell made of κC-AuNPs. Phase change material (PCM) comprising a eutectic mixture of lauric acid and myristic acid with the melting point of 43 °C was encapsulated in the presence of a hydrophilic anticancer drug of doxorubicin (Dox), in which the PCM has played multiple functions such as drug-holding matrix and thermoresponsive gating material for drug release. Once liberated with the heat generated by the AuNPs upon a near-infrared (NIR) irradiation at 808 nm, the PCM by itself exhibited not only chemical cytotoxicity but also physical toxic effects such as membrane destabilization of the cells and a possible cellular fixative effect toward cancer cells by the solidified PCM at body temperature. Moreover, the PCM was shown to facilitate the intranuclear localization of Dox. As a result, the DDS comprising κC-AuNP microcapsules containing Dox-loaded PCM was demonstrated to show a powerful anticancer effect upon the NIR irradiation, which unleashed several toxic agents such as Dox, PCM, heat-generating AuNPs, and tissue-immobilizing solidified PCM. Therefore, the κC-AuNP microcapsules would serve as an anticancer system into which diverse chemical and physical therapeutic agents could be combined to effectively remove the heterogeneous and drug resistant cancer cells.

Seismic evaluation of isolation performance on single layer cylindrical reticulated shells supported along four sides

This study investigated the dynamic characteristics and seismic isolation performance of a single-layer cylindrical grid shell structure with lower support structures and different seismic isolation schemes, which encompass the installation of layered rubber bearings and new three-dimensional isolation bearings. Seven reduced-scale models of the structure were tested on a shaking table, with acceleration, strain, and displacement sensors positioned in typical locations. The results showed that the seismic response of the upper cylindrical grid shell structure was amplified by the lower support structure, which indicates that separate seismic designs for both the upper structure and lower support structure are unsafe. The use of layered rubber bearings at the foundation effectively reduced horizontal seismic response but amplified vertical seismic response. To address this issue, the new three-dimensional isolation bearing was proposed, which showed better overall seismic isolation performance compared to the rubber bearings. Additionally, a new seismic isolation scheme was proposed, using a combination of three-dimensional isolation bearings at both the foundation and column tops. This scheme showed superior seismic isolation efficiency compared to other schemes and can reduce the volume and installation difficulty of the three-dimensional isolation bearing. Considering the functional requirements, cost, and technical difficulty is crucial when selecting suitable seismic isolation measures since different schemes have their advantages and disadvantages and perform differently under various seismic conditions.

Stability of cylindrical anisotropic composite shells under torsion in a three-dimensional formulation

The article presents a calculation of the stability of non-thin cylindrical anisotropic layered shells under the action of end torsional moments in a spatial formulation. The anisotropy of the used material is characterized by one plane of elastic symmetry of characteristics. This is caused by the mismatch between the main elastic directions of the composite fibrous orthotropic material and the axes of the curvilinear cylindrical coordinate system.
 A three-dimensional inhomogeneous system of partial differential equations describing the subcritical stress-strain state within the linear theory of elasticity is derived using the Hu-Washizu variational principle. Reducing the dimension of the problem under consideration from three-dimensional to one-dimensional is carried out by taking into account the axial symmetry of the deformation of the cylindrical shell and using the method of straight lines along the generatrix.
 Based on the modified Hu-Washizu variational principle, a three-dimensional system of homogeneous partial differential stability equations is derived within the framework of the spatial theory of elasticity. The reduction of a three-dimensional system to a one-dimensional one is carried out along the generatrix and in the circular direction - by expanding the components of stresses and displacements into double trigonometric series when applying the procedure of the Bubnov-Galorkin method, as well as taking into account the periodicity of the resolving functions.
 An algorithm has been developed, implemented in the form of application software packages for PCs. In it, in a single computational process using the numerical method of discrete orthogonalization in the direction normal to the middle surface of the shell, the establishment of the parameters of the subcritical stress-strain state and the solution on this basis of stability problems for non-thin anisotropic cylindrical shells under the influence of torsion are combined.
 The problem of the influence on the stability of an anisotropic cylindrical non-thin shell of an increase in the number of cross-reinforced layers depending on the angle of rotation of the main directions of elasticity of the material and the direction of application of torque is considered. The obtained results of stability calculations according to the proposed approach were compared with critical torsion loads calculated using an orthotropic model for calculating anisotropic shells. It is shown that for single-layer cylindrical shells the difference between the compared results reaches 69%. An increase in the number of cross-reinforced layers leads to a decrease in this discrepancy, and with seven to eight layers, the difference between the critical loads obtained using the described approach and the orthotropic model is within 5%. This result is consistent with those obtained using classical or refined theories of calculations of both thin and non-thin anisotropic cylindrical shells.

A homogenization method for natural frequencies and damping of sandwich panels based on representative volume elements

The existing representative volume element (RVE) homogenization method, grounded in finite element analysis, assumes a planar configuration for the sections of sandwich panels, implying rigidity. To accommodate non-planar displacements, this study introduces a novel homogenization method reliant on the displacements obtained from four-point bending and four-point torsion. The present method is employed to investigate the mode shapes, natural frequencies, and loss factors of sandwich panels utilizing an equivalent single-layer shell model. Validation of the present method is conducted through the analysis of lattice sandwich panels and corrugated sandwich panels incorporating viscoelastic layers. Comparative analyses encompassing the results of the experiment, the conventional solid model method, the present method, and the conventional plane method are undertaken. The universality of the present method is substantiated. The present method enhances the precision of natural frequency prediction.

Engineering Single-Layer Hollow Structure of Transition Metal Dichalcogenides with High 1T-Phase Purity for Hydrogen Evolution Reaction.

Rational design and controllable synthesis of hollow structures based on transition metal dichalcogenides (TMDs) have gained tremendous attention in the field of clean energy. However, the general synthetic strategies to fabricate single-layer hollow structures of TMDs, especially with unconventional phases (e.g., 1T or 1T'), still pose significant challenges. Herein, a scalable method is reported for the synthesis of single-layer hollow spheres (SLHS) of TMDs with high 1T-phase purity by etching bismuth (Bi) cores from pre-synthesized Bi@TMDs core-shell heterostructures including SLHS-1T-MoS2 , SLHS-1T-MoSe2 , SLHS-1T-WS2 , and SLHS-1T-WSe2 . Additionally, the etched Bi ions can be adsorbed on the single-layer TMDs shells in the form of single atoms (SAs) via the Bi─S bond. Due to the benefits of the single-layer hollow structure, high conductivity of 1T phase, and synergistic effect of Bi SAs and TMDs supports, the fabricated SLHS-1T-MoS2 exhibits superior electrocatalytic performance for hydrogen production. This work provides a way to manufacture advanced functional materials based on the single-layer hollow structures of 1T-TMDs and to expand their applications.

Experimental study of the double-layer cylindrical shell under uniform axial pressure

In this paper, the buckling performance of the double-layer cylindrical structure with different layers of materials under uniform axial pressure is studied. Three identical double-layer and single-layer cylindrical thin shells are fabricated, measured, and tested respectively. The results indicate that the average ultimate strength of the double-layer cylinder is about 1.91 times that of the single-layer cylinder.

Collapse-resistance optimization of fabricated single-layer grid shell based on sequential approximate optimization

In this work, the surrogate model of the collapse load in terms of the structural morphology is established based on the radial basis function (RBF) network, and the form-finding optimization of the fabricated single-layer grid shell aiming at the improvement of collapse-resistance capacity is realized. To improve the accuracy of the optimal solution, the density function is used to determine the sparse region in the design domain and add new sample points in the sparse region. Avoiding that the optimization is trapped in a poor local optimum, the starting point is updated to approach the global optimum. Three types of fabricated single-layer grid shells, including cylindrical surface, free-form surface with symmetric supports, and free-form surface with asymmetric supports, are selected for form-finding optimization. The results prove the efficiency of the optimization algorithm. The proposed optimization method considers the mechanical properties of assemble joints and reflects the mechanical characteristics of the actual structure. It can be used for form-finding optimization and shape selection in structural design and thus has engineering significance.

Exact solution of a geometrically nonlinear problem for a long three-layer cylindrical panel of oval section

A statement is given and an exact solution of a geometrically nonlinear problem is given for a long open three-layer cylindrical shell of an oval cross-section susceptible to transverse shear under the action of a uniform surface load. The main equations are written according to the geometrically nonlinear theory of smooth shells in the quadratic approximation, in which Tymoshenko's hypotheses hold for the entire package of shell layers. The solution of the problem is obtained in a parametric form with the value of the tangential force as a parameter. For a shell with hinged longitudinal edges, the exact values of the components of the stress-strain state were obtained, the limit values of the generalized geometric parameter were determined, and a system of equations for finding the critical load was constructed. As partial cases, the obtained solution yields the corresponding results for the Kirchhoff–Leav model, the shell of a circular cross-section, and the single-layer shell. The obtained results can be a reference for approximate and numerical methods.

Higher-order static and free vibration analysis of doubly-curved FGM sandwich shallow shells

Plenty of research papers are available on the static and free vibration analysis of single-layer FG shells, however, literature on the analysis of FGM sandwich shells of double curvature is limited. Especially, the authors have not found any paper on the analysis of hyperbolic and elliptical paraboloid FGM sandwich shells. Therefore, FGM sandwich shallow shells with double curvature are analyzed in this study for the static and free vibration conditions. Face sheets of sandwich shells are made up of functionally graded material whereas the core is made up of isotropic material. A functionally graded material considered herein is a combination of alumina and aluminum. Sandwich shallow shells on rectangular planform are modeled using various equivalent single-layer shell theories via unified formulation considering the effects of shear deformation and rotary inertia. Different shell theories recovered from the present unified formulation satisfy the transverse shear stress-free conditions on the lower and upper surfaces of the shell. Hamilton's principle is applied to the present unified formulation for establishing equations of motion. Solutions to free vibration and static problems of simply-supported sandwich shells are obtained using Navier's technique. The numerical results of frequencies, displacements, and stresses are obtained for various types of shells, different sandwich schemes, different values of the power-law factor, and radii of curvature. The results available in the literature are used for the comparison of the present results and found in good agreement with those. However, many new and useful results are also reported in this paper for the reference of readers.

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.

Geometrically nonlinear analysis of functionally graded composite shells using MITC4 and MITC9 elements

In this paper, the geometrically nonlinear behaviors of functionally graded composite shells under large displacements and large rotations are analyzed. Instead of constructing conventional layer-wised models, equivalent single-layer composite shell elements based on general displacement fields are developed to model the inhomogeneity of composite materials. The mixed interpolation of tensorial components technique is used to eliminate membrane locking and shear locking phenomena. The assumed covariant strain fields are initially constructed before being used to evaluate the second Piola–Kirchhoff stress and construct stiffness matrices in local Cartesian coordinates. The standard full Newton–Raphson method is utilized to solve a system of nonlinear equations. Geometrically nonlinear analyses are performed on different thin-walled composite structures including thin cantilever beams, slit annular plates, pinched cylindrical shells, and hemispherical shells. Obtained results demonstrate good convergence characteristics and modeling capability of the developed quadrilateral composite shell elements in analyzing thin-walled composite structures.

Analytical study on sandwich shells considering partial degree of composite action

This paper is focused on a new structural type - sandwich shell, which includes inner and outer shells connected by hoop connectors to achieve composite action; and a functional layer in the middle. Considering that the hoop connectors are not completely rigid, there will be limited slip between the inner and outer shells, which will lead to partial Degree of Composite Action (DCA). Due to the existence of the hoop connectors and shear lag effect, the stress distribution along the width direction of the shell is uneven, which can be described by effective width. Considering all these factors, this paper first develops an analytical model for sandwich shells with different configurations of connectors; and uses finite element analysis results to verify the analytical model. Next, a parametric study is conducted using the analytical model to study the effects of material strength, the ratio of the thickness of the functional layer to the thickness of the single layer shell, and the ratio of the arc length to the width of the sandwich shell on the effective width. It is found that DCA can significantly affect the stress and strain distributions of the sandwich shell. The effective width for 100% DCA can be used as a conservative value to represent those of other DCAs. Finally, a simplified calculation formula, which can be used in practical design, is derived based on the effective width for 100% DCA.

Experimental and numerical study on hysteretic behavior of Double-Layer and Single-Layer aluminum alloy gusset joints

In order to strengthen the members around holes and supports in a single-layer aluminum alloy shell, the method of laminated double-layer members is used to form a double-layer aluminum alloy gusset joint. Hysteresis behavior of this new type of joint is still unclear. Full-scale models were conducted to study the hysteresis behavior of this joint, which was subsequently compared with that of a single-layer joint. The failure mode, bearing capacity, ductility coefficient, and energy dissipation capacity were analyzed. Finite element models were built using ABAQUS to validate the test results and perform a parametric analysis. Research shows that the failure mode of the double-layer aluminum alloy gusset joint under the quasi-static test is a shear rupture of bolts, which is the same as that of single-layer joints. Compared with a single-layer joint, a double-layer joint can significantly increase the ultimate bearing capacity and ability to dissipate energy. However, the double-layer joints have poor ductility. Parametric analysis shows that the bolt material affects the ultimate bearing capacity and failure mode of the aluminum alloy gusset joints.

Static performance of steel temcor joints subjected to axial tension and compression loads

In this study, steel temcor joints with Huck bolts (10.9 grade) for single-layer grid-shell structures were investigated. Experimental, numerical, and theoretical methods were adopted to explore the behaviour of the temcor joint of steel under axial tension and compression loads. In the beginning, six specimens with a single Huck bolt were designed to investigate the failure mode and the shear strength of the Huck bolt. And then, steel temcor joints (TC1, TC2, and TC3) were designed and tested considering the number of Huck bolts and the gusset plate thickness. In the test, the TC1 joint with only eight Huck bolts exhibited the lowest load-bearing capacity with main bolt shear failure under tension and compression loads. Moreover, the TC2 and TC3 joints exhibited higher bearing capacities with bolt shear failure in the tension tests, while they generated the same compressive bearing capacities with the main failure occurring in the H-shaped beam. A 1/6 FE models for three types of specimens in the tension and compression tests were established using Abaqus software. Simultaneously, a parametric analysis was conducted to explore the impact of the gusset plate thickness on the performance of steel temcor joints. The tension and compression theoretical solutions were derived. Finally, the steel temcor joint with Huck bolt exhibited excellent stiffness and bearing capacity which can satisfy the design requirements for the single-layer grid shell structures.

Electronic Structure of CdS Nanoparticles and CdSe/CdS Nanosystems

The electronic states of “wurtzite” CdS nanoparticles and CdSe/CdS nanosystems with up to 80 pairs of Cd-Se or CdS atoms were calculated.The results for CdS particles were compared with the results obtained earlier for CdSe particles of the same size and with published calculations of other authors. The calculated gap values in the range of 2.84 eV ~ 3.78 eV are typical for CdS particles of studied sizes in accordance with results of published data. The CdSe/CdS nanosystems were considered as layered ones and as quantum dots. The layered CdSe/CdS systems with twolayer CdS coverings can be interpreted in terms of combinations of two semiconductors with different energy band gaps (2.6 eV and 3.3 eV), while analogous systems with single-layer CdS coverings do not demonstrate a two-gap electron structure. Simulation of a CdSe/CdS quantum dot shows that the single-layer CdS shell demonstrates a tendency for the formation of the electronic structure with two energy gaps: approximately of 2.5 eV and 3.0 eV.

Robustness study of fabricated single-layer grid shell structures based on component sensitivity and vulnerability

Using discrete beam elements (DBE) to simulate the mechanical properties of assemble joints, the refined analysis model of fabricated single-layer grid shell structures for progressive collapse simulation was established. Based on the component sensitivity and vulnerability, the evaluation indexes of component importance and structural robustness were proposed. The effects of meshing sizes, rise-span ratios and connection behaviors on the collapse performance of K6 type spherical surface grid shell were also investigated. The following conclusions are mainly obtained: (1) By conducting the integral scaled model test, the accuracy of the refined analysis model was verified. (2) Considering the sensitivity and vulnerability of components, the evaluation indexes of component importance and structural robustness were proposed, and the reliability of the component importance coefficient was examined. (3) The effects of grid sizes, rise-span ratios and connection behaviors on the collapse performance of the gird shell were studied, and the rules of structural collapse loads changing with grid sizes and rise-span ratios were explained. (4) To ensure the structure with good collapse resistant capacity, the rise-span ratio should not be less than 1/4 for the K6 type spherical surface grid shell, and failure of the connection region should be avoided.