Thin Shell Theory Research Articles

Study on theoretical model of burst pressure of fiber reinforced arc-shaped rubber hose with good balance performance

This paper focus on the optimum design of the arc-shaped rubber hose, so that the hose has a good balance performance and a higher burst pressure. Based on the thin shell theory without considering bending moments and shear force, the equilibrium equation was established to obtain the internal force of the arc-shaped hose under internal pressure, and the burst pressure of the arc-shaped rubber hose was obtained by using Tsai-Hill failure criterion. According to the mechanical model of burst pressure, the influence of structural parameters on the burst pressure and distribution of vulnerable positions of arc-shaped rubber hose was studied. Then, in order to determine the structural parameters of the hose satisfying the balance performance, the deformation of the arc-shaped rubber hose was divided into two stages, including braiding angle deflection and tensile deformation of fiber, and the mechanical model of balance performance of the arc-shaped rubber hose was established. Eventually, on the basis of satisfying the balance performance of the hose, the hose was optimized for higher burst pressure. The correctness of the theoretical model and the optimization results were verified by experiments.

Asymptotic derivation of refined dynamic equations for a thin elastic annulus

Low-frequency vibrations of a thin elastic annulus are considered. The dynamic equations of plane strain are subjected to asymptotic treatment beyond the leading-order approximation. The main peculiarity of the considered problem is a specific degeneration associated with the effect of the almost inextensible midline of the annulus, resulting in a few unexpected features of the mechanical behaviour. In particular, it is discovered that the leading-order even component of the circumferential stress is not uniform across the thickness, as is usually assumed, and can be determined only at the next order. The derived refined equations also govern vibrations of a cylindrical shell at the lowest cut-off frequencies. The two-term asymptotic formula obtained for the latter fully agrees with the expansion of the transcendental dispersion relation for plane strain but does not coincide in the second term with the prediction of the Kirchhoff–Love theory for thin shells.

An Exact and Practical Analyzing Model for Radial Vibration of Piezoelectric Spherical Transducers With Arbitrary Wall Thickness.

The piezoelectric spherical transducers have attracted extensive attention in hydroacoustics and health monitoring. However, most reported piezoelectric spherical transducers are merely analyzed by the thin spherical shell theory, which is unsuitable for the gradually increased spherical shell thickness. Therefore, it is necessary to develop the radial vibration theory of the piezoelectric spherical transducer with arbitrary wall thickness. Herein, an exact analyzing model for the radial vibration of the piezoelectric spherical transducer with arbitrary wall thickness is proposed. The radial displacement and electric potential for radial vibration of the piezoelectric spherical transducer are precisely given, and then, the electromechanical equivalent circuit is obtained. Based on the electromechanical equivalent circuit, the resonance/antiresonance frequency equations of piezoelectric spherical transducers in the radial vibration are obtained. Besides, the relationship between performance parameters and wall thicknesses is discussed. The wall thickness has a significant influence on the performance parameters of the spherical transducer. The accuracy of the theory is validated by comparing the results with the experiment and finite element analysis.

Dynamic stiffness – based free vibration study of open circular cylindrical shells

In this paper, the dynamic stiffness method has been applied in the free vibration analysis of open circular cylindrical shells based on Flügge thin shell theory. The dynamic stiffness matrix for a completely free open cylindrical shell element has been derived and coded in MATLAB to compute the natural frequencies and mode shapes. The results of the numerical study have been compared with the results from the finite element analysis, as well as with the results from the literature. After a detailed convergence study, considering the number of terms in the proposed solution, applied boundary conditions and geometry, limitations and recommendations for application of the proposed method have been given.

Tug-of-war between stretching and bending in living cell sheets.

The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling transition. Recently, experimental results in suspended living epithelial monolayers have shown that, due to the asymmetry in surface stresses generated by molecular motors across the thickness e of the epithelium, the free edges of such tissues spontaneously curl out-of-plane, stretching the sheet in-plane as a result. This suggests that a competition between bending and stretching sets the morphology of the tissue margin. In this paper, we use the framework of non-Euclidean plates to incorporate active pre-strain and spontaneous curvature to the theory of thin elastic shells. We show that, when the spontaneous curvature of the sheet scales like 1/e, stretching and bending energies have the same scaling in the limit of a vanishingly small thickness and therefore both compete, in a way that is continuously altered by an external tension, to define the three-dimensional shape of the tissue.

Sound transmission through micro-perforated double-walled cylindrical shells lined with porous material

Sound transmission through a double-walled cylindrical shell with porous cores and the inner shell micro-perforated is studied analytically in this paper. The Donnell's thin shell theory is used to govern shell motions and the Biot's theory is applied to describe sound propagation in the porous layer. Boundary condition at the perforated shell is presented by the mean particle velocity model. When excited by an oblique plane wave with external mean flow, transmission losses through typical configurations are numerically computed. Results show that perforating the inner shell of different sandwich configurations would produce improvement of transmission loss below the ring frequency. In further analysis regarding the perforated configuration with two airgaps in annular space, it retains superiority against the corresponding non-perforated one in the low frequency range despite alteration of the incidence angle, the azimuthal angle or the external flow. In parametrical studies, increase of either the aperture diameter or the perforation ratio is validated to enhance low-frequency sound insulation of this configuration through the imaginary part of the impedance constant.

Free vibration of partially fluid-filled or fluid-surrounded composite shells using the dynamic stiffness method

In this paper, the dynamic stiffness method (DSM) is developed for the vibration analysis of laminated cylindrical and conical shells, which are partially filled or surrounded by quiescent fluid. The Reissner and Naghdi’s thin shell theory and incompressible fluid equations are employed on the structures and fluid, respectively, so as to characterize the fluid–structure coupling model. Shell elements with/without fluid loadings are derived and assembled by using the dynamic stiffness method. Numerical examples of the free vibration analysis for both empty and fluid-filled shells are validated against previous studies. Remarkable advantages regarding computational efficiency and accuracy of the DSM, especially in high-frequency domain, are presented through response curves compared with finite element calculations. As for partially fluid-filled or fluid-surrounded laminated shells, parametric studies are made to find the effects of material properties, fluid heights and semi-vertex angles on the dynamic characteristics.

Study on Mechanical Model of Balance and Stiffness Characteristics of Fiber Reinforced Bellows Type Rubber Hose

The mechanical model related to the balance and stiffness characteristics of the bellows type rubber hose under internal pressure was studied. Based on the thin shell theory without considering bending moments and shear force, the equilibrium equation of the bellows type hose was established to obtain the mechanical equilibrium angle under different mechanical environments. Considering the deformation characteristics of the rope structure and the mechanical equilibrium angle of the hose, the deformation of the bellows type rubber hose was divided into two stages, including winding angle deflection and tensile deformation of fiber. Then the constitutive model of anisotropic material was introduced, and the physical equation of the bellows type hose was established to obtain the mechanical model of the balance and stiffness characteristics. According to the mechanical model, the influence of initial fiber winding angle, fiber layer thickness, the radius at the two ends of the hose, the length of hose, the curvature radius and internal pressure of hose on the balance and stiffness characteristics of hose was studied. Eventually, the structure of the hose was designed based on the mechanical model, to optimize the balance and stiffness characteristics of hose. The balance and stiffness characteristics of the optimized hose were verified by experiments. The theoretical and experimental results indicated that, the mechanical model of the balance and stiffness characteristics of the hose can be the theoretical basis for the optimization of structural parameters.

Post-buckling analysis of geometrically imperfect nanoparticle reinforced annular sector plates under radial compression

Buckling and post-buckling behaviors of geometrically imperfect annular sector plates made from nanoparticle reinforced composites have been investigated. Two types of nanoparticles are considered including graphene oxide powders (GOPs) and silicone oxide (SiO2). Nanoparticles are considered to have uniform and functionally graded distributions within the matrix and the material properties are derived using Halpin-Tsai procedure. Annular sector plate is formulated based upon thin shell theory considering geometric nonlinearity and imperfectness. After solving the governing equations via Galerkin\'s technique, it is showed that the post-buckling curves of annular sector plates rely on the geometric imperfection, nanoparticle type, amount of nanoparticles, sector inner/outer radius and sector open angle.

Vibration analysis of shell‐like curved carbon nanotubes using nonlocal strain gradient theory

The performance of nanotube‐based resonators is significantly affected by the variation of their natural frequencies. In reality, nanotubes may have some levels of initial imperfection, which definitely changes their vibrational characteristics. In the present article, the vibrational behavior of initially curved nanotubes is investigated on the basis of thin shell theory incorporating the nonlocal strain gradient theory. The three‐dimensional governing equations of motion are derived by adopting the curvilinear coordinate system through Hamilton's principle. A new formulation of Eringen's model containing the higher‐order strain gradients is employed to capture the effects of nonlocality and small scale parameter. Galerkin decomposition method is employed to acquire a bi‐cubic relation for the natural frequency of the considered nanoshell. The effects of different parameters like the ratio of radius of curvature to the cross section radius, small scale and nonlocality, and length‐to‐radius ratio on the variation of the natural frequency are presented. Excellent agreements are found in some comparative studies between the results of this work and those obtained by molecular dynamics and experimental findings in the literature. Finally, some interesting results are found by plotting the variation of natural frequency of the system versus the length‐to‐radius ratio. It is exhibited that by increasing the ratio L/r, the natural frequencies associated with different values of wavenumber m converge to the lower one and the convergence speed is highly dependent to the circumferential wavenumber n.

Motion equations of hemispherical resonator and analysis of frequency split caused by slight mass non-uniformity

The mass non-uniformity of hemispherical resonator is one of reasons for frequency split, and frequency split can cause gyroscope to drift. Therefore, it is of great significance to analyze the relationship between mass non-uniformity and frequency split, which can provide a theoretical basis for mass balance of imperfect resonator. The starting point of error mechanism analysis for gyroscope is the motion equations of resonator. Firstly, based on the Kirchhoff-Love hypothesis in the elastic thin shell theory, the geometric deformation equations of resonator are deduced. Secondly, the deformation energy equation of resonator is derived according to the vibration mode and relationship between the stress and strain of hemispherical thin shell. Thirdly, the kinetic energy equation of resonator is deduced by the Coriolis theorem. Finally, the motion equations of resonator are established by the Lagrange mechanics principle. The theoretical values of precession factor and natural frequency are calculated by the motion equations, which are substantially consistent with the ones by the finite element method and practical measurement, the errors are within a reasonable range. Simultaneously, the varying trend of natural frequency with respect to the geometrical and physical parameters of resonator by the motion equations is consistent with that by the finite element analysis. The above conclusions prove the correctness and rationality of motion equations. Similarly, the motion equations of resonator with mass non-uniformity are established by the same modeling method in case of ignoring the input angular rate and damping, and the state equations with respect to the velocity and displacement of vibration system are derived, then two natural frequencies are solved by the characteristic equation. It is concluded that one of reasons for frequency split is the 4th harmonic of mass non-uniformity, and thus much attention should be paid to minimizing the 4th harmonic of mass non-uniformity in the course of mass balancing for imperfect resonator.

Nonlinear vibrations of variable thickness curved panels made of multi-scale epoxy/fiberglass/CNT material using Jacobi elliptic functions

This article deals with nonlinear vibration study of variable thickness cylindrical panels made of multi-scale composite materials containing epoxy matrix, glass fibers, and carbon nanotubes (CNTs). The elastic properties of multi-scale material have been defined in the context of 3D Mori-Tanaka scheme considering unidirectional aligned macro-fibers and randomly oriented CNTs. It is considered that the panel thickness is varying in axial direction and may have linear and parabolic changes. The governing equations of variable thickness curved panel have been stablished using thin shell theory containing geometric nonlinearity. Then, Jacobi elliptic functions are proposed for solving the governing equations since they leads to exact frequency-amplitude curves of the curved panels. It is reported that frequency-amplitude curves are varying with the changes of CNT weight fraction, fiber orientation, fiber volume, variable thickness parameters, panel curvature radius, and length-to-radius ratio of CNTs.

Geometrically nonlinear vibration analysis of eccentrically stiffened porous functionally graded annular spherical shell segments

This article investigates nonlinear free vibrations of porous functionally graded (FG) annular spherical shell segments surrounded by elastic medium and reinforced by circumferential stiffeners. Porous FG material contains distributed even and un-even porosities and is modeled based on refined power–law function. The governing equations of stiffened porous annular spherical shell segments have been derived according to thin shell theory with the geometrical nonlinear in von Karman–Donnell sense and the smeared stiffeners method. An analytical trend has been provided for solving the nonlinear governing equations. Obtained results demonstrate the significance of porosity distribution, geometric nonlinearity, foundation factors, stiffeners and curvature radius on vibration characteristics of porous FG annular spherical shell segments.

Optimization design of neutrally buoyant hull for underwater gliders

The net buoyancy, driving force of underwater gliders, decreases gradually when the gliders dive or climb in the seawater, which increases the energy consumption and reduces the gliding range. The neutrally buoyant hull is an effective measure to reduce this buoyancy loss of underwater gliders. In this paper, a multiple intersecting spheres (MIS) pressure hull is designed to provide neutral buoyancy. A mechanical model of the hull is established with the thin shell theory, based on which the optimization is carried out by combining the penalty function method (PFM) and multiple population genetic algorithm (MPGA). Thickness of the spherical shell, reinforcing rib, width of the reinforcing rib, and intersection angle of the spherical shell are optimized for minimizing the buoyancy factor which is defined as the ratio of pressure hull mass to the undeformed displacement. Additionally, the mechanical model is verified by the finite element analysis and the pressure test. The results show that the MIS pressure hull can increase the buoyancy compensation by 69.69% and increase battery capacity of the glider by 12.89% as compared with conventional cylindrical hull. This will improve the navigation range and duration of Petrel-L glider more obviously when its hotel load is lower.

Establishment and verification of theoretical model for forming design of balanced curved rubber hose

This article focuses on the establishment of theoretical model for the formation of balanced curved rubber hose under pressure. According to the rotation angle of the cord along the axial direction in the curved rubber hose is the same as that in the straight hose before forming, the theoretical model of the straight hose length was established. Then based on the thin shell theory without considering bending moments and shear force, and considering the deformation characteristics of the rope structure and the mechanical equilibrium angle of the hose, the theoretical model of the balance performance was established. According to the theoretical model, the influence of structural parameters of curved hose on the length of the straight hose and the balance performance of hose was studied. Eventually, the finite element model was established to simulate the deformation process of the curved hose. Based on the calculation results of the theoretical and simulation model, the experiment of forming and balance performance of the curved hose was carried out. The experimental results are in good agreement with the theoretical and simulation model.

Modeling and solving the dynamic problem of a porous rotational shell based by modified Boit’s theory

Combined the Boit’s theory and the classical elastic theory of thin shell, a new model for analyzing the vibrations of a thin fluid-saturated porous rotational shell is proposed and solved by the extended homogeneous capacity precision integration method and the precise element method. The present model is precise and closer to the real materials as it takes the fluid-solid coupling effect into account and doesn’t make any hypothesis for the fluid displacement. At the end of the paper, the accuracy of the model had been verified by experiment and FEM methods.

An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff-Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell's mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith's theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires $C^1$-continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-$\alpha$ method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton-Raphson scheme. The interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.

Nonlinear normal modes, resonances and energy exchange in single-walled carbon nanotubes

The nonlinear resonance interaction and energy exchange between bending and circumferential flexure modes in single-walled carbon nanotubes is studied. First, the results of an analytical model of the resonance interaction between the considered nonlinear normal modes previously developed are reported. This approach was based on a reduced form of the Sanders–Koiter thin shell theory obtained by using simplifying hypotheses on the shell deformations. The analytical model predicted that the nonlinear resonance interaction leads to energy localization in a certain coherence domain over the carbon nanotube surface within a specific range of the initial oscillation amplitude. Then, a numerical model of the resonance interaction between the analysed nonlinear normal modes in the framework of the complete Sanders–Koiter thin shell theory is reported. Numerical simulations are performed to verify the energy localization phenomenon over the carbon nanotube surface and to compute the threshold values of the initial oscillation amplitude giving rise to energy localization. Finally, from the comparison between the two different approaches, it is obtained that the results of the numerical model for the threshold values of the nonlinear energy localization confirm with very good accuracy the predictions of the analytical model.

Strain gradient based static stability analysis of composite crystalline shell structures having porosities

This paper studies nonlinear stability behavior of a nanocrystalline silicon curved nanoshell considering strain gradient size-dependency. Nanocrystallines are composite materials with an interface phase and randomly distributed nano-size grains and pores. Imperfectness of the curved nanoshell has been defined based on an initial deflection. The formulation of nanocrystalline nanoshell has been established by thin shell theory and an analytical approach has been used in order to solve the buckling problem. For accurately describing the size effects related to nano-grains or nano-pores, their surface energies have been included. Nonlinear stability curves of the nanoshell are affected by the size of nano-grain, curvature radius and nano-pore volume fraction. It is found that increasing the nano-pore volume fraction results in lower buckling loads.

Finite strip method for the analysis of diaphragm supported cylindrical shell

This work relates to the formulation of finite strip for the analysis of thin circular cylindrical shells. The thin shell supported on diaphragms at circular ends has been taken for the analysis by finite strip method. The diaphragms are infinitely rigid in their own planes and flexible perpendicular to the plane. The behavior of thin cylindrical shell is governed by Love-Kirchhoff assumptions. Koiter’s [1] theory of thin cylindrical shell is used as a base for the derivation of strain components. The discretization of half shell has been done in to finite strips are taken along the length of the shell.