Shell Geometry Research Articles

Skanowanie laserowe w diagnostyce imperfekcji geometrycznych hiperboloidalnych chłodni kominowych

Hyperboloid cooling towers are distinctive tower structures designed to cool industrial waters by discharging their heat into the ambient air. Geometric imperfections of the hyperboloid cooling tower shell are the main, easily measurable symptom of structural strain and a significant factor in the development of safety hazards and failures of these thin-walled shell structures. This article presents an analysis of the use of a ToF and a phase laser scanner in the diagnosis of geometric imperfections of the reinforced concrete cooling tower shell. The reliability of TLS data in mapping the actual shape of the hyperboloid structure was confirmed on the basis of precise reflectorless tachymetry, which serves as reference data. Geometric imperfections of the hyperboloid cooling tower shell were determined by referring the TLS observation sets to a modified model hyperboloid, adjusted to the external surface by taking into account the actual, variable distribution of the shell thickness. Statistically confirmed compliance of the shell geometry analysis results, carried out on the basis of data obtained with two scanners with different parameters, showed no influence of the distance measurement system used in the scanning instrument on the effectiveness of detection of geometric imperfections of the hyperboloid structure. The results of the analyses of the shape of the cooling tower shell were consistent with the information on the geometric state of the structure, collected in the company archive. The imperfection maps generated on the basis of data obtained with the phase and the ToF pulse laser scanner clearly confirmed the deformations of the critical areas of the structure, which do not pose a real threat to the stability of the facility.

MESHING TRANSFERS IN AUTODESK INVENTOR

In order to improve the execution of drawings of gear elements in the Autodesk Inventor package, an approach to the presentation of geometric information in accordance with the requirements of current standards is proposed, based on the use of developed three-dimensional models of assembly units of gear elements in parametric shells. The basis for the development of the sketch geometry of parametric shells were the basic geometric parameters of the tooth crowns of the elements, since when making drawings of gear meshing elements, the images of the tooth crowns are made in violation of the requirements of current standards. In order to simplify the construction of drawings of gear elements in the Autodesk Inventor package, an algorithm was developed to provide geometric information through the developed three-dimensional models of the parametric shells of the gear crowns of their elements. That is, the geometric information is embedded in the parametric assembly units "gearing in shells". The algorithm is based on working with the parametric shells of the elements of the constituent units, where all the necessary geometric information is represented by a function of the main geometric parameters of real gear crowns. The method of parametric shells considers the issues of touching, implementation, methods of formation of such shells with detailed coverage of their properties and geometric parameters. The rigorous mathematical theory of parametric shells, which involves the joint processing of analytical and geometric information obtained on the basis of the geometry of the gear elements as forming elements, is characterized by generalization in approach and mathematical rigor. At the same time, the presence of toothed crowns of three-dimensional models of gear elements by meshing is ignored. The algorithm for simplified creation of gearing drawings involves making cuts based on sketches, adjusting contour lines and changing the properties of areas in accordance with the requirements of current standards. The library of parametric shells and the algorithm for creating working drawings of both elements and gearing are implemented in the educational process.

On the size‐dependent vibrations of doubly curved porous shear deformable FGM microshells

AbstractThis paper aims to analyse the free vibrations of doubly curved imperfect shear deformable functionally graded material microshells using a five‐parameter shear deformable model. Porosity is modeled via the modified power‐law rule by a logarithmic‐uneven variation along the thickness. Coupled axial, transverse, and rotational motion equations for general doubly curved microsystems are obtained by a virtual work/energy of Hamilton's principle using a modified first‐order shear deformable theory including small size dependence. The modal decomposition method is then used to obtain a solution for different geometries of microshells: spherical, elliptical, hyperbolic, and cylindrical. A detailed study on the influence of material gradation and porosity, small‐length scale coefficient, and geometrical parameters on the frequency characteristics of the microsystem is conducted for different shell geometries.

Machine learning assisted buckling analysis of cantilever bio-inspired helicoidal laminated composite cylindrical shells with cutouts

Buckling behavior of laminated composite shells changes drastically with introduction of cut outs. The present work aims to predict the buckling behavior of bio-inspired helicoidal laminated composite cantilever cylindrical shells using finite element-assisted multi-output Support Vector Machine (SVM) learning algorithm. The model is trained to predict the value for the non-dimensional critical buckling load with the number of layers, geometry of shell, orientation and thickness of each layer, and dimension of circular cut out are adopted as input parameters with critical buckling load for perfect, shell containing one circular or square hole at the center of the length, and shell containing two circular or square hole at the center of the length of the shell are predicted. Thus, single surrogate can predict critical buckling load for five cases in a single rum. Two different types of cut outs i.e., circular and square shaped cut outs are studied. Influence of helicoidal scheme, number of layers, and dimension and number of holes on the buckling behavior of shell is studied. For shell without cut outs, conventional layup schemes such as cross-ply and quasi-isotropic are found to give highest values of the non-dimensional critical buckling load compared to the helicoidal schemes. For shells with cut outs, Fibonacci helicoidal and helicoidal semi-circular (HS3) schemes gives maximum values for the non-dimensional critical buckling loads.

Free vibration characteristics of honeycomb sandwich cylindrical shells reinforced with graphene nanoplatelets/polymer coatings

This study conducts a comprehensive analysis of the free vibration characteristics of honeycomb sandwich cylindrical shells reinforced with graphene nanoplatelets (GNPs). The shells are modeled with a hexagonal honeycomb core, which not only provides a lightweight structure but also enhances the stiffness and dynamic stability. This core design is ideal for high-performance applications such as aerospace and light transport equipment. In addition, the incorporation of graphene nanoplatelet/polymer coatings further improves the structural stiffness, making these shells suitable for demanding environments where both strength and lightweight properties are critical. In the theoretical model, the refined trigonometric shear deformation theory (RTSDT) is applied to accurately represent both bending and shear deformations, capturing the complex behavior of honeycomb sandwich cylindrical shells without requiring shear correction factors. Various parameters, including axial and circumferential wave numbers, as well as geometry and material properties, are examined to assess their impact on natural frequencies. Comparisons with existing literature validate the theoretical models, demonstrating strong agreement with previous results. The analysis reveals that the fundamental natural frequency and other natural frequencies are significantly affected by the inclusion of GNPs and variations in sandwich cylindrical shell geometry. The findings underscore the effectiveness of the RTSDT in modeling these complex sandwich structures.

Recent advances of core–shell nanocrystals dispersed liquid crystal nanocomposites for their applications in electronic devices: A mini review

The core–shell nanocrystals (CSNCs) have been one of the potential additives that resulted remarkable improvements in the physical, electro-optical and emissive properties of LCs. The novel CSNCs could serve as efficient alignment mediators for LC mesophases due to their core–shell geometry that prevents charge transfer to offer stability to the composite. The parameters of CSNCs such as size, properties of core material, capping agents, their miscibility and segregation in LC matrix plays crucial role in envisaging the optimal performance of CSNCs/LCs composites. The intense and tuneable luminescence of CSNCs could significantly enhance the brightness and contrast to result low powered brighter display devices based on CSNCs/LC composites. In this mini review, we have compiled the results of the studies based on CSNCs/LCs composites and discussed about the possible interactions that took place to induce interesting phenomena including low threshold and operating voltage, faster switching response, and high luminescence LC displays. The challenges in fabricating CSNCs/LCs composites and their suitability to be commercialized has also been outlined.

Buckling analysis of PMMA hemispherical pressure shells with thickness variation

The buckling behaviour of polymethyl methacrylate (PMMA) hemispherical pressure shells under uniform external pressure was investigated experimentally and numerically. Six PMMA hemispherical pressure shells were prepared via the free blow-forming process. The geometry and wall thickness of each hemispherical shell were measured. The collapse loads and final failure modes of all shells were obtained via a hydrostatic pressure device. In addition, through optical 3D scanning, a numerical model of the hemispherical shell that reflects the actual geometric imperfection was established and used in the finite element buckling analysis. The numerical results were in agreement with the test results. These findings provide a reference for evaluating the buckling load of PMMA hemispherical shells prepared via the free blow-forming process.

Nonlinear finite element formulation for thin-walled conical shells

This study presents a novel finite element formulation to predict the geometrically nonlinear response of conical shells under a wide range of practical loading conditions. The formulation expresses the discretized equilibrium equations in terms of the first Piola-Kirchhoff stress tensor and its conjugate gradient of the virtual displacements, is based on the kinematics of Love-Kirchhoff thin shell theory and the Saint-Venant-Kirchhoff constitutive model, and captures the follower effect of pressure loading. The formulation takes advantage of the axisymmetric nature of the shell geometries by adopting a Fourier series to characterize the displacement distributions along the circumferential direction while using Hermitian interpolation along the meridional direction. Comparisons with general shell models show the accuracy of the formulation under various loading conditions with a minimal number of degrees of freedom, resulting in a significant computational efficiency compared to conventional general-purpose shell solutions.

Free vibration analysis of sandwich shells with cutouts: An experimental and numerical study with artificial neural network modelling

This article investigates the free vibration and damping characteristics of cylindrical sandwich shells with cutouts using both experimental and numerical approaches. The effects of cutout shape, size, and position on the dynamic response of cylindrical sandwich shells are explored. Moreover, Artificial Neural Network (ANN) models are constructed to predict the dynamic behavior of the sandwich shell with a cutout. A user-friendly application, Sandwich Shell Vibration Analysis (SSVibA), is developed, incorporating the ANN models to predict the non-dimensionalized natural frequencies and modal loss factors of the sandwich shell under different shell geometries, boundary conditions and cutout configurations. The objective of the present research is to advance the understanding of the dynamic behavior of sandwich structures by integrating experimental investigations, numerical analyses, and ANN modeling.

Study on stress singularities in cylindrical shells with an arbitrary oriented crack using digital gradient sensing technique

In this paper, the transmitted digital gradient sensing (DGS) technique is applied to analyze stress singularity at the tip of an arbitrary oriented crack in a cylindrical shell. A thoretical model of the opitcal path near the tip of the inclined crack in a cylindrical shell under mixed-mode fracture is proposed based on the geometric optical imaging principle. An optical governing equation of DGS technique is established to relate the mixed-mode stress intensity fractors (SIFs) at the crack tip to the shell geometry parameters and the inclined crack sizes, and the angular deflection contours are theoretically plotted using this govering equation. Uniaxial tensile tests are carried out on polymethyl methacrylate (PMMA) cylindrical shells containing an edge crack with different inclined angles, and the optimal calculation area for the exaction of SIFs is determined from linear elasitic fracture mechanics. The effects of shell radius, shell thick, crack length, and crack angle on the mixed-mode SIFs are studied, respectively. These results show that the DGS technique is effective and accurate to evalute the stress singulary around an arbitrary oriented cracks in cylindrical shells.

Thermal buckling analysis of reinforced composite conical shells in acidic environments: Numerical and experimental investigation on the effects of nanoparticles

This study investigates the effects of acid penetration and temperature on the buckling behavior of conical composite shells, to enhance structural integrity and longevity in corrosive environments. The study explores the impact of acid exposure on thermal properties and examines the efficacy of incorporating nano-silica and nano-clay in preventing buckling. Additionally, it analyzes the influence of nanoparticles on the thermal, moisture, and mechanical properties of the composite material. Experimental assessments are conducted to measure material properties during exposure to a sulfuric acid solution, providing a comprehensive understanding of the material's behavior under extreme conditions. However, due to the complexity of investigating the combined effects of temperature, acid, and nanoparticles on composite shell buckling, a combined numerical and experimental approach is adopted to predict the critical buckling load. To this end, equations of conical shells under hygrothermal loading are derived, and the critical buckling load is determined through pre-buckling analysis. The Generalized Differential Quadrature (GDQ) method is employed to solve the hygrothermal buckling of the composite shell using experimentally obtained material properties. Comparative results are presented for different nanoparticles, shell geometries, and exposure times in acidic environments. The experiments reveal that adding nanoparticles enhances mechanical properties and reduces thermal and moisture expansion coefficients. Conversely, the acidic conditions deteriorate these properties. Numerical analysis demonstrates that incorporating nanoparticles significantly increases the critical buckling temperature, with nano-silica and nano-clay particles resulting in an 11.5 % and 34.2 % increase, respectively. However, acidic environments decrease the critical buckling temperature, with reductions of 32 % for unreinforced, 29 % for nano-silica reinforced, and 46 % for nano-clay reinforced composites after three months of exposure.

Numerical study of granulation in anelastic thermal convection in spherical shells

The present work investigates granulation or convective flow patterns in density-stratified (or anelastic) convection in spherical shells. The density-stratified thermal convection is typically present in astrophysical systems (such as solar convection); motivated by this, we performed a series of three-dimensional anelastic convection simulations in a spherical shell geometry using an in-house developed hybrid solver. We explored the effect of Rayleigh number and density scale height on the convective flow patterns. The granulation (or cell-like structures) are more prominent at higher density scale height and Rayleigh number. The granulation is further characterized by kinetic energy and helicity spectra. Our results support the argument that the convective flow patterns (or granulation) emerge due to inverse cascade owing to the presence of density stratification. Convective patterns (or granulation) are identified based on length scales, time scales, and flow velocity. The length scale of granules is further verified using a solar granulation model. Our analysis suggests the existence of inverse cascade and supergranulation on the spherical surface due to density-stratified thermal convection in spherical shells.

Flutter in functionally graded conical shell under follower force

Truncated conical shells are essential components of rocket booster nozzles and thrust vector control (TVC) systems for the propulsion of multi-stage launch vehicles. The TVCs assist the ascent of launch vehicles by directing the resultant thrust from the boosters, acting as a follower force that might trigger instability. Previous studies on the instability of aerospace structures have mostly focused on beams, plates, and cylindrical shells. This study analyses a truncated conical shell under a follower force of constant magnitude, considering thickness-wise gradation of material properties employed for thermal management. The governing equations are derived following Hamilton's principle, considering first-order shear deformation theory, and solved using the finite element method. Clamped and free boundaries are assumed at the small and large ends. The influence of mass and stiffness proportional damping is considered. Although strong flutter appears as the dominant instability mode, instances of erratic weak instabilities are also observed for undamped and lightly damped cases. Damping enhances stability, but its effect becomes saturated. The flutter loads are presented for varying non-dimensional parameters, characterizing the shell geometry and material properties.

Comparative Pore Structure and Dynamics for Bacterial Microcompartment Shell Protein Assemblies in Sheets or Shells.

Bacterial microcompartments (BMCs) are protein-bound organelles found in some bacteria that encapsulate enzymes for enhanced catalytic activity. These compartments spatially sequester enzymes within semipermeable shell proteins, analogous to many membrane-bound organelles. The shell proteins assemble into multimeric tiles; hexamers, trimers, and pentamers, and these tiles self-assemble into larger assemblies with icosahedral symmetry. While icosahedral shells are the predominant form in vivo, the tiles can also form nanoscale cylinders or sheets. The individual multimeric tiles feature central pores that are key to regulating transport across the protein shell. Our primary interest is to quantify pore shape changes in response to alternative component morphologies at the nanoscale. We used molecular modeling tools to develop atomically detailed models for both planar sheets of tiles and curved structures representative of the complete shells found in vivo. Subsequently, these models were animated using classical molecular dynamics simulations. From the resulting trajectories, we analyzed the overall structural stability, water accessibility to individual residues, water residence time, and pore geometry for the hexameric and trimeric protein tiles from the Haliangium ochraceum model BMC shell. These exhaustive analyses suggest no substantial variation in pore structure or solvent accessibility between the flat and curved shell geometries. We additionally compare our analysis to hydroxyl radical footprinting data to serve as a check against our simulation results, highlighting specific residues where water molecules are bound for a long time. Although with little variation in morphology or water interaction, we propose that the planar and capsular morphology can be used interchangeably when studying permeability through BMC pores.

Comparative analysis and enhancement of conical component calculation under internal pressure in European pressure vessel Standards

This paper presents a comprehensive analysis of conical components in pressure vessels emphasizing their significance when utilized to transition between different diameters or slopes. A thorough design and analysis are underscored as essential for ensuring the safety and reliability of these components under diverse loading circumstances. The paper aims to propose enhancements to the European Pressure Vessel Standards concerning conical components under internal pressure, with a focus on improving safety, reliability, and compliance with industry standards. Existing European standards are reviewed, identifying potential gaps and proposing practical solutions. The paper also presents research findings on the influence of cone apex angles, shell geometries and design pressure on cone plate thickness calculations. A new methodology for the design and analysis of conical components in pressure vessels is proposed, offering a potential pathway to safer and more efficient pressure vessels. A range of cylinder diameter between 1000 and 2500 mm and cone angles between 30° and 60° are used as input to quantify the difference in cone thickness for a design pressure ranging between 10 and 200 barg. The proposed method yields results much closer to AD2000 compared to EN13445, leading to slightly thicker cones (up to 2.2 mm for the selected range of cone diameters and angles) compared to the former, resulting in safer pressure vessel design, and thinner cones (up to 22 mm) compared to the latter resulting in significant material savings. A comparative analysis was performed through Finite Element Analysis validating the EN13445 unsuitability for cone thickness calculations. A modification is proposed for equation (7.6)-(8) in EN13445 resulting in thinner plates reducing the cone plate thickness difference to 0.9 % on average compared to the current deviation of -9.6 % on average for the selected range of cylinder diameters and cone angles.

Multi-segmented fifth-order polynomial–shaped shells under hydrostatic pressure

The design and construction of submerged complex shells for new applications in offshore structures are increasingly popular. Therefore, the purpose of this study is to present the analytical model and Lagrange multipliers associated with the constraint equation for large displacement analysis of a fifth-order polynomial–shaped shell under hydrostatic pressure for the first time. The shell geometry can be computed using differential geometry with a fifth-order polynomial. The energy functional of the fifth-order polynomial–shaped shell is derived based on the principle of virtual work and written in the appropriate form. The nonlinear static responses of the fifth-order polynomial–shaped shell under hydrostatic pressure can be calculated using the nonlinear finite element method via the fifth-order polynomial shape function. This study develops the model using one-dimensional beam elements divided along the shell radius. To avoid the slope of a meridian curve at the equatorial plane approaching infinity, the shell is divided into two regions defined by different surface parameters. At the junction of two adjacent regions, the continuity requirements are established as the constraint conditions using Lagrange multipliers. The numerical results from the proposed methods are demonstrated and discussed, along with the effects of varied seawater depth, thickness, and elastic modulus on the deformed configuration and principal curvature at the deformed state. The results show that the nonlinear displacement is higher than the linear one in the case of the hydrostatic pressure, whereas the case of the internal pressure has an opposite result. For principal curvatures at the apex, the principal curvatures increase as the seawater depth increases, whereas the principal curvatures decrease when the thickness and elastic modulus increase.

Method for Generating Closely Packed Orbital Shells and Orbital Capacity Implications

Shell-wise orbital coordination in low Earth orbit can improve space safety, simplify space traffic coordination and management, and optimize orbital capacity. This work describes two methods to generate 2D lattice flower constellations (2D-LFCs) that are defined with respect to either an arbitrary zonal, or zonal, sectoral, and tesseral Earth geopotential. By generating orbital shells that are periodic with respect to the Earth geopotential, it is possible to safely stack shells with vertical separation distances smaller than the osculating variation in semimajor axis and radial distance of each shell, or a corresponding Keplerian 2D-LFC propagated under an aspherical geopotential. These methods exploit previous work on constellations based on time distributions and designs of closed 2D-LFCs under arbitrary Earth geopotentials using repeating ground track orbits. Factors that influence the widths and shapes of these shells are identified. Additionally, simplified formulas for estimating shell geometry and thickness are presented. Based on these results, it is shown that geopotential-aware periodic orbital shells significantly increase the number of admissible orbital shells while preserving shell separation. Finally, this work shows that sequencing shells to group similar or ascending inclinations can further improve capacity versus arbitrary inclination ordering, particularly for smaller shell separation distances.

Structure evolution of Cu3Pd single-particles under CO2 hydrogenation

Encapsulating metal nanoparticles into a porous silica shell, forming a core–shell geometry, has been popularly applied to prevent the particles from sintering at the elevated temperatures and under reactive gases. However, structure evolution of the metal particles under reaction conditions is less known. Here, the dynamic behavior of Cu3Pd single-particles, confined by a permeable silica shell, during CO2 hydrogenation have been examined by microscopic and spectroscopic characterizations. It was found that H2-reduction of the bimetallic particle at 673 K led to the partial enrichment of Cu on the surface, while H2-treatment at 873 K resulted in the surface segregation of Pd owing to the stronger adsorption of H2 on Pd. When subjected to CO2 hydrogenation at 517–673 K, the enriched Pd surface atoms and the electron-deficient Cu atoms synergistically activated H2/CO2 molecules and promoted the activity for the reverse water–gas shift. However, the Cu atoms partially migrated onto the SiO2 shell and formed tiny Cu clusters, induced by the strong adsorption of O-containing reaction intermediates, forming a core@shell@satellite (CuPd@SiO2 @Cu) architecture.

Topological defects as nucleation points of the nematic-isotropic phase transition in liquid crystal shells.

The transition from a nematic to an isotropic state in a self-closing spherical liquid crystal shell with tangential alignment is a stimulating phenomenon to investigate, as the topology dictates that the shell exhibits local isotropic points at all temperatures in the nematic phase range, in the form of topological defects. The defects may thus be expected to act as nucleation points for the phase transition upon heating beyond the bulk nematic stability range. Here we study this peculiar transition, theoretically and experimentally, for shells with two different configurations of four +1/2 defects, finding that the defects act as the primary nucleation points if they are co-localized in each other's vicinity. If the defects are instead spread out across the shell, they again act as nucleation points, albeit not necessarily the primary ones. Beyond adding to our understanding of how the orientational order-disorder transition can take place in the shell geometry, our results have practical relevance for, e.g., the use of curved liquid crystals in sensing applications or for liquid crystal elastomer actuators in shell shape, undergoing a shape change as a result of the nematic-isotropic transition.

Dynamic Analysis of Functionally Graded Sandwich Doubly Curved Nanoshells Using Variable Nonlocal Elasticity Theory

Sandwich nanoshells consisting of functionally graded materials (FGMs) offer promise in aerospace, energy and biomedical applications due to their tunable properties. However, a comprehensive understanding of the vibration behavior of such shells is lacking. This work develops an efficient analytical model to study free vibration of sandwich nanoshells with three FGM configurations: FGM face-sheets and metal core (Type A), FGM face-sheets and ceramic core (Type B), and FGM core and face-sheets (Type C). A doubly curved shell geometry representing spherical, hyperbolic–parabolic and cylindrical shells in addition to flat plates is considered. Effective material properties of nanolaminates are computed using a volume fraction-based model. First-order shear deformation theory and modified nonlocal elasticity theory with variable nonlocal parameters are employed to derive the governing equations. Hamilton’s principle is used to obtain the equations of motion. Navier’s solution technique analytically solves the equations for simply supported boundary conditions. Accuracy is validated through comparisons with literature results. Parametric studies analyze the influence of thickness ratio, material gradation, nonlocal parameter, and shell type on frequencies. Results show that Type A configuration yields the highest frequencies. Dimensionless frequency decreases with increasing nonlocal parameter and side-to-thickness ratio. The model provides design insights into vibration behavior of such nanosandwich structures with potential applications in nanodevices and energy harvesting.