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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.

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.

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.

We derive a hyperelastic shell formulation based on the Kirchhoff–Love shell theory and isogeometric discretization, where we take into account the out-of-plane deformation mapping. Accounting for that mapping affects the curvature term. It also affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the material. In fluid–structure interaction analysis, when the fluid is inside a shell structure, the shell midsurface is what it would know. We also propose, as an alternative, shifting the “midsurface” location in the shell analysis to the inner surface, which is the surface that the fluid should really see. Furthermore, in performing the integrations over the undeformed configuration, we take into account the curvature effects, and consequently integration volume does not change as we shift the “midsurface” location. We present test computations with pressurized cylindrical and spherical shells, with Neo-Hookean and Fung’s models, for the compressible- and incompressible-material cases, and for two different locations of the “midsurface.” We also present test computation with a pressurized Y-shaped tube, intended to be a simplified artery model and serving as an example of cases with somewhat more complex geometry.

In this work, the nonlinear forced vibrations of doubly curved shells are studied. For this, the Forced Resonance Curves of four different shells were determined: a shallow cylindrical panel, a shallow spherical panel, a non-shallow spherical panel, and a hyperbolic paraboloid. To model the shells, the Koiter’s nonlinear shell theory, for both shallow and non-shallow shells, was applied. The forced resonance curves were determined using an adaptive harmonic balance method and through a reduced-order model (ROM) via parameterization method for invariant manifolds. The findings of this study reveal the complex dynamic behavior exhibited by doubly curved shells, with various types of bifurcations such as Saddle–Node, Neimark–Sacker, and Period Doubling bifurcations. Thanks to the general treatment of the forcing term implemented in the parameterization method, the results highlight how complex high-order resonances can be retrieved by the ROM, up to a comfortable range of vibration and forcing amplitudes tested. Finally, it clearly demonstrates how the Nonlinear Normal Modes as invariant manifolds provide accurate and efficient ROMs for nonlinear vibrations of shells.