Circular Shells Research Articles

Nonlinear vibro-acoustic analysis of an axially moving submerged circular cylindrical shell

In this study, the nonlinear vibro-acoustic dynamics and stability of doubly-clamped axially moving cylindrical shell are investigated. The exterior surface of the shell is in contact with fluid and subjected to oblique incident plane sound wave. Donnell’s nonlinear shallow shell theory is used to derive the nonlinear partial differential equation of the cylindrical shell for the radial motion. The Galerkin method is employed to discretize the equations of motion into the set of coupled nonlinear nonhomogeneous ordinary second order differential equations. Considering both driven and companion modes, Multiple Scales Method is used to obtain the response of the system. The effects of sound level, incident angle and axially velocity on the frequency response of the system are studied. The results show that, with increase in the shell velocity transmission loss of the circular shell increases. In addition, at low shell axial velocities simultaneous excitation of the driven and companion modes occurs.

Numerical and Experimental Validation for Connecting Nature with Architecture by Mimicking Cranium into a Shell Roof

This study focuses on a structural element bio-mimicked from the human cranium (HC) into a shell element. As the HC is effective in resisting intracranial pressure developed by the brain, a water tank was considered to use a bio-mimicked shape of a shell as a roof. An optimized numerical model was validated experimentally and compared with a conventional specimen. The structural behavior of the bio-mimicked specimen is similar and performs more efficiently than the conventional specimen in capacity ratio, crack formation, and load-carrying capacity. Methodology followed: A Computed Tomography (CT) scan of the HC was obtained in Digital Imaging and Communications in Medicine (DICOM) format for finite element analysis (FEA). From the geometric parameters of the HC, the radius of the curvature-to-thickness ratio was derived for the shell. The span and thickness of the shell under two criteria were considered. The spherical and circular shell behaviors were found to be similar to those of the HC, whereas the elliptical shell behavior was not. We studied the shape effect of the HC with the conventional slab and found that the HC shape has an impact on the behavior and is the most efficient. A bio-mimicked mono column was considered as a supporting column for the water tank and analyzed. Overall, adopting this bio-mimicking of the HC into the shell roof connects nature with sustainable architecture.

Stable Isotope Analysis and Chronology Building at the Hokfv-Mocvse Cultural Site, the Earliest Evidence for South Atlantic Shell-Ring Villages

Abstract Circular shell rings along the South Atlantic coast of the United States are vestiges of the earliest sedentary villages in North America, dating to 4500–3000 BP. However, little is known about when Indigenous communities began constructing these shell-ring villages. This article presents data from the Hokfv-Mocvse Shell Ring on Ossabaw Island, Georgia. Although shell rings are often associated with the earliest ceramics in North America, no ceramics were encountered in our excavations at Hokfv-Mocvse, and the only materials recovered were projectile points similar to points found over 300 km inland. Bayesian modeling of radiocarbon dates indicates that the ring was occupied between 5090 and 4735 cal BP (95% confidence), making it the earliest dated shell ring in the region. Additionally, shell geochemistry and oyster paleobiology data suggest that inhabitants were living at the ring year-round and had established institutions at that time to manage oyster fisheries sustainably. Hokfv-Mocvse therefore provides evidence for Indigenous people settling in year-round villages and adapting to coastal environments in the region centuries before the adoption of pottery. The establishment of villages marks a visible archaeological shift toward settling down and occupying island ecosystems on a more permanent basis and in larger numbers than ever before in the region.

Analytical Study on the Buckling of Cylindrical Shells With Circumferential Thickness Variation Under Varying External Pressure

Abstract In this article, the analytical buckling load coefficient formula for a cylinder with circumferential thickness variation subjected to varying external pressure is established for the first time by developing a quadratic perturbation method. Based on the presented formula, some specific examples that consider either circumferential shell thickness variation or varying lateral pressure are studied and compared with those in the published literature. First, classical cosine thickness variation is analyzed. The computed results of buckling load coefficients indicate that most of differences between the proposed formula and finite element (FE) analyses in previous literature are less than 5%. Second, wind-type pressure load is discussed, and the maximum difference of predicted buckling load coefficients between our formula and results in published article is 2.3%. Third, both circumferential thickness variation and linear liquid pressure are analyzed by the proposed analytical formula and validated by the Galerkin method when both thickness and load variations are small. Therefore, accuracy and reliability of the established formula are validated. For the purpose of engineering application, buckling of a circular shell with local circumferential thickness variation due to weld shrinkage under wind-type pressure is analytically investigated. The effects of thickness variation amplitude, load parameter, half angle of thickness variation, and shell dimensions on buckling load coefficients are studied in detail.

A hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress: II. An isogeometric discretization method for incompressible materials

This is Part II of a multipart article on a hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress. We introduce an isogeometric discretization method for incompressible materials and present test computations. Accounting for the out-of-plane normal stress distribution in the out-of-plane direction affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the shell. The return is more than what we get from accounting for the out-of-plane deformation mapping. The traction acting on the shell can be specified on the upper and lower surfaces separately. With that, the model is now free from the “midsurface’ location in terms of specifying the traction. In dealing with incompressible materials, we start with an augmented formulation that includes the pressure as a Lagrange multiplier and then eliminate it by using the geometrical representation of the incompressibility constraint. The resulting model is an extended one, in the Kirchhoff–Love category in the degree-of-freedom count, and encompassing all other extensions in the isogeometric subcategory. We include ordered details as a recipe for making the implementation practical. The implementation has two components that will not be obvious but might be critical in boundary integration. The first one is related to the edge-surface moment created by the Kirchhoff–Love assumption. The second one is related to the pressure/traction integrations over all the surfaces of the finite-thickness geometry. The test computations are for dome-shaped inflation of a flat circular shell, rolling of a rectangular plate, pinching of a cylindrical shell, and uniform hydrostatic pressurization of the pinched cylindrical shell. We compute with neo-Hookean and Mooney–Rivlin material models. To understand the effect of the terms added in the extended model, we compare with models that exclude some of those terms.

Wind-structure interaction mechanism of circular storage shells- a critical review

A critical review on the valuable researches about the aerodynamic load and consequent structural behavior of cylindrical storage shells, has been carried out. The wind-shell interaction mechanism has been explored through literatures to understand aerodynamic pressure characteristics, wind-induced vibration, buckling and design of cylindrical storage shell and stiffener. Important input parameters have been presented in a tabulated manner so as to correlate and compare critical output parameters (graphically) with an emphasis on circumferential wind pressure coefficient and radial deflection per unit thickness under wind-induced buckling. The scopes for future studies in this field of research have also been recommended.

Enhancing thermal performance in shell-and-tube latent heat thermal energy storage units: An experimental and numerical study of shell geometry effects

This study investigates the influence of shell geometry on the thermal performance of latent heat storage (LHS) units. Three transparent shell-and-tube LHS units, featuring circular, horizontal, and vertical obround shell geometries, each possessing a similar shell volume, were fabricated and filled with paraffin as the phase change material (PCM). Employing a combination of visualization experiments and numerical simulations, the thermal performance of LHS units with horizontally and vertically oriented obround shell geometries was comprehensively analyzed and compared with conventional circular shell-and-tube heat exchangers (HX), commonly utilized in the industry. Data derived from image processing of photographs, coupled with recorded temperatures, were used to calculate liquid fractions, analyze heat transfer characteristics, and ascertain the dominant heat transfer mechanisms during the melting process. The results reveal that the utilization of a horizontal obround shell enhances the heat transfer rate, thereby expediting the melting process. A comparative analysis of melting photographs demonstrates that the horizontal obround shell reduces the melting time by 32% compared to the circular shell, while the vertical obround shell extends the total melting time by 13%. In contrast to the circular shell, the horizontal obround shell exhibits a substantial improvement of 41% in the time-averaged heat transfer rate, whereas the vertical obround shell shows a decrease of 12%.

Study on Carrying Capacity of Square shell and Parameter analysis

Square shell is one structural type which is quite common to be seen in engineering. This paper focuses on the carrying capacity of square shell, and studies the influence of round radius and shell thickness on the ratio of mass to external volume and load factor under linear buckleing of shell. Numerical results show that, With the increase of round radius, the ratio will first decrease, then increase and approach that of circular shell, while the load factor will also increase. With the increase of shell thickness, the ration of shell will increase and the load factor will rapidly increase. This will help to better design of pressure hull of submarines.

Mechanical response of a novel square dome shell with bistable behavior: Improved analytical method and empirical model

In this study, a novel square dome-shaped shell with a fascinating bistable behavior is proposed, which is able to quickly switch to a new stable configuration within its elastic range under a certain load, due to its elastic instability. Compared to most circular shells currently studied, it is easier to arrange multiple structures in three-dimensional space to obtain multistable responses. Numerical and experimental methods were adopted for the study of the mechanical response of the square shell, and main influence parameters were also investigated. In addition, an improved piecewise fitting method is introduced to establish an empirical formula for predicting the mechanical response of bistable shells, which can be used to guide the design of bistable shells. Finally, two types of metamaterials, uniaxial compressible metamaterials and triaxial compressible metamaterials, are successfully designed according to the above theory, the typical behaviors of which are studied via simulations. This novel structure presented in this paper has broad application prospects in the fields of energy absorption and programmable deformation structures.

Nonlinear forced vibrations of functionally graded three-phase composite cylindrical shell subjected to aerodynamic forces, external excitations and hygrothermal environment

In this paper, the new functionally graded three-phase composite cylindrical shell is assumed as a common structure in the carrier rocket in the future, and we creatively study the nonlinear forced vibration of this cylindrical shell considering the interaction of different factors in the complex operating environment, including the aerodynamic forces, external excitations, and hygrothermal environment. Based on the first-order shear deformation theory, Von-Karman geometric nonlinear theory, and Hamilton's principle, we derive the nonlinear partial differential equations of motion of the functionally graded three-phase composite cylindrical shell. Considering the axisymmetry of the perfect circular shell, there is a 1:1 internal resonance between the conjugate modes of this cylindrical shell. On this basis, the nonlinear forced vibration of the cylindrical shell is investigated by a combination of Galerkin's method and the pseudo-arc length continuation method. Matcont toolbox can directly solve the ordinary differential equations to obtain the nonlinear frequency response curves. The method can effectively obtain both stable and unstable solutions, avoiding the mathematical difficulties encountered in the formulation process, and facilitating the study of the effects of parametric variables on the resonance response in complex environments. The results show that the variation of material parameters and the complex environment have important effects on the nonlinear resonance response of functionally graded three-phase composite cylindrical shell.

Implicit differentiation-based reliability analysis for shallow shell structures with the Boundary Element Method

A novel methodology for evaluating the response sensitivities of shallow shell structures using the Boundary Element Method (BEM) is presented in this work. The implicit derivatives of the BEM formulations for shallow shell structures, with respect to the geometrical variables, such as curvature and thickness, have been derived for the first time and incorporated into an Implicit Differentiation Method (IDM). The IDM is employed in conjunction with the First Order Reliability Method (FORM) to evaluate the reliability of shallow shell structures. The accuracy of the IDM formulation is first validated against an analytical solution, with results showing a maximum difference of only 2.61%. The IDM was later validated against the Finite Difference Method (FDM), with results showing a maximum difference of only 0.11%. The IDM was also found to be significantly more efficient than the FDM, requiring 35% less CPU time when calculating sensitivities. This is further compounded by the fact that, unlike the FDM, the IDM does not require a step size. A numerical example featuring a circular shallow shell is used to demonstrate the application of the IDM-based FORM for assessing structural reliability. The uncertainty in curvature is set as a variable for the purpose of investigating its impact on reliability. The results of the reliability index obtained from the IDM-FORM are compared to the results obtained from FDM-FORM and were found to be very similar. An analysis of sensitivity is conducted to identify the most significant variables affecting reliability. It is found that uncertainties in curvature, thickness, and applied pressure distribution parameters have the largest impact on structural reliability. To demonstrate how the IDM could be used in practice, it was employed as gradient-based optimisation procedure featuring shallow-shell structures. The IDM was found to be a very efficient and accurate alternative to existing methods for calculating structural response sensitivities.

Postbuckling Characteristics of Angle-Ply Laminated Joined Conical-Cylindrical-Conical Circular Shells

The postbuckling behaviour of angle-ply composite laminated joined circular conical-cylindrical- conical shells, subjected to external pressure, torsion, axial compression and thermal loading, is studied considering the variation of stiffness coefficients along the meridional direction in the conical sections. The analysis is carried out using the semi-analytical finite element method based on first-order shear deformation theory. The nonlinear governing equations are solved using Newton-Raphson iterative technique coupled with the displacement control method. An asymmetric perturbation in the form of a small magnitude load spatially proportional to the linear buckling mode shape is considered. The effect of semi-cone angle and number of circumferential waves on the prebuckling/postbuckling response of angle-ply laminated joined circular conical-cylindrical-conical shells is investigated. The effect of inclusion of rotation about normal to the middle surface in the strain-displacement relations is also studied

Thermal Postbuckling Characteristics Of Angle-ply Laminated Truncated Circular Conical Shells

Here, the nonlinear thermoelastic pre- and post-buckling characteristics of angle-ply laminated composite conical shells subjected to uniform temperature rise are studied using semi-analytical finite element approach. The finite element formulation is based on first-order shear deformation theory and field consistency principle. The nonlinear governing equations, considering geometric nonlinearity based on von Karman’s assumption for moderately large deformation, are solved using Newton-Raphson iteration procedure coupled with displace- ment control method to trace the prebuckling followed by postbuckling equilibrium path. The presence of asymmetric perturbation in the form of small magnitude load spatially proportional to the linear buckling mode shape is assumed to initiate the bifurcation of the shell deformation. The study is carried out to highlight the influences of semi-cone angle, ply-angles, number of layers and number of circumferential waves on the nonlinear prebuckling/postbuckling thermoelastic response of the laminated circular conical shells. The participation of axisymmetric and asymmetric modes in the total response of the shells is brought out through the deformation shape analysis.

Postbuckling of Laminated Composite Circular Conical Shells Under Combined Thermo-Mechanical Loads

In this paper, the postbuckling characteristics of cross- and angle-ply laminated composite conical shells subjected to combined thermo-mechanical loading are studied using shear deformable semi-analytical finite element. The nonlinear governing equations, considering geometric nonlinearity based on Sanders type of kinematic approximations, are solved using Newton-Raphson iteration procedure coupled with adaptive displacement control method to trace the postbuckling equilibrium path. It is brought out from the study that the inward displacement in the postbuckling region is significantly higher as compared to the outward one. The ratio of the lowest load in the postbuckling path and the bifurcation load increases with the increase in the pressure loading proportion and decreases with the increase in the axial loading proportions. The relative load carrying capacity of shells under different set of loading combinations changes with the increase in the maximum postbuckling displacement. It is also observed that the nonlinearity in the load interaction relation corresponding to lowest load in the postbuckling path is less compared to that for bifurcation load.

Prying model and mechanism for circular all-FRP flange integrally formed with tube

This paper focuses on prying action of integrally-formed circular all-FRP flanges intended for assembly of FRP members. The connection is manufactured by prepreg hand-work layup and compression moulding process. Tensile tests have been performed on three connections of different flange thickness (2.2 mm, 3.0 mm, 3.8 mm). The influences of flange thickness and bolt preloads on prying force have been investigated. Corresponding displacements and strains on tube and flange plate were also analyzed. Then, an analytical model for prying force as well as displacement, strain and stress fields is developed based on the lamination theory of circular shells and plates and the compatibility equations. Quite good agreement is obtained when predicting prying effect factor and fairly good agreement is achieved for flange separation and strains. The experimental and theoretical results indicate that prying force has negative correlation with flange thickness when flange is thick enough, but contrary when flange is very thin. Further theoretical analysis shows that reducing bolt stiffness by BFRP bolts will significantly reduce prying force, by the maximum 39.06% for the connection with 23 mm-thick flange.

STRESS-DEFORMED STATE OF VERTICAL CILINDRICAL METAL SHELL UNDER TEMPERATURE CLIMATE IMPACT

Vertical cylindrical containers are widely used for storage of granular bulk materials. The enclosing side surface of such containers is made in the form of cylindrical metal circular shells with a wall thickness that is constant or piecewise constant along the height of the shell. Known designs for storage of bulk materials of the reservoir type with the installation of a cylindrical shell on the annular foundation with hinged fixed attachment of the shell to the foundation. Thin-walled shells are made suspended from the supporting structures of the storage facilities. To stabilize the cylindrical shape of the shell and its position in space, the suspended shells are pre-tensioned in the vertical direction. During operation, storage facilities are empty and filled with bulk materials, exposed to the environment in the form of wind and temperature climatic influences. The object of study of this work is the enclosing structures of storages of granular bulk materials in the form of vertical circular cylindrical thin-walled metal shells, in the general case of piecewise constant thickness, subject to temperature and climatic influences of the environment ‒ changes in the temperature of the outside air, direct and diffuse solar radiation. The subject of the study is the components of the stress-strain state of the shell due to changes in temperature and climatic influences. The performed studies of the temperature fields of storage shells on models and full-scale objects made it possible to substantiate the assignment of the temperature field of cylindrical storage shells by Fourier series. One-sided solar heating of cylindrical storage shells completely illuminated by the sun induces in the shell wall a flat temperature field symmetrical with respect to the normal of incidence of sunlight, which can be represented by a Fourier series with five terms of the cosine expansion series. In the presence of a structure located next to the shell, which covers half of the shell along the entire height in the circumferential direction, the temperature field is described by a Fourier series containing 10 harmonics of expansion in sines and cosines. The small thickness of the shell, the significant radius of curvature of the shells, the large thermal diffusivity of metals provides a small variability of the temperature of the shell over the thickness, the ability to describe the stress-strain state of the shell, the momentless theory and a simple edge effect. Formulas are obtained in Fourier series for the forces of a momentless state, the residuals of which at the joints of shell chords of different thicknesses and in the support zones are eliminated by a simple edge effect.

Buckling Analysis of Thin-Walled Circular Shells under Local Axial Compression using Vector Form Intrinsic Finite Element Method

The buckling failure of thin-walled circular shells under local axial compression is common in engineering. This study uses the vector form intrinsic finite element (VFIFE) method to investigate the buckling behavior of thin-walled circular shells under local axial compression by introducing a multilinear hardening model, taking into account geometric and material nonlinearity. A buckling analysis program based on the VFIFE method was developed and verified by comparison with experimental results. The buckling mode and postbuckling behavior of thin-walled circular shells were studied by using the verified program. The results show that the VFIFE method with a multilinear hardening model can accurately calculate the buckling load of local axially compressed thin-walled circular shells, and effectively simulate the buckling development process, which offers great advantages in predicting the postbuckling of structures.

Numerical investigation of hydraulic instability of circular arc shell-type fuel elements under axial flow conditions

Shell-type fuel elements in nuclear assemblies can collapse under high-speed coolant flows and impede channels, which is known as hydraulic instability. Stiffer than flat plates, curved shells are commonly in involute shape and circular arc shape. In this study, two parallel circular arc shells with three channels are numerically simulated for hydraulic instability prediction. Fluid-structure interaction between shells and fluid is achieved, and results show that the two arc shells are asymmetrically deformed in opposite directions. A “valley morph” pops near the leading edge at a channel velocity and becomes increasingly visible as the flow rate rises. The maximum deflection occurs at the leading edge, which is linearly related to the squared channel velocity below a value but nonlinearly steeply ascends otherwise. The two characteristic velocities are congruent and thus can be deemed as the “critical velocity” at which the response of fuel elements changes although shells remain elastic all through. The derived critical velocity is about 80% of Miller’s theoretical estimate.

The bright supernova 1996cr in the circinus galaxy imaged with VLBI: shell structure with complex evolution

ABSTRACTWe present broad-band radio flux-density measurements supernova (SN) 1996cr, made with MeerKAT, ATCA, and ALMA, and images made from very long baseline interferometry (VLBI) observations with the Australian Long Baseline Array. The spectral energy distribution of SN 1996cr in 2020, at age t ∼8700 d, is a power-law, with flux density, S ∝ ν−0.588 ± 0.011 between 1 and 34 GHz, but may steepen at >35 GHz. The spectrum has flattened since t = 5370 d (2010). Also since t = 5370 d, the flux density has declined rapidly, with $S_{\rm 9 \, GHz} \propto t^{-2.9}$. The VLBI image at t = 8859 d shows an approximately circular structure with a central minimum reminiscent of an optically-thin spherical shell of emission. For a distance of 3.7 Mpc, the average outer radius of the radio emission at t = 8859 d was (5.1 ± 0.3) × 1017 cm, and SN 1996cr has been expanding with a velocity of 4650 ± 1060 km s−1 between t = 4307 and 8859 d. It must have undergone considerable deceleration before t = 4307 d. Deviations from a circular shell structure in the image suggest a range of velocities up to ∼7000 km s−1, and hint at the presence of a ring- or equatorial-belt-like structure rather than a complete spherical shell.

The Buckling Load of Cylindrical Shells Under Axial Compression Depends on the Cross-Sectional Curvature

It is known that the famous theoretical formula by Koiter for the critical buckling load of circular cylindrical shells under axial compression does not coincide with the experimental data. Namely, while Koiter’s formula predicts linear dependence of the buckling load $$\lambda (h)$$ of the shell thickness h ( $$h>0$$ is a small parameter), one observes the dependence $$\lambda (h)\sim h^{3/2}$$ in experiments; i.e., the shell buckles at much smaller loads for small thickness. This theoretical prediction failure is believed to be caused by the so-called sensitivity to imperfections phenomenon (both, shape and load). Grabovsky and the first author have rigorously proven in (J Nonlinear Sci 26(1):83–119, 2016) , that in the problem of circular cylindrical shells buckling under axial compression, a small load twist leads to the buckling load scaling $$\lambda (h)\sim h^{5/4},$$ while shape imperfections are likely to result in the scaling $$\lambda (h)\sim h^{3/2}.$$ In this work, we prove that in fact the buckling load $$\lambda (h)$$ of cylindrical (not necessarily circular) shells under vertical compression depends on the curvature of the cross section curve. When the cross section is a convex curve with uniformly positive curvature, then $$\lambda (h)\sim h,$$ and when the cross-sectional curve has positive curvature except at finitely many points, then $$C_1h^{8/5}\le \lambda (h)\le C_2h^{3/2}$$ for h small thickness $$h>0.$$