Hemispherical Shell Research Articles

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.

Thermoelastic damping properties in hemi-ellipsoidal shells with variable thickness

Thermoelastic damping (TED) is a fundamental dissipation mechanism that inevitably exists in shell resonators with high quality factors. Based on the thermal energy method, this paper demonstrates an effective method for the TED characterization of the hemi-ellipsoidal shells with variable thickness which manifest lower TED compared with the hemispherical shells. The equation of motion of the hemi-ellipsoidal shell under clamped-free boundary conditions is established by Hamilton's principle and the assumed mode method, and the natural frequencies and mode shape functions of the hemi-ellipsoidal shell with variable thickness are obtained by solving the eigenvalue problem. The temperature field is acquired by solving the heat conduction equation along the radial direction, and an analytical model for the TED of the hemi-ellipsoidal shell with variable thickness is presented by calculating the maximum elastic potential energy and the work lost per cycle of vibration due to irreversible heat conduction. Analysis on TED at the vibration patterns of meridional wave number m = 1 and the circumferential wave number n = 2 or 3 where the shell resonators typically operate is carried out. The analytically calculated TED results are compared with those of the finite element method (FEM) to verify the feasibility and correctness of the present method. The influences of the geometrical parameters on the TED characteristics of the hemi-ellipsoidal shells with variable thickness are analyzed in detail. A meaningful discovery is that compared with the hemispherical shell, the hemi-ellipsoidal shell with variable thickness has a smaller TED when its semiminor axis is shorter than the semimajor axis, which is particularly significant for optimizing the design of the shell resonators with high quality factors.

Semi-analytical vibration modeling of complex axisymmetric shells using shifted Legendre series

This paper presents a semi-analytical approach based on the shifted Legendre series for vibration modeling of complex axisymmetric shells. This method divides the structure along its generator into complex axisymmetric shells comprised solely of conical and spherical shell segments. A global cylindrical coordinate system is established to unify the coordinate system of complex axisymmetric shells. Coupling between segments and the simulation of arbitrary boundary conditions are achieved using artificial spring technology. Based on the first-order shear deformation theory (FSDT), the energy functional of each segment is derived. The circumferential displacement is expanded using Fourier series, while the meridional displacement is expanded using the shifted Legendre series at shifted Gauss-Lobatto nodes. Utilizing the inner product matrix and differential matrix of the shifted Legendre series, the integration and differentiation processes in the vibration characteristic equation are simplified into a product form, significantly enhancing computational efficiency. Through convergence analysis and comparison of the computational results of the present method with numerical simulation results, experimental results and literature results demonstrate the advantages of high convergence, high accuracy and fast solution speed of this solution method. On this basis, the vibration characteristics of ring-stiffened double-layer hemispherical shells are investigated. The results demonstrate the great applicability of this method for vibration modeling of complex axisymmetric shells in engineering.

Wrinkling suppression in cryogenic forming of high-strength Al-alloy ultra-thin shells by controlling interface shear stress

Avoiding wrinkling defects is extremely difficult in the sheet metal forming of ultra-thin components made from high-strength aluminum alloys. A novel cryogenic forming is thus proposed for solving this very challenging problem, wherein a thicker cladding blank is stacked above the thinner target blank to establish interface shear stress for reducing the hoop compressive stress, so that the critical wrinkling stress is increased. The enlarged radial deformation is transferred and withstood by the increasing hardening and ductility at cryogenic temperatures. The wrinkling suppression mechanism is revealed through mechanical and numerical analyses. Systematic experiments were conducted for studying the feasibility of high-strength AA7075 in cryogenic forming with different stacking sequences of cladding and target blanks, cladding blanks including three material strength levels (AA1060-O, AA5052-O, and SUS-304), two thicknesses (3.0, and 2.0 mm), and blank-holder forces. The effects of the cladding blank and blank-holder forces were clarified as reflected by forming defects, thickness, and strain distributions. The mechanical and numerical analyses can indicate that contact pressure can be produced by the wrinkling tendency of thinner target blank and limitation of cladding blank to wrinkling, which is accompanied by a decrease in the hoop compressive stress and increase in the critical wrinkling stress. Therefore, applying a relatively thicker blank on the punch side can prevent the wrinkling of ultra-thin components. The wrinkling tendency decreases with increasing strength and thickness of the cladding blank, which results in an increase in deformation or even splitting, which can be solved by the cryogenic temperature. The thickness of the cladding blank can be reduced by increasing the blank-holder force, which further reduces the material cost. AA5052-O, which has a strength similar to that of the target blank, is more suitable as a cladding blank for AA7075-W because the balance preventing wrinkling, improving thickness uniformity, and controlling the forming force. A Φ200 mm hemispherical shell with an initial thickness of 0.3 mm was formed successfully, and the corresponding thickness-to-diameter ratio reached 0.8‰, which almost increased one time on the basis of direct cryogenic forming. This new approach can be used for fabricating ultra-thin components from high-strength aluminum alloys.

Low-frequency noise attenuation through hybrid perforated hemispherical shells and membrane-type acoustic metamaterial

We propose a novel hybrid acoustic metamaterial that can achieve broadband sound insulation below 452 Hz and almost perfect sound absorption at 864 Hz. The metastructure was fabricated using additive manufacturing. Finite element method simulations were used to study the acoustic properties of the fabricated metamaterials. An equivalent electrical circuit was built using an electro-acoustic analogy to evaluate the sound absorption coefficient. The unique design of this meta-structure possesses two resonant frequencies. Low-frequency sound insulation is found due to the effective negative density at frequencies lower than the cutoff frequency of the elastic membrane. In contrast, a negative effective bulk modulus is the reason behind the broadband sound absorption. The theoretical and simulation results were validated through experiments. Experiments carried out showed an overall average sound transmission loss of 26.31 dB between 50 and 1600 Hz and 24.72 dB in the low-frequency zone (<400 Hz). Furthermore, over 69% of the sound intensity is absorbed in the 500–1000 Hz frequency range. The designed meta-structure exhibits broadband effective negative density below 452 Hz and effective negative bulk modulus from 864 to 1220 Hz. The design specifies a sample thickness of 3.8 cm, corresponding to a subwavelength thickness of approximately λ/10. As a result, the developed meta-structure can potentially be employed for sound insulation and absorption at low frequencies in the aerospace and automotive industries and in-room acoustic applications.

Investigating the impact of cross-sectional area on the crushing characteristics of axially-loaded hemispherical composite shells

The research focus has shifted towards lightweight structures with high energy absorption capabilities due to advancements in automotive safety technology. This study specifically investigates the impact of cross-sectional area on the energy absorption characteristics of hemispherical composite shells. The experimental phase involves characterizing a glass fiber epoxy composite, followed by the manufacture of hemispherical composite shell specimens with varying cross-sectional areas. These specimens undergo quasi-static axial compressive loading, and the energy absorption parameters are analyzed. The results indicate a significant influence of the composite cross-sectional area on the crushing behavior of hemispherical shells, with a observed decrease in specific energy absorption as the cross-sectional area increases. Additionally, a 3D Finite Element (FE) model is created using ABAQUS FE code to numerically simulate the crushing process. The model’s predictions are compared and validated against experimentally measured values, demonstrating a satisfactory correlation.

Study of Ceramic Hollow Buoyant Balls Prepared Based on Slip Mold Casting and Brazing Process

In the domain of deep-sea buoyancy material applications, hollow ceramic spheres, known for their high strength and low mass-to-drainage ratio, contribute to increased buoyancy and payload capacity enhancement for deep submersibles, constituting buoyancy materials of exceptional overall performance. This study entails the brazing of two ceramic hemispherical shells, obtained through slurry molding, to form a ceramic float. This process, which integrates slurry molding and ceramic brazing, facilitates buoyancy provision. Further refinement involves welding a ceramic connector onto the ceramic shell, incorporating a top opening to create a ceramic float equipped with an observation window seat. The ceramic float maintains uniform wall thickness, while the observation window facilitates external environmental observation in deep-sea research. Two pressure-resistant spherical shells, produced using this process, underwent testing, revealing the wall thickness of the prepared alumina ceramic hollow spheres to be 1.00 mm, with a mass-to-drainage ratio of 0.47 g/cm3 and a buoyancy coefficient of 53%. The resultant ceramic hollow floating ball can withstand hydrostatic pressure of 120 MPa, while the pressure-resistant ball shell with an observation window seat can endure hydrostatic pressure of 100 MPa, ensuring safe operation at depths of 5000–6000 m. This process provides a production method for subsequent large-scale ceramic float manufacturing for the transportation of objects or personnel.

Tactile Sensing and Grasping Through Thin‐Shell Buckling

Soft and lightweight grippers have greatly enhanced the performance of robotic manipulators in handling complex objects with varying shape, texture, and stiffness. However, the combination of universal grasping with passive sensing capabilities still presents challenges. To overcome this limitation, a fluidic soft gripper is introduced based on the buckling of soft, thin hemispherical shells. Leveraging a single fluidic pressure input, the soft gripper can grasp slippery and delicate objects while passively providing information on this physical interaction. Guided by analytical, numerical, and experimental tools, the novel grasping principle of this mechanics‐based soft gripper is explored. First, the buckling behavior of a free hemisphere is characterized as a function of its geometric parameters. Inspired by the free hemisphere's two‐lobe mode shape ideal for grasping purposes, it is demonstrated that the gripper can perform dexterous manipulation and gentle gripping of fragile objects in confined spaces and underwater environments. Last, the soft gripper's embedded capability of detecting contact, grasping, and release conditions during the interaction with an unknown object is proved. This simple buckling‐based soft gripper opens new avenues for the design of adaptive gripper morphologies with tactile sensing capabilities for applications ranging from medical and agricultural robotics to space and underwater exploration.

Dynamic modeling and vibration suppression evaluation of composite honeycomb hemispherical shell with functional gradient protective coating

The vibration reduction performance of composite honeycomb hemispherical shells (CHHSs) coated with functional gradient protection coating (FGPC) are investigated in this work. Using the first-order shear deformation theory and the power-law distribution rule, the virtual spring technique, the regional decomposition method, and the Newmark-Beta approach, etc., a dynamic model of the FGPCCHHSs under base excitation is formulated to solve the inherent characteristics and displacement responses in time and frequency domains. After a set of convergence analyses are completed to ascertain an appropriate segment number and the stiffness values of virtual springs employed in the predictive model, the forecasted vibration parameters are verified using the literature and experimental results that are performed on uncoated and coated shells. The maximal natural frequency errors of the current model compared to the experimental results are 3.8% and 4.8%, and the displacement response errors under different excitation amplitudes are less than 10.3% and 12.7%, respectively, which demonstrate the correctness of such a model. Finally, the impact of key structural and material parameters on the vibration behaviors of the FPGCCHHSs is evaluated. To improve their vibration suppression capability, it is recommended to choose a high gradient index of coating material and a large thickness ratio of the FGPC to the overall shell with a reasonable moduli ratio of Material A to Material B of the FGPC to improve vibration reduction capability. This study offers a practical model tool and several important design recommendations for vibration prediction and dynamic attenuation of honeycomb sandwich hemispherical shell structures in aerospace engineering.

Frequency mismatch analysis of hemispherical shell resonators with both radius and thickness imperfections

The hemispherical shell resonator (HSR) is the core element of the hemispherical resonator gyroscope (HRG), and its frequency mismatch is a key property influencing gyroscope accuracy. Investigating the mechanism of frequency mismatch is vital for improving the quality of HSRs and performance of HRGs. Midsurface radius imperfections and thickness imperfections are two principal causes of frequency mismatch, but their combined effects have rarely been discussed. This paper develops a model to comprehensively analyze the frequency mismatch of HSRs with both radius and thickness imperfections. The model derives a quantitative relation between the frequency mismatch and the two imperfections, and provides principles for evaluating dominant imperfections. To validate the model, we conduct experiments on a batch of 12 HSRs with random geometric imperfections. We apply the model in calculating the theoretical frequency mismatches of these HSRs, and the results agree well with the experimental data. The experiment also confirms that for macro-HSRs, thickness imperfections have a larger impact than radius imperfections, and the frequency mismatch is approximately linear to the fourth thickness harmonic. Our research can be a useful reference for the design and fabrication of HSRs and may open new possibilities for high-precision manufacture of HRGs.

Vibrations and thermoelastic quality factors of hemispherical shells with fillets

In engineering applications, hemispherical shell resonators are typically machined with fillets to reduce stress concentration and enhance structure strength. The fillets will inevitably affect the dynamic properties and the mechanical quality factor of hemispherical shell resonators, which has been seldom investigated before. In this paper, an effective analytical method is developed to explore the free vibration and thermoelastic damping (TED) characteristics of the hemispherical shell with fillets. The fillets are characterized by the variation in the thickness of the hemispherical shell during modelling. The first-order shear deformation theory (FSDT) is used to describe the theoretical formulas of the hemispherical shell with fillets. By employing the unified Jacobi polynomials and Fourier series as the assumed mode shape functions, the equation of motion of the structure is established by Hamilton's principle and the assumed mode method. The analytical model for thermoelastic quality factor (QTED) which is determined by TED is obtained by computing the dissipated energy and the maximum elastic potential energy of the hemispherical shell with fillets. The validity and accuracy of the present method are confirmed by comparing the present solutions with the published results and those obtained from the finite element method (FEM). The influences of fillets on the vibration behaviors and QTED characteristics of the hemispherical shells are analyzed in detail. The present model can be used to optimize the design of the fillets of the hemispherical shell resonators with high quality factors.

Experimental study of flat-collared hemispherical shells under shock loading

Experimental study of flat-collared hemispherical shells under shock loading

Investigation of the formation mechanism of the pepper starch-piperine complex

In this study, a new carrier for loading piperine was prepared using pepper starch, and its interaction mechanism was investigated. The porous pepper starch-piperine complex (PPS-PIP) showed higher loading efficiency (76.15 %) compared to the porous corn starch-piperine complex (PCS-PIP (52.34 %)). This may be ascribed to the hemispherical shell structure of porous pepper starch (PPS) compared to the porous structure of porous corn starch (PCS) based on the SEM result. PPS-PIP had smaller particle size (10.53 μm), higher relative crystallinity (38.95 %), and better thermal stability (87.45 °C) than PCS-PIP (17.37 μm, 32.17 %, 74.35 °C). Fourier transform infrared spectroscopy (FTIR) results implied that piperine not only forms a complex with amylose but may also be physically present in porous starch. This was demonstrated by the short-range order and X-ray type. Molecular dynamics simulations confirmed that hydrogen bonding is the primary interaction between amylose and piperine. Besides the formation of the amylose-piperine complex, some of the piperine is also present in physical form.

A confocal measurement method for surface profile variations and shell thickness uniformity of hemispherical shell resonator

Here we present a confocal measurement method for the precise measurements of variations in the inner and outer surface profiles (IOSPs) and shell thickness uniformity (STU) of the hemispherical shell resonator (HSR). In this method, the unilateral-shift-subtracting confocal technique is applied to determine the focus of the sensor on the IOSPs of the HSR. The normal tracking technique is employed for measuring the outer surface, while the normal direction of the outer surface serves as the reference for measuring the inner surface, thereby enhancing the accuracy of relative position measurements for the HSR. Furthermore, we applied a trajectory-prediction method to narrow down the scanning range of the confocal sensor, which significantly improved the measurement efficiency. The experimental results showed that the repeated accuracies of the proposed methods are better than 40 nm for IOSP variations measurement and better than 50 nm for HSR STU measurement.

Uncovering the dual role of dimensionless radius in buckling of spherical shells with random geometric imperfections

Localized deformation and randomly shaped imperfections are salient features of buckling-type instabilities in thin-walled load-bearing structures. However, it is generally agreed that their complex interactions in response to mechanical loading are not yet sufficiently understood, as evidenced by buckling-induced catastrophic failures which continue to today. This study investigates how the intimate coupling between localization mechanisms and geometric imperfections combine to determine the statistics of the pressure required to buckle (the illustrative example of) a hemispherical shell. The geometric imperfections, in the form of a surface, are defined by a random field generated over the nominally hemispherical shell geometry, and the probability distribution of the buckling pressure is computed via stochastic finite element analysis. Monte-Carlo simulations are performed for a wide range of the shell's radius to thickness ratio, as well as the correlation length of the spatial distribution of the imperfection. The results show that over this range, the buckling pressure is captured by the Weibull distribution. In addition, the analyses of the deformation patterns observed during the simulations provide insights into the effects of certain characteristic lengths on the local buckling that triggers global instability. In light of the simulation results, a probabilistic model is developed for the statistics of the buckling load that reveals how the dimensionless radius plays a dual role which remained hidden in previous deterministic analyses. The implications of the present model for reliability-based design of shell structures are discussed.

How modular porous metal augments have changed the management of acetabular bone loss at primary or revision total hip arthroplasty.

The advent of modular porous metal augments has ushered in a new form of treatment for acetabular bone loss. The function of an augment can be seen as reducing the size of a defect or reconstituting the anterosuperior/posteroinferior columns and/or allowing supplementary fixation. Depending on the function of the augment, the surgeon can decide on the sequence of introduction of the hemispherical shell, before or after the augment. Augments should always, however, be used with cement to form a unit with the acetabular component. Given their versatility, augments also allow the use of a hemispherical shell in a position that restores the centre of rotation and biomechanics of the hip. Progressive shedding or the appearance of metal debris is a particular finding with augments and, with other radiological signs of failure, should be recognized on serial radiographs. Mid- to long-term outcomes in studies reporting the use of augments with hemispherical shells in revision total hip arthroplasty have shown rates of survival of > 90%. However, a higher risk of failure has been reported when augments have been used for patients with chronic pelvic discontinuity.

Management of acetabular bone loss in revision total hip replacement: a narrative literature review.

Due to growing numbers of primary total hip replacement (THR), the revision THR burden is also increasing. Common indications for revision are osteolysis, infection, instability, and mechanical failure of implants, which can cause acetabular bone loss. Massive acetabular bone defects and pelvic discontinuity are extremely challenging problems. Many techniques have been utilized to address bone loss while maintaining a stable revision THR. Structural allografts, cemented prosthesis, reconstruction cages, and custom triflanged implants have all been used successfully albeit with relatively high complications rates. We have tried to highlight emerging trends to utilize Custom Made Monoflange or Triflange Acetabular Components to reconstruct massive acetabular defects with favourable midterm implant survival, better functional outcomes, relatively lesser complications, and almost similar cost of prosthesis as compared to conventional reconstruction techniques. However, long-term data and study is still recommended to draw a definitive conclusion. In this narrative review article, we searched PubMed and Cochrane for studies on managing acetabular bone loss in revision THR with a focus on recent literature for mid to long-term outcomes and compared results from various studies on different reconstruction methods. Hemispherical cementless acetabular prosthesis with supplemental screws are commonly utilized to manage mild to moderate acetabular bone loss. Recent trends have shown much interest and paradigm shift in patient specific custom triflange acetabular components (CTAC) for reconstructing massive acetabular defects and pelvic discontinuity. Studies have reported high patient satisfaction, improved patient reported daily functioning, high mid-term implant survival, similar complications, and encouraging all cause re-revision rate. However, more prospective and quality studies with larger sample sizes are needed to validate the superiority of CTACs over conventional acetabular implants. There is no consensus regarding the best option for reconstructing massive acetabular defects. Thorough preoperative workup and planning is an absolute requirement for successful revision THR. While most of the moderate acetabular bone loss can be managed with cementless hemispherical acetabular shells with excellent long-term outcomes, reconstructing massive acetabular bone defects in revision THR remains a challenge. Depending on the size and location of the defect, various constucts have demonstrated long-term success as discussed in this review, but complications are not negligible. CTACs provide a treatment for massive bone loss that may be otherwise difficult to achieve anatomic stability with other constructs. Although long-term data is sparse, the cost and complication rate is comparable to other reconstruction methods.

Design of a hemispherical shell shaped natural ventilation temperature observation instrument.

Atmospheric temperature is fundamental information for various industries, such as production, life, and scientific research. The temperature error induced by the solar rays can reach 1 °C or even higher. A hemispherical shell-shaped atmospheric temperature measuring instrument that can reduce heat pollution and increase air velocity was designed. First, the instrument was optimized using computational fluid dynamics (CFD) software packages. Then, the CFD software packages were employed to quantify the temperature errors of the instrument with varying situations. A neural network model was employed to develop a temperature error correction model that can be targeted for multi-variable changes. This model provides accurate correction data when the influencing factors change continuously. Finally, field experiments were performed. The experimental data analysis indicates that the mean temperature error and the maximum error of the instrument before correction are 0.08 and 0.25 °C, respectively. The root mean square error, the mean absolute error, and the correlation coefficient between measured temperature errors from experiments and corrected temperature errors from the correction model are 0.099, 0.016, and 0.952 °C, respectively. By utilizing a temperature error correction model, the measuring error of the instrument can be minimized to a range between -0.05 and 0.04 °C. Consequently, the instrument is anticipated to enhance temperature measurement accuracy to ∼0.1 °C.

Optimization of Hemispherical Shell Resonator Structure Based on Thermoelastic Dissipation

Optimization of Hemispherical Shell Resonator Structure Based on Thermoelastic Dissipation

Sidewall wrinkling suppression in the hydro-mechanical deep drawing for the curved surface shell of titanium/iron composite sheets

As a new type of metal sheet, titanium/iron composite sheets are crucial in various fields. However, in the forming of the curved shells of the titanium/iron composite sheets with small thickness-to-diameter ratios, sidewall wrinkling is extremely easy to form, and it is hard to control. In this paper, an experimental setup for hydro-mechanical deep drawing was designed, and sidewall wrinkling on the hemispherical shell with a flat bottom and 0.47% thickness-to-diameter ratio of titanium/iron composite sheets was effectively suppressed while avoiding splitting. Mechanical and numerical analyses were conducted to reveal the deformation mechanism, and the effect of chamber pressure was studied. The forming defects, thickness, and stress distributions were determined to reflect the deformation behavior. Results show the greater the chamber pressure, the more significant the effect of wrinkling suppression. When the chamber pressure reaches 20 MPa, the sidewall wrinkles disappear. Enough hydraulic pressure can produce a strong backward-bulging effect, which increases the wrinkling suppression pressure and improves plastic deformation instability. Moreover, the stress state of the sidewall changes under the action of hydraulic pressure, thereby changing the in-plane deformation behavior. Thus, the wrinkles already formed in the earlier stage of sidewall formation were adjusted after contact with the punch. The forming process has considerable potential to fabricate thin-shell components.