Semi-cylindrical Shell Research Articles

Numerical Investigation on the Ballistic Performance of Semi-Cylindrical Nacre-like Composite Shells under High-Velocity Impact.

The nacre has excellent impact resistance performance, and it is attracting attention in the field of aerospace composite research. Inspired by the layered structure from nacre, semi-cylindrical nacre-like composite shells of brittle silicon carbide ceramic (SiC) and aluminum (AA5083-H116) were established. Two types of tablet arrangements (regular hexagonal and Voronoi polygons) of the composites were designed, and the same size of ceramic and aluminum shell were established for the impact resistance analyzed numerically. In order to better compare the resistance performance of the four types of structures under different impact velocity, the following parameters were analyzed including energy variation, damage characteristic, bullet residual velocity, and semi-cylindrical shell displacement. The results show that the semi-cylindrical ceramic shells have higher rigidity and ballistic limit, but the severe vibration after impact causes penetrating cracks, and the whole structure failure occurred eventually. The nacre-like composites have higher ballistic limits than semi-cylindrical aluminum shells, and the impact of bullets only causes local failure. In the same conditions, the impact resistance of regular hexagons is better than Voronoi polygons. The research analyzes the resistance characteristic of nacre-like composites and single materials, and provides a reference for the design of nacre-like structures.

Multi-impact response of semicylindrical composite laminated shells with different thicknesses

Nowadays, composite materials are increasingly used in the most diverse areas of engineering, where non-planar geometries begin to be quite frequent. However, the existing knowledge about its mechanical performance is still not enough for structural applications. Therefore, experimental tests were carried out to study the thickness effect on static compression and multi-impact response of laminated E-glass/Polyester semicylindrical shells. For this purpose, specimen with thicknesses of 1.1 mm, 1.6 mm and 2.1 mm (corresponding to 6, 9 and 12 woven fabric layers) were considered. In terms of static response, higher thicknesses are responsible for higher compressive strength and stiffness, reaching, in the first case, differences of 252.6 % between the thinnest and thickest shells. Regarding the multi-impact response, the impact fatigue life increases 17.4 times for the analysed thickness range, which can be explained by the different damage mechanisms observed. It was observed that impact damage becomes more localized with increasing thickness, because the energy is dissipated by more interfaces.

Research on the accuracy of the generalized Lévy’s solution for deflection of open cylindrical shell structures

In the last century, the plate and shell theory has been developed and matured through the research of many theoretical workers at home and abroad. The generalized Lévy’s solution can be used to obtain the static response of a semi-cylindrical shell with curved ends simply supported under arbitrary load. However, the solution is complex and difficult to calculate, so on this basis, a series of simplified methods under specific working conditions are developed, such as the moment-free theory and semi-moment-free theory of cylindrical shells. In this paper, MATLAB will be used to calculate the generalized Levi’s solution and semi-moment-free theory, and compare them with the finite element results of ANSYS. Finally, it is found that the two theoretical solutions can only roughly predict the distribution form of displacement, with an order of magnitude difference. The engineering significance is limited, and the results still need to be improved.

Ballistic response and energy dissipation characteristic of single and double curvature shell against projectile impact: a comparative study

This study provides the comparative study of energy dissipation characteristics of semi-cylindrical and hemispherical structures subjected to projectile impact. The experimental tests were conducted by using a compressed air gun against hemispherical and ogive projectile. Numerical study was performed by employing Abaqus/explicit solver. Also, numerical analysis was further stretched to find out the absorbed energy dissipation in different direction. The impact response of both the structures was examined in terms of ballistic resistance, transverse deformation, failure mechanics and energy dissipation in plastic works. The semi-hemispherical shell exhibits higher ballistic resistance and absorbed energy than semi-cylindrical shell structure against both projectiles.

Hysteretic behavior of CHS X-joints under in-plane bending moment

In this paper, hysteretic behavior of circular hollow section (CHS) X-joints under in-plane bending moment (IPBM) is investigated. Firstly, carried out experimental study on three CHS X-joints with different brace-to-chord diameter ratio (β) and brace-to-chord angle (θ) under cyclic IPBM. Test results show that three specimens eventually failed by tearing of the chord wall in the brace/chord connection region. Before cracking, the chord wall in the connection region experienced large plastic deformation which provide significant energy dissipation; and the resistance decreases slowly after cracking due to ductile crack propagation. Test results also indicate that flexural hysteretic of the X-joints is greatly affected by the two parameters (β and θ). Specifically, either increasing β (from 0.73 to 0.89) or deceasing θ (from 90° to 70°) is benefit to ductility ratio, flexural strength and energy dissipation behavior. The test observation is further explained and confirmed by a model of load transfer mechanism (a semi-cylindrical shell constrained by the directional supports) and the finite element (FE) parameters analysis with extended range of the above two parameters. Then, a hysteretic model is proposed to simulate in-plane flexural hysteretic behavior of the CHS X-joints, and the hysteric model is verified by test and FE results. Finally, effect of chord moment and brace axial force on the in-plane flexural behavior of the X-joints was investigated by FE analysis.

Reconstruction of time-dependent forces acting on a vibrating structure from pressure measurements.

This paper proposes an approach to reconstruct the time-dependent forces acting on a vibrating structure from pressure measurements. In the approach, the pressures measured in the near field of the structure are related to the exciting forces at the reconstruction points by the transfer functions determined in an experimental way, whereupon the time-dependent forces can be reconstructed with these pressures as inputs. In the reconstruction process, an additional regularization with a mixed lp , q-norm term is introduced to resolve the ill-posed inverse problem, which is able to take advantage of the prior knowledge of space and time characteristics of the forces. A numerical simulation of reconstructing the time-dependent forces acting on a plate and two experiments of reconstructing the impact forces acting on a semi-cylindrical shell and an elliptically shaped structure are carried out. The results demonstrate the feasibility of the proposed approach for reconstructing the forces in both temporal and spatial domains from pressure measurements. The proposed approach provides a non-contact and real-time way to identify the locations of forces and reconstruct their time histories, which can be further used to reveal the mechanical cause of the radiated noise.

In-plane buckling of semi-cylindrical shells with elastic edge restraints under a central radial load

The present study investigates the elasto-plastic buckling behaviour of semi-cylindrical shells with elastic edge restraints under the action of a central radial load, both numerically and experimentally. Several design parameters are expressed to characterize the influence of elastic edge restraints on load-bearing capacity. A reduction factor equation is developed as a multivariate function of the shell parameters, which evaluates the amount of decrease in load-bearing capacity of the structure caused by elastic edge restraints. Additionally, an equation to predict load-bearing capacity under clamped edge conditions is introduced, which is used as a reference value in the reduction factor equation. Conditions for the elasto-plastic buckling occurrence are identified with the help of normalized parameters. An exclusive validation process is applied to the proposed expressions using a large series of numerical, experimental data and statistical methods to ascertain the accuracy of the predictions at a wide range of design parameters. Furthermore, parametric studies are performed in which the influence of elastic edge restraints, material plasticity and radius-to-thickness ratio on the limit load as well as deformation patterns of the semi-cylinders, is investigated. The results show that elastic edge restraint stiffness has a significant effect on the limit load of semi-cylindrical shells under in-plane loading and, therefore, cannot be underestimated.

Energy dissipation characteristics of single curvature metallic shells subjected to ballistic impact

The impact resistance of single curvature semi-cylindrical shell targets of aluminum 1100-H12 was explored against hard steel cylindrical projectiles. Experimental as well as numerical investigations were carried out to observe the performance of shell targets against ogive, conical, blunt and hemispherical nosed projectiles. Effect of oblique impact was studied on the ballistic performance of the shell targets at 0 (normal), 15 and 30° obliquity. Further, the impact performance of 2 mm thick monolithic and in-contact layered targets of equivalent thickness was evaluated and compared. The projectiles were driven by a pneumatic air gun and the projectile flight path was captured with a high-speed camera. The experimental results obtained in terms of incidence and residual velocities, and deformation profile of the targets, were validated with the numerical analyses conducted in ABAQUS/Explicit solver. Johnson-Cook constitutive strength and damage material model was employed to simulate the deformation and damage evolution in the targets. The ballistic performance of both monolithic and layered targets impacted at oblique incidence, was compared in terms of ballistic limits, failure mechanisms, local and global plastic deformations and plastic strain energy absorbed in radial, circumferential, axial and shear deformation modes. The in-contact layered shell targets exhibited significantly higher impact resistance than the monolithic targets against all projectiles. Target configurations impacted at oblique incidence with conical and ogive nosed projectiles showed increase in global deformation, while, opposite behaviour was observed in case of blunt and hemispherical nosed projectiles. The plastic strain energy absorbed in various deformation modes correlated with the failure patterns observed in the target material during ballistic impact.

Development of an electrical analogue for modeling natural vibrations of a viscoelastic structure with piezoelectric element

This paper focuses on the development of an equivalent electrical model with lumped parameters capable of describing the natural vibrations of an electromechanical system comprising a viscoelastic structure with a piezoelectric element attached to its surface. The important advantage of the model is that it takes into account the energy losses associated with the viscoelastic properties of the material of the main structure. Two versions of the equivalent electric analogue of the initial electro-viscoelastic system in the form of electric circuits, the elements of which are described by the real or complex quantities, are considered. The approaches to the formulation of the problem of natural vibrations in the developed electric analogue are based on Kirchhoff’s laws for electric circuits and Ohm’s law for alternating current. Special attention is paid to the identification of model parameters. A procedure for determining the parameters for the equivalent electrical model is based on the results gained from the solution of a coupled problem of natural vibrations of the initial electromechanical system; problem formulation is also given here. The effectiveness and reliability of the developed equivalent electric models with lumped parameters for the determination of complex eigenfrequencies of the electromechanical system containing energy dissipation elements are demonstrated by analyzing the behavior of structures in the form of a rectangular plate and a semi-cylindrical shell.

Investigation on compression-springback behavior of metal semi-cylindrical shell in thermal environment

The elastic-plastic deformation of materials provides limited displacement for metal gaskets, so as to ensure the sealing performance of flanges. In order to study the sealing performance of a novel metal gasket with a convex structure of a semi-cylindrical shell between two flanges, the compression-springback behavior of semi-cylindrical shell is investigated. By introducing the rebound and anti-coupled system consisting of the compressed body and the resilient body, meanwhile based on von Kármán nonlinear theory and Mises yield criterion, the incremental thermo-elastoplastic stress-strain constitutive relation of the semi-cylindrical shell is theoretically derived. Utilizing the finite difference method in space domain and nonlinear term iteration technique, the plastic stage problem including the semi-cylindrical shell and the sheet with flattening single-corrugated structure is solved. The influence factors of material properties, temperature, geometrical parameters of semi-cylindrical shells and cyclic loads are considered. Results show that the compression-springback behavior of nickel-based alloy is better than that of stainless steel in thermal environment, while the compression-springback behavior of stainless steel is closed to that of nickel-based alloy at room temperature. The width of semi-cylindrical shell and depth of base material significantly affect the compression-springback behavior of stainless steel. In addition, the cyclic load can cause the plastic hardening of stainless steel.

Damping Characteristics of Laminated Semi-Cylindrical Shells: Technical Note

The natural frequencies and damping co-efficient were obtained in a half-cylindrical shell made up of epoxy resin reinforced with glass fibre. The impact load is given by an impact hammer and the effect of impact load is sensed using an accelerometer, which is fixed at the edge of the cylinder. Results are manipulated directly by the system through the accelerometer. The laminated shells were tested with various boundary conditions such as free-free, fixed–fixed and simply supported end. The same tests were conducted on the shells with longitudinal stiffeners. The damping characteristics were compared. From the results it was found that shells without stiffener have a damping co-efficient of 0.177 and the shells with stiffener have a damping co-efficient of 0.311 in free-free end condition. Here it is understood that the shells with stiffener showed 43% improvement in damping co-efficient also. It was also observed that with the addition of rubber particles to the reinforcing polymer, the shells with stiffeners may lead to significant increase in damping co-efficient

Receiver array design for sonothrombolysis treatment monitoring in deep vein thrombosis

High intensity focused ultrasound (HIFU) can disintegrate blood clots through the generation and stimulation of bubble clouds within thrombi. This work examined the design of a device to image bubble clouds for monitoring cavitation-based HIFU treatments of deep vein thrombosis (DVT). Acoustic propagation simulations were carried out on multi-layered models of the human thigh using two patient data sets from the Visible Human Project. The design considerations included the number of receivers (32, 64, 128, 256, and 512), their spatial positioning, and the effective angular array aperture (100° and 180° about geometric focus). Imaging array performance was evaluated for source frequencies of 250, 750, and 1500 kHz. Receiver sizes were fixed relative to the wavelength (pistons, diameter = λ/2) and noise was added at levels that scaled with receiver area. With a 100° angular aperture the long axis size of the −3 dB main lobe was ~1.2λ—i.e. on the order of the vessel diameter at 250 kHz (~7 mm). Increasing the array aperture to span 180° about the geometric focus reduced the long axis by a factor of ~2. The smaller main lobe sizes achieved by imaging at higher frequencies came at the cost of increased levels of sensitivity to phase aberrations induced during acoustic propagation through the intervening soft tissue layers. With noise added to receiver signals, images could be reconstructed with peak sidelobe ratios < −3 dB using single-cycle integration times for source frequencies of 250 and 750 kHz (NRx ⩾ 128). At 1500 kHz, longer integration times and/or higher element counts were required to achieve similar peak sidelobe ratios. Our results suggest that a modest number of receivers(i.e. NRx = 128) arranged on a semi-cylindrical shell may be sufficient to enable passive acoustic imaging with single-cycle integration times (i.e. volumetric rates up to 0.75 MHz) for monitoring cavitation-based HIFU treatments of DVT.

Numerical Analysis on Process-Induced Residual Stress in Thick Semi-Cylindrical Composite Shell Using a State-Dependent Viscoelastic Model

A two-step state-dependent analysis model corresponding to the flow state before gelation and the viscoelastic state after gelation was proposed for the prediction of the residual stresses developed in polymer matrix composites (PMCs) during cure. The evolution of the viscoelasticity of PMCs during cure was analyzed based on the non-dimensional viscoelasticity parameters 1/Dem, and the gelation time was determined at the condition of Min(1/Dem) = 102. The proposed model was used to predict the process-induced residual stress and distortion in a thick semi-cylindrical composite shell. By comparing the predictions with those of the original cure-dependent viscoelastic model, the proposed model was verified and the computing time and memory storage were significantly reduced. The results show that during the cure of thick semi-cylindrical composite shell, the residual stresses caused by the cure shrinkage at high cure temperature are quickly relaxed, and most of the residual stress develops during cool-down. The spring-in deformation of the semi-cylindrical shell when release from the mould is mainly caused by the significant hoop stress gradient in the thickness direction developed during cure. Obvious warpage is not present in the composite semi-cylindrical shell due to the high bending stiffness.

Pinching an open cylindrical shell: Extended deformation and its persistence

Against external loads, shells with ideal symmetries, such as perfect spheres and cylinders, show enhanced rigidities, whose origin is known to be largely geometric and is often termed “geometric rigidity.” In contrast, shells with free boundaries (i.e., open shells) may respond quite differently to external loads. They may deflect significantly as free boundaries may allow (almost) inextensional bending deformations that are impossible in the case of closed surfaces. Herein, we investigate the smooth deformation of an open cylindrical shell induced by pinching through a combination of experiment, simulations, and theory. To be more specific, we apply a localized pinch at one end of a long semi-cylindrical shell, and investigate the distance at which the shell recovers its undeformed form; we call this distance the persistence length of a pinch. We establish a new scaling law for the persistence length of shallow shells, which is shown to be valid for an arbitrarily deep shell. We show that the persistence length of a sufficiently deep open cylinder exceeds that of a closed cylinder, thereby highlighting the importance of the subtle interplay between the intrinsic curvature and the free edges on shell mechanics. These findings are rationalized by a detailed asymptotic analysis of the shallow shell equations. Our results reveal how the free boundaries essentially alter the balance between bending and stretching in thin shells.

A search for optimal parameters of resonance circuits ensuring damping of electroelastic structure vibrations based on the solution of natural vibration problem

In this paper, with the aim of providing passive control of structure vibrations a new approach has been proposed for selecting optimal parameters of external electric shunt circuits connected to piezoelectric elements located on the surface of the structure. The approach is based on the mathematical formulation of the natural vibration problem. The results of solution of this problem are the complex eigenfrequencies, the real part of which represents the vibration frequency and the imaginary part corresponds to the damping ratio, characterizing the rate of damping. A criterion of search for optimal parameters of the external passive shunt circuits, which can provide the system with desired dissipative properties, has been derived based on the analysis of responses of the real and imaginary parts of different complex eigenfrequencies to changes in the values of the parameters of the electric circuit. The efficiency of this approach has been verified in the context of natural vibration problem of rigidly clamped plate and semi-cylindrical shell, which is solved for series-connected and parallel –connected external resonance (consisting of resistive and inductive elements) R-L circuits. It has been shown that at lower (more energy-intensive) frequencies, a series-connected external circuit has the advantage of providing lower values of the circuit parameters, which renders it more attractive in terms of practical applications.

Experimental and finite element study of residual thermal stresses in veneered Y-TZP structures

The main complications of zirconia-based laminated systems are chipping and delamination of veneering porcelain, which has been found to be directly associated with the development of residual thermal stresses in the porcelain layer. This study investigates the effects of cooling rate and specimen geometry on the residual stress states in porcelain-veneered zirconia structures. Bilayers of three different shapes (bars, semi-cylindrical shells, and arch-cubic structures) with 1.5mm and 0.7mm thickness of dentin porcelain and zirconia framework, respectively, were subjected to two cooling protocols: slow cooling (SC) at 32°C/min and extremely-slow cooling (XSC) at 2°C/min. The residual thermal stresses were determined using the Vickers indentation method and validated by finite element analysis. The residual stress profiles were similar among geometries in the same cooling protocol. XSC groups presented significantly higher tensile stresses (p=0.000), especially for curved interfaces. XSC is a time-consuming process that showed no beneficial effect regarding residual stresses compared to the manufacturer recommended slow cooling rate.

Some Differential Geometric Relations in the Elastic Shell

The theory of the elastic shells is one of the most important parts of the theory of solid mechanics. The elastic shell can be described with its middle surface; that is, the three-dimensional elastic shell with equal thickness comprises a series of overlying surfaces like middle surface. In this paper, the differential geometric relations between elastic shell and its middle surface are provided under the curvilinear coordinate systems, which are very important for forming two-dimensional linear and nonlinear elastic shell models. Concretely, the metric tensors, the determinant of metric matrix field, the Christoffel symbols, and Riemann tensors on the three-dimensional elasticity are expressed by those on the two-dimensional middle surface, which are featured by the asymptotic expressions with respect to the variable in the direction of thickness of the shell. Thus, the novelty of this work is that we can further split three-dimensional mechanics equations into two-dimensional variation problems. Finally, two kinds of special shells, hemispherical shell and semicylindrical shell, are provided as the examples.

Piezoelectric energy harvester operated by noncontact mechanical frequency up-conversion using shell cantilever structure

In this study, we propose and demonstrate a piezoelectric energy harvester with a shell cantilever for mechanical frequency up-conversion to generate electric power in a low-frequency vibration environment. The proposed device is composed of a clamped semicylindrical shell cantilever as a driving beam and a piezoelectric cantilever attached to the proof mass of the shell cantilever as a generating beam. The shell cantilever bends downward when the external acceleration is over the threshold value for buckling transition. When the acceleration direction is reversed, the shell cantilever makes abrupt stop at its initial position, inducing impact-like force on the generating beam and resulting in free vibration at high resonance frequencies. Experimental results show that a maximum power of 101 µW at 20 Hz can be obtained.

Hierarchically structured polymer blends based on silsesquioxane hybrid nanocomposites with quaternary ammonium units for antimicrobial coatings

Abstract The paper reports the first study on hierarchical assemblies (nanofibrillar micelles confined within semi-cylindrical shells) with silsesquioxane and quaternary ammonium units obtained through polymer blending intended for antimicrobial/antifungal stone coatings. The formation of hierarchical structures on solid surfaces is due to the multiple intermolecular ionic interactions, intermolecular Van der Waals and hydrophobic interactions acting among the component molecules. Their antimicrobial/antifungal properties toward the Gram-negative bacteria, Escherichia coli, Gram-positive bacteria, Staphylococcus aureus, and Candida albicans fungus were determined in aqueous solution and were found to be strongly dependent of the topographical features of the coating.

Curvature Condensation and Bifurcation in an Elastic Shell

We study the formation and evolution of localized geometrical defects in an indented cylindrical elastic shell using a combination of experiment and numerical simulation. We find that as a symmetric localized indentation on a semicylindrical shell increases, there is a transition from a global mode of deformation to a localized one which leads to the condensation of curvature along a symmetric parabolic defect. This process introduces a soft mode in the system, converting a load-bearing structure into a hinged, kinematic mechanism. Further indentation leads to twinning wherein the parabolic defect bifurcates into two defects that move apart on either side of the line of symmetry. A qualitative theory captures the main features of the phenomena but leads to further questions about the mechanism of defect nucleation.