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Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two ‘self-equilibrated’ states, one natural and the other inside out (or ‘everted’). Though this is familiar from everyday life—an umbrella is remarkably stable, yet a contact lens can be easily turned inside out—the precise shell geometries for which bistability is possible are not known. Here, we use experiments and finite-element simulations to determine the threshold between bistability and monostability for shells of different solid angle. We compare these results with the prediction from shallow shell theory, showing that, when appropriately modified, this offers a very good account of bistability even for relatively deep shells. We then investigate the robustness of this bistability against pointwise indentation. We find that indentation provides a continuous route for transition between the two states for shells whose geometry makes them close to the threshold. However, for thinner shells, indentation leads to asymmetrical buckling before snap-through, while also making these shells more ‘robust’ to snap-through. Our work sheds new light on the robustness of the ‘mirror buckling’ symmetry of spherical shell caps.

In the present study, we analyze the nonlinear forced vibration of thin-walled metal foam cylindrical shells reinforced with functionally graded graphene platelets. Attention is focused on the 1:1:1:2 internal resonances, which is detected to exist in this novel nanocomposite structure. Three kinds of porosity distribution and different kinds of graphene platelet distribution are considered. The equations of motion and the compatibility equation are deduced according to the Donnell’s nonlinear shell theory. The stress function is introduced, and then, the four-degree-of-freedom nonlinear ordinary differential equations (ODEs) are obtained via the Galerkin method. The numerical analysis of nonlinear forced vibration responses is presented by using the pseudo-arclength continuation technique. The present results are validated by comparison with those in existing literature for special cases. Results demonstrate that the amplitude–frequency relations of the system are very complex due to the 1:1:1:2 internal resonances. Porosity distribution and graphene platelet (GPL) distribution influence obviously the nonlinear behavior of the shells. We also found that the inclusion of graphene platelets in the shells weakens the nonlinear coupling effect. Moreover, the effects of the porosity coefficient and GPL weight fraction on the nonlinear dynamical response are strongly related to the porosity distribution as well as graphene platelet distribution.

The nonlinear forced vibrations of functionally graded material (FGM) sandwich cylindrical shells with porosities on an elastic substrate are studied. A step function and a porosity volume fraction are introduced to describe the porosities in FGM layers of sandwich shells. Using the Donnell’s nonlinear shallow shell theory and Hamilton’s principle, an energy approach is employed to gain the nonlinear equations of motion. Afterwards, the multi-degree-of-freedom nonlinear ordinary differential equations are carried out by using Galerkin scheme, and subsequently the pseudo-arclength continuation method is utilized to perform the bifurcation analysis. Finally, the effects of the core-to-thickness ratio, porosity volume fraction, power-law exponent, and external excitation on nonlinear forced vibration characteristics of FGM sandwich shells with porosities are investigated in detail.

Molluscan shells, mainly composed of calcium carbonate, also contain organic components such as proteins and polysaccharides. Shell organic matrices construct frameworks of shell structures and regulate crystallization processes during shell formation. To date, a number of shell matrix proteins (SMPs) have been identified, and their functions in shell formation have been studied. However, previous studies focused only on SMPs extracted from adult shells, secreted after metamorphosis. Using proteomic analyses combined with genomic and transcriptomic analyses, we have identified 31 SMPs from larval shells of the pearl oyster, Pinctada fucata, and 111 from the Pacific oyster, Crassostrea gigas. Larval SMPs are almost entirely different from those of adults in both species. RNA-seq data also confirm that gene expression profiles for larval and adult shell formation are nearly completely different. Therefore, bivalves have two repertoires of SMP genes to construct larval and adult shells. Despite considerable differences in larval and adult SMPs, some functional domains are shared by both SMP repertoires. Conserved domains include von Willebrand factor type A (VWA), chitin-binding (CB), carbonic anhydrase (CA), and acidic domains. These conserved domains are thought to play crucial roles in shell formation. Furthermore, a comprehensive survey of animal genomes revealed that the CA and VWA–CB domain-containing protein families expanded in molluscs after their separation from other Lophotrochozoan linages such as the Brachiopoda. After gene expansion, some family members were co-opted for molluscan SMPs that may have triggered to develop mineralized shells from ancestral, nonmineralized chitinous exoskeletons.

In this article, the nonlinear dynamic responses of sandwich functionally graded (FG) porous cylindrical shell embedded in elastic media are investigated. The shell studied here consists of three layers, of which the outer and inner skins are made of solid metal, while the core is FG porous metal foam. Partial differential equations are derived by utilizing the improved Donnell’s nonlinear shell theory and Hamilton’s principle. Afterwards, the Galerkin method is used to transform the governing equations into nonlinear ordinary differential equations, and an approximate analytical solution is obtained by using the multiple scales method. The effects of various system parameters, specifically, the radial load, core thickness, foam type, foam coefficient, structure damping, and Winkler-Pasternak foundation parameters on nonlinear internal resonance of the sandwich FG porous thin shells are evaluated.

Defect and interface engineering are efficient approaches to adjust the physical and chemical properties of nanomaterials. In order to effectively utilize these strategies for the improvement of microwave absorption properties (MAPs), in this study, we reported the synthesis of hollow carbon shells and hollow carbon@MoS 2 nanocomposites by the template-etching and template-etching-hydrothermal methods, respectively. The obtained results indicated that the degree of defect for hollow carbon shells and hollow carbon@MoS 2 could be modulated by the thickness of hollow carbon shell, which effectively fulfilled the optimization of electromagnetic parameters and improvement of MAPs. Furthermore, the microstructure investigations revealed that the precursor of hollow carbon shells was encapsulated by the sheet-like MoS 2 in high efficiency. And the introduction of MoS 2 nanosheets acting as the shell effectively improved the interfacial effects and boosted the polarization loss capabilities, which resulted in the improvement of comprehensive MAPs. The elaborately designed hollow carbon@MoS 2 samples displayed very outstanding MAPs including strong absorption capabilities, broad absorption bandwidth, and thin matching thicknesses. Therefore, this work provided a viable strategy to improve the MAPs of microwave absorbers by taking full advantage of their defect and interface engineering.

This study investigates the free vibration of metal foam circular cylindrical shells under various boundary conditions. The elasticity modulus and mass density of the shells vary gradually and continually in the thickness direction. Two types of porosity distribution are taken into account including symmetrical and unsymmetrical distributions. Love’s shell theory is employed to formulate the governing equations and then the Rayleigh–Ritz method is utilized to solve natural frequencies of the system. The results show that the porosity coefficient has important effect on the natural frequencies of metal foam shells. Its effect also relates to the boundary conditions of the shells. Moreover, different porosity distributions make the metal foam shells possess different vibration characteristics, which is quite obvious at large porosity coefficient. As the circumferential wave number increases, the natural frequencies of the metal foam shells tend to the same under various boundary conditions. Additionally, the present results are verified by the comparison with the published ones in the literature.

With the pace of time, synthesis of nanomaterials has paved paths to blend two or more materials having different properties into hybrid nanoparticles. Therefore, it has become possible to combine two different functionalities in a single nanoparticle and their properties can be enhanced or modified by coupling of two different components. Core–shell technology has now represented a new trend in analytical sciences. Core–shell nanostructures are in demand due to their specific design and geometry. They have internal core of one component (metal or biomolecules) surrounded by a shell of another component. Core–shell nanoparticles have great importance due to their high thermal stability, high solubility and lower toxicity. In this review, recent progress in development of new and sophisticated core–shell nanostructures has been explored. The first section covers introduction throwing light on basics of core–shell nanoparticles. Following section classifies core–shell nanostructures into single core/shell, multicore/single shell, single core/multishell and multicore/multishell nanostructures. Next main section gives a brief description on types of core–shell nanomaterials followed by processes for the synthesis of core–shell nanostructures. Ultimately, the final section focuses on the application areas such as drug delivery, bioimaging, solar cell applications etc.Graphic abstract

Molluscs fabricate shells of incredible diversity and complexity by localized secretions from the dorsal epithelium of the mantle. Although distantly related molluscs express remarkably different secreted gene products, it remains unclear if the evolution of shell structure and pattern is underpinned by the differential co-option of conserved genes or the integration of lineage-specific genes into the mantle regulatory program. To address this, we compare the mantle transcriptomes of 11 bivalves and gastropods of varying relatedness. We find that each species, including four Pinctada (pearl oyster) species that diverged within the last 20 Ma, expresses a unique mantle secretome. Lineage- or species-specific genes comprise a large proportion of each species’ mantle secretome. A majority of these secreted proteins have unique domain architectures that include repetitive, low complexity domains (RLCDs), which evolve rapidly, and have a proclivity to expand, contract and rearrange in the genome. There are also a large number of secretome genes expressed in the mantle that arose before the origin of gastropods and bivalves. Each species expresses a unique set of these more ancient genes consistent with their independent co-option into these mantle gene regulatory networks. From this analysis, we infer lineage-specific secretomes underlie shell diversity, and include both rapidly evolving RLCD-containing proteins, and the continual recruitment and loss of both ancient and recently evolved genes into the periphery of the regulatory network controlling gene expression in the mantle epithelium.