Deformation Of Shells Research Articles

Vibration characteristics of smart laminated carbon nanotube-reinforced composite cylindrical shells resting on elastic foundations with open circuit

This study analyzes the vibration of smart laminated carbon nanotube (CNT)-reinforced composite cylindrical shells integrated with piezoelectric materials and resting on elastic foundations. The effect of open circuit electrical boundary condition on vibration characteristics is investigated when a quadratic variation is considered for the electrical potential. Furthermore, the elastic foundations are included in the mathematical modeling to see their effects when the open circuit electrical boundary condition is applied. The first-order shear deformation shell theory and Maxwell’s static electricity equation are employed to derive the governing equations, and natural frequencies are calculated by solving an eigenvalue problem. Vibration characteristics with the open circuit electrical boundary condition are compared with those of closed (short) circuit electrical boundary condition for various mechanical boundary conditions and shell and piezoelectric geometrical parameters. The results demonstrate that the open circuit electrical boundary condition leads to higher frequencies than the closed circuit condition and it must be noticed in the design of smart composite structures with embedded or surface-bonded piezoelectric materials.

Analysis of Uneven Wear Mechanism of Narrow-Face Copper Wall of Funnel Mold

In thin-slab continuous casting, due to the influence of the special shape of the funnel mold, cracks at the corner of the slab shell are more likely to occur than those in conventional slab shells, and a serious wear phenomenon also appears on the narrow face of the copper wall of the mold. Aimed at the corner cracks of thin slabs and the wear phenomenon of the copper wall, a new 3D stress analysis model in a funnel mold has been developed to simulate the stress-–train behavior of the slab shell under high-speed continuous casting. The results show that at the position 600 mm below the meniscus, the gap begins to appear at the corner of the slab; the maximum value of the first principal stress appears at the corner. The shell is squeezed by the copper wall during the downward movement in the funnel mold, and the slab shell in the funnel area moves towards the narrow face. The displacement causes the deformation of the slab shell to extend to the corners, the deformed shell is pressed against the corner of the copper wall. A new type of copper wall was designed for production, and it was found that the cracks at the corner of the slab shell were greatly reduced.

Application of GDQ method to large amplitude response of FGM joined spherical-conical shells under rapid surface heating

Geometrically non-linear thermally induced vibrations of functionally graded material (FGM) joined spherical-conical shells are analyzed in the current research. Thermo-mechanical properties of the shells are assumed to be temperature and position dependent. The system of joined spherical-conical shells is subjected to thermal shock on the ceramic-rich surface, whereas the metal-rich one is kept at reference temperature. The one-dimensional transient heat conduction equation is established and solved via the generalized differential quadrature (GDQ) and Crank-Nicolson methods. This equation is non-linear since the thermo-mechanical properties of the shells are temperature dependent. The total functional of the shells is obtained under the assumptions of uncoupled thermoelasticity laws, first order shear deformation shell theory, and the von Kármán type of geometrical non-linearity. Non-linear coupled equations of motion are solved via the iterative Picard method accompanied with the β-Newmark time approximation technique. Numerical results are well-validated with the available data for the case of single FGM spherical shell. Parametric studies are conducted to examine the influences of conical and spherical shell geometries, material composition, temperature dependence, in-plane and out-of-plane mechanical boundary conditions, various configuration of conical/spherical shell system, and thermal boundary conditions. It is highlighted that thermally induced vibrations indeed exists.

Free vibration analysis of bi-directional functionally graded cylindrical shells with varying thickness

The article presents a semi-analytical solution for the free vibration problem in bi-directional functionally graded (FG) cylindrical shells with varying thickness, utilizing a modified shear deformation shell theory (MSDT). In this model, the mechanical properties of the cylindrical shells change along both the axial and thickness directions. Classical analytical methods for shell structures often face limitations in terms of boundary conditions, transverse shear deformation, and rotary inertia, making the use of MSDT and Galerkin procedure necessary for solving the problem of free vibration analysis in this study. The boundary conditions of the bi-directional FG cylindrical shells are chosen to be simply supported and clamped, and the presented method is compared to relevant results in the literature to validate its effectiveness. Moreover, a comprehensive parametric investigation is conducted to evaluate the influence of material and geometrical parameters on the natural frequencies. The results show that the natural frequency of the FG cylindrical shells is significantly affected by the material and geometrical parameters, including the power-law index, the thickness variation, the aspect ratio, and the boundary conditions.

Porosity and size effects on electro-hygrothermal bending of FG sandwich piezoelectric cylindrical shells with porous core via a four-variable shell theory

The sinusoidal four-variable shear deformation shell theory is employed, for the first time, to investigate the size dependent electro-hygrothermal bending of functionally graded (FG) sandwich piezoelectric cylindrical shells integrated with porous core. This model is assumed to be rested on two-parameter elastic foundations and subjected to elevated temperature, moisture concentration and external electric voltage as well as transverse mechanical loads. In order to take into account the size effect, the modified couple stress theory is employed containing only one length scale parameter. The core layer is assumed to be functionally graded porous material. Whereas, the face sheets are made of a functionally graded piezoelectric material which having gradient change along the thickness direction. Based on the sinusoidal four-variable shell theory, four governing equations are obtained involving external forces and foundation interaction, in addition to an equation associated to the electrical potential. An analytical solution for the obtained equations is presented to get the displacements and stresses of the FG sandwich piezoelectric cylindrical shells. Influences of the geometric parameters, material length scale parameter, temperature rise, moisture concentration, electric voltage, porosity factor, core thickness and foundation coefficients on the bending of the FG sandwich piezoelectric cylindrical shells resting on elastic foundations are discussed.

Who bears the load? IOP-induced collagen fiber recruitment over the corneoscleral shell

Collagen is the main load-bearing component of cornea and sclera. When stretched, both of these tissues exhibit a behavior known as collagen fiber recruitment. In recruitment, as the tissues stretch the constitutive collagen fibers lose their natural waviness, progressively straightening. Recruited, straight, fibers bear substantially more mechanical load than non-recruited, wavy, fibers. As such, the process of recruitment underlies the well-established nonlinear macroscopic behavior of the corneoscleral shell. Recruitment has an interesting implication: when recruitment is incomplete, only a fraction of the collagen fibers is actually contributing to bear the loads, with the rest remaining “in reserve”. In other words, at a given intraocular pressure (IOP), it is possible that not all the collagen fibers of the cornea and sclera are actually contributing to bear the loads.To the best of our knowledge, the fraction of corneoscleral shell fibers recruited and contributing to bear the load of IOP has not been reported. Our goal was to obtain regionally-resolved estimates of the fraction of corneoscleral collagen fibers recruited and in reserve. We developed a fiber-based microstructural constitutive model that could account for collagen fiber undulations or crimp via their tortuosity. We used experimentally-measured collagen fiber crimp tortuosity distributions in human eyes to derive region-specific nonlinear hyperelastic mechanical properties. We then built a three-dimensional axisymmetric model of the globe, assigning region-specific mechanical properties and regional anisotropy. The model was used to simulate the IOP-induced shell deformation. The model-predicted tissue stretch was then used to quantify collagen recruitment within each shell region. The calculations showed that, at low IOPs, collagen fibers in the posterior equator were recruited the fastest, such that at a physiologic IOP of 15 mmHg, over 90% of fibers were recruited, compared with only a third in the cornea and the peripapillary sclera. The differences in recruitment between regions, in turn, mean that at a physiologic IOP the posterior equator had a fiber reserve of only 10%, whereas the cornea and peripapillary sclera had two thirds. At an elevated IOP of 50 mmHg, collagen fibers in the limbus and the anterior/posterior equator were almost fully recruited, compared with 90% in the cornea and the posterior sclera, and 70% in the peripapillary sclera and the equator. That even at such an elevated IOP not all the fibers were recruited suggests that there are likely other conditions that challenge the corneoscleral tissues even more than IOP. The fraction of fibers recruited may have other potential implications. For example, fibers that are not bearing loads may be more susceptible to enzymatic digestion or remodeling. Similarly, it may be possible to control tissue stiffness through the fraction of recruited fibers without the need to add or remove collagen.

Application of the finite element moment scheme to the investigation of thin elastic shells of inhomogeneous structure

The work is devoted to the problem of developing a universal method for studying the deformation, buckling, postbuckling behavior and vibrations of thin and medium-thickness shells of complex shape and structure under the action of mechanical and thermal loads. A wide class of shells is considered: of constant and smooth-variable thickness, with ribs and cover plates, channels and cavities, holes, sharp bends of the mid-surface, and with a multilayer structure of the material. The method is based on the positions of the 3D geometrically nonlinear theory of thermoelasticity without the use of simplifying hypotheses of the theory of shells. The development of the computational model is based on the use of a universal isoparametric spatial finite element with multilinear shape functions, which is the same for all sections of the shell with stepwise variable thickness. The governing equations are constructed in accordance with the requirements of the finite element moment scheme. The mid-surface of the shell’s casing is taken as a single reference surface. All matrices of governing equations for a universal spatial multilayer finite element are obtained in explicit form by analytical integration. This speeds up the execution of calculations in the algorithmic implementation of the method. Such an approach, based on a unified methodology, makes it possible to study the behavior of multilayer shells with different geometric features in terms of thickness under complex thermo-mechanical loading.

Acoustic Radiation From Stiffened Double Concentric Large Cylindrical Shells: Part I Circumferential Harmonic Waves

Abstract Acoustic radiation from stiffened double concentric large cylindrical shells with periodic cavities is analytically investigated via circumferential harmonic waves driven by a point force. The vibration of double isotropic circular cylindrical shells is described by the first-order shear deformation shell theory. One set of uniformly spaced annular bulkheads connects the inner and outer cylindrical shells. In-plane motion equations of the annular bulkheads are expressed by two displacement potential functions. Sound pressure loadings of periodic cavities exerting on the inner and outer cylindrical shells are derived according to the Fourier transform and Poisson summation formula. Far-field sound pressure of the stiffened double cylindrical shells is obtained using the stationary phase method and acoustic radiation features of stiffened double concentric large cylindrical shells with periodic cavities are analyzed in terms of sound pressure power spectra and sound pressure level. Acoustic propagation features of stiffened double cylindrical shells with or without acoustic cavities are shown.

<i>Francisella halioticida</i> Infection of Intermediately Cultured Juvenile Scallops <i>Mizuhopecten yessoensis</i> in Southern Hokkaido

Field surveys of the bacterium Francisella halioticida infection among intermediate-cultured juvenile scallops Mizuhopecten yessoensis in southern Hokkaido revealed that the mortality of juvenile scallops was positively associated with the prevalence of F. halioticida, and that both mortality and prevalence increased in September and January. ​In the intermediate culture experiments, juvenile scallops reared under high density during September and October resulted in high prevalence of F. halioticida and scallop mortality after October, while rearing density from October to March was not associated with infection and mortality, indicating that the high rearing density between September and October determined the infection of F. halioticida and scallop mortality in the following period. ​Furthermore, shell deformity rates, as a proposed index for poor physiological condition of juvenile scallops, were high in the experimental groups with higher density from September to October. ​The high rearing density in this term may have caused a decline in physiological status and, reduced resistance to francisellosis in juvenile scallops, although there is still a possibility that shell deformity was caused by francisellosis.

Generalized differential quadrature element solution, swarm, and GA optimization technique to obtain the optimum frequency of the laminated rotary nanostructure

Optimization of the fiber angle in the laminated composite material to achieve the highest strength or stability has great importance in structural design. In the present study, we aim to utilize genetic algorithm (GA) and particle swarm optimization (PSO) together to find the best angle of composite layers in a multilayer cylindrical shell structure. To this aim, a detailed formulation of the composite cylindrical structure is presented using nonlocal strain gradient theory (NSGT), zigzag theory, and Hamilton's principle for a shear deformable shell displacement field. The modal equations of motion are further solved using the general differential quadrature element method (GDQEM). Having the route of obtaining the resonance frequency of the cylindrical composite structure, GA-PSO is engaged to obtain the optimal angle of the laminate composite to achieve the highest frequency. It is revealed that angle θ = 37.5° provides the highest frequency for a single-layer cylindrical shell. Using this angle, stacking sequences for 3, 5, and 7 layers’ composite are optimized to have the highest frequency. In the end, a detailed parametric study is presented using optimum condition shell composite. The results show that after 30 composite layers, changing the number of layers seems to be not effective on the resonance frequency of the cylinder for both simply supported and clamped boundary conditions.

Modeling of Dynamic Thermo-Elastic-Viscous-Plastic Deformation of Flexible Shallow Reinforced Shells

A mathematical model of non-isothermal elastic-viscous-plastic deformation of flexible shallow shells with multidirectional reinforcement structures has been developed. Wave processes and weak resistance to transverse shear in curved panels are modeled in terms of Ambartsumian’s bending theory. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The composition components are assumed to be isotropic materials, and their plasticity is described by the flow theory with a loading function depending on the strain rate and temperature. The connectedness of the thermomechanical problem under dynamic loading of composite shallow shells is taken into account. In the transverse direction of constructions, the temperature is approximated by a 7th order polynomial. The formulated two-dimensional nonlinear initial-boundary value problem is solved using an explicit numerical scheme of time steps. The thermo-elastic-visco-plastic and thermo-elastic-plastic behavior of fiberglass and metal-composite shallow shells orthogonally reinforced in two tangential directions, loaded in the transverse direction by an air blast wave, has been studied. It is shown that flexible curved fiberglass panels at certain points can additionally heat up by 14…27°C, and similar metal-composite conctructions – by 70°С or more. In this case, peak temperature values are kept at short-term intervals – on the order of fractions of 1 ms. It is shown that, unlike flexible plates, similar shallow shells (with the same reinforcement structure and the same characteristic dimensions) under dynamic loading in the transverse direction must be calculated not only taking into account the dependence of the plastic properties of the composition components on their strain rate, but also taking into account thermal response in such thin-walled constructions. A more intense inelastic deformation of curved composite panels is observed when they are loaded from the side of the convex front surface.

Nonlinear analytical solution for cylindrical shell deformations under asymmetric axial and transverse loads using FSDT

Nonlinear analytical solution for cylindrical shell deformations under asymmetric axial and transverse loads using FSDT

Magneto-electric analysis of higher-order deformable sandwich cylindrical shell

This work presents an analytical framework for magnetoelectroelastic analysis of a higher-order shear deformable sandwich cylindrical shell through a thickness-stretched model and piezomagnetoelasticity relations. The sandwich cylindrical shell is subjected to a combination multifield loadings. Based on the thickness-stretched model, the transverse deflection is decomposed into bending, shear, and stretching parts where the third term is responsible for strain along the thickness direction. The sandwich cylindrical shell is fabricated from an elastic core sandwiched by two piezoelectric/piezomagnetic face-sheets subjected to an electromagnetic environment. The multifield equations are derived using the principle of virtual work. After performing a verification study, the comprehensive numerical results are presented in terms of multifield loading. The results indicate that the radial displacement is significantly improved using the thickness-stretched model.

Effect of deformation dependence and mirror nucleus corrections energy on multinucleon transfer reaction cross sections

Multinucleon transfer reactions are currently a powerful way to synthesize neutron-rich nuclei. To explore the effect of nucleus deformation and mirror nucleus shell correction energy in the nucleus mass model on the calculation of multinucleon transfer reaction cross sections in the dinuclear system (DNS) model, three macroscopic microscopic mass models are selected and the transfer reaction cross sections are calculated for 136Xe+208Pb and 64Ni+238U by improved DNS model+GEMINI++, respectively. The mirror nucleus shell correction energy does not improve the accuracy of the cross section of the transfer reaction. The introduction of a different dependence of the Coulomb and surface energy on the deformation can improve the calculation of the transfer reaction cross section when the projectile and target nuclei are deformed nuclei.

Relationship of Population Attributes of a Dominant Macrofaunal Species with Environmental Conditions in a Eutrophic Estuary (Guanabara Bay, Brazil)

Hydrobioid gastropods are abundant in coastal systems and ecologically important for ecosystem functioning. We aimed to unravel the relationship between usual and stress-related population attributes of the dominant macrofaunal species Heleobia australis with indicators of environmental quality and coastal pollution. Using Guanabara Bay (GB, Brazil) as a model of a multi-impacted coastal system, our hypothesis is that increased amounts of rainfall during the warm season reduce the bay’s environmental quality and induce shifts in snail population attributes. A suite of environmental variables, population attributes, and sediment quality descriptors was assessed by combining field and laboratory evaluations with literature compilation. Results indicate high organic pollution levels with environmental degradation and reinforce GB status as a severely contaminated system. Some environmental conditions can be applied as seasonal predictors of changes in warm-rainy (rainfall and salinity), intermediate (silicate), and cold-dry seasons (nitrite and nitrate). Three selected usual population attributes (snail density, fecundity, and recruitment) were not affected by changes in environmental conditions, but significant effects were detected on two stress-related attributes (relative penis length index and shell deformity). For the first time, shell deformity was recorded in H. australis snails. Low variation in usual population attributes highlight the high tolerance of H. australis to shifts in environmental conditions.

Research on the dynamic response of pressurized cylindrical shell structures subjected to a near-field underwater explosion

To study the dynamic response of a pressurized thin-walled circular tube structure subjected to a near-field underwater explosion, deformation and damage tests of a pressurized cylindrical tube shell with different internal pressures and wall thicknesses with the effects of an underwater explosion from 2 g of explosives at different stand-off distances were carried out in a water tank. LS-DYNA finite element software was used to carry out relevant numerical simulations to explore the anti-explosion mechanism of a pressurized cylindrical shell structure affected by factors including the initial internal pressure, the thickness of the cylindrical shell, and the stand-off distance. The simulation inputs are high-speed photography images and the damage results of the cylindrical shell. The simulation results highlight the bubble pulsation, action process deformation, and energy change of the cylindrical shell. The results indicate that an increase in the initial pressure of the cylindrical shell can effectively improve its anti-explosion ability, while the different stand-off distances of r = 12 cm and r = 9 cm correspond to the same initial internal pressure. Increasing the initial internal pressure also causes the deflection difference of the cylindrical shell to decrease. The modeling results also indicate that an increase in the wall thickness may weaken the anti-explosion ability of the cylindrical shell, which has an initial internal pressure of Pr = 0.7 MPa. After an underwater explosion, the maximum displacement difference of a cylindrical shell with thicknesses of h = 1 mm and h = 1.5 mm is less than the maximum rebound distance difference. With this decrease in the distance, the proportion of the high-pressure cylindrical shell subjected to a shock wave increases while the proportion of bubble pulsation decreases. Specifically, the maximum proportions of bubble pulsation are 30% and 92% at the stand-off distances of 3 and 12 cm, respectively.

A novel spatial parallel multi-stable mechanism with eight stable states

A multi-stable flexible mechanism is a mechanical device that can switch to different stable equilibrium states under external power. Most existing multi-stable mechanisms are achieved by splicing bi-stable mechanisms. This paper proposes a novel Spatial Parallel Multi-stable Mechanism (SPMM) without bi-stable mechanisms connected, which even could achieve eight stable equilibrium states and meanwhile contain bi-stable mechanisms’ advantages such like simple structure and reliable abilities. To identify the equilibrium states, the paper develops a kinetostatic model using the Energy-Kinematics Differential Equations (EKDE) for the proposed SPMM. Based on the equilibrium states, the multi-stability topologies are drawn referring to direct groups, including the distribution of various equilibrium states and the switching paths between every two stable states. At last, the paper shows the experimental results of a 3D printed prototype and verify the eight-stability behaviors and the switching paths through unstable equilibrium states. A concept of the application in deformable cable protection shell using the SPMM is introduced.

Structural behaviour of post-installed reinforcement for 3D concrete printed shells – A case study on water tanks

Incorporating sufficient reinforcement to ensure a ductile structural behaviour is a persisting challenge in digitally fabricated concrete structures. This paper investigates the structural performance of a reinforcement approach for 3D concrete printed elements, consisting of an unreinforced 3D printed concrete shell and a sprayed shell reinforced with a conventional reinforcing mesh for application in water tanks. Four reinforced concrete elements produced with this approach were tested in direct tension and compared to a reference test of a monolithic specimen to analyse the behaviour of circular water tanks under hoop stresses. Two eccentric reinforcement arrangements and two different printing patterns were investigated. Despite the testing setup not perfectly representing the actual behaviour of circular water tanks, in which shell deformations are kinematically restrained, the feasibility of the fabrication method could be examined. The results did not show significant differences in the behaviour of the different fabrication methods, with similar ductility as expected in a conventionally reinforced shell. The eccentric reinforcement caused the crack formation to originate on the surface close to the reinforcement, accompanied by out-of-plane deformations. The cracks on the far side of the reinforcement opened suddenly and reduced the out-of-plane deformations. The predictions with models neglecting the eccentricity of the reinforcement overestimated the crack opening. The best predictions were obtained from the tension chord model by only considering the concrete area defined by twice the mechanical cover of the reinforcement.

Structural Response of Double-Layer Steel Cylinders under Inside-Explosion Loading

The research on the structural response of explosive vessel is an important basis for the design of explosive vessels. Double-layer cylinder structures are widely used in the design of various explosive vessels. This paper studied the deformation of a steel cylindrical shell under internal explosion and proposes a new method for measuring shell deformation by PDV (photonic Doppler velocimetry). We carried out many spherical explosive experiments and obtained useful results that show displacement of the double-layer cylinders and the explosion time. The above process is a simulated LS-DYNA with a finite element numerical simulation. The vibration period of the outer cylindrical shell and the time for reflection of the stress wave in the outer cylindrical shell were obtained by numerical simulation and PDV measurement, respectively. The results of both can be verified against each other. Through the above research, the structural response of the multilayer cylinders can be obtained, which can provide further help with research of the structural design of multilayer cylinders.

Non-axisymmetric problems of unsteady deformation of cylindrical shells with filler

Circular cylindrical shells, as structural elements, have found wide application in various fields of mechanical engineering. Thin-walled layered shells have also found wide application as components in underwater objects, air and space vehicles and in many other engineering structures. The aim of this work is to study the action of a non-axisymmetric moving wave of normal pressure on a cylindrical shell interacting with an ideal compressible fluid. The problem statement is given, solution methods are developed, and numerical results are obtained for new problems of stationary deformation of infinitely long viscoelastic cylindrical shells on a viscoelastic foundation when a non-axisymmetric normal pressure wave moves along the shell axis with up to resonant velocity. As an example, considered the action of a non-axisymmetric moving wave of normal pressure on a cylindrical shell interacting with an ideal compressible fluid. The solution methods are based on the joint application of the integral Fourier transform along the axial coordinate and the expansion of all given and desired values into Fourier series along the angular coordinate. An efficient algorithm for the joint calculation of integrals and Fourier series has been developed and implemented on a computer. It has been established that paying to attention the viscoelastic properties of the shell material reduces the deflections by 10–15%, and also makes it possible to evaluate the damping capabilities of the system.