Deformation Of Cylindrical Shells Research Articles

Deformation characteristics of a ring-stiffened cylindrical shell induced by shock waves and coalesced bubbles in double-charge underwater explosions

This study investigates the deformation characteristics of a ring-stiffened cylindrical shell induced by shock waves and coalesced bubbles in double-charge underwater explosions. A numerical model for coupling underwater multi-point explosion loads with the cylindrical shell is established by the Arbitrary Lagrange Euler method, and underwater explosion experiments with double charges are also conducted. The numerical model's effectiveness is validated by comparing shock wave superposition characteristics, bubble coalescence processes, and bubble pulsation periods with the experimental results. Based on the numerical model, the influences of detonation intervals and layout angles of charge on shock wave superposition effects, temporal and spatial distribution characteristics of shock waves, and the evolution process of coalesced bubbles in underwater explosions with double charges are explored. Additionally, the deformation characteristics of cylindrical shells induced by shock waves and coalesced bubbles for double charges with different detonation intervals and layout angles of charge are analyzed. The results indicate that double charges can induce more substantial deformation on the cylindrical shell at a specific detonation interval than a single charge with equal total mass. During the shock wave phase, the cylindrical shell's deformation decreases nonlinearly with an increased layout angle. Conversely, during the bubble load phase, the deformation of the cylindrical shell shows an approximately linear decrease with an increase in layout angle. A critical angle exists, below which the impact of double charges on the cylindrical shell is more substantial when detonated with an interval than simultaneous detonation.

Free vibration analysis of graphene origami-reinforced nano cylindrical shell

Vibrational behavior of a shear deformable cylindrical shell is studied in this article based on Hamilton’s principle. The shell is manufactured by a Copper (Cu) core reinforced with graphene origami auxetic metamaterial and subjected to mechanical and thermal loads. The constitutive relations are developed based on the shear deformable model where the effective modulus of elasticity, Poisson’s ratio, and density are evaluated using micromechanical models including volume fraction and folding degree of graphene origami auxetic metamaterial, geometric characteristics of graphene, material properties of matrix, and reinforcement and local temperature. The natural frequencies are obtained based on Navier’s and Galerkin’s approaches for simply supported, clamped-simply, and clamped-clamped boundary conditions. The formulation, solution procedure, and numerical results are confirmed through comparison with the available results of the literature. The complete numerical results are presented in terms of volume fraction and folding degree of graphene origami auxetic metamaterial, thermal loading, and various types of boundary conditions.

Thermal Nonlinear Buckling of Shear Deformable Functionally Graded Cylindrical Shells with Porosities

In this paper, for the first time, two-term deflection is suggested for nonlinear analysis of shear deformable cylindrical shells and, to the authors’ knowledge, a first investigation on thermal nonlinear buckling behavior of functionally graded material (FGM) cylindrical shells including porosities is presented. Material properties are assumed to be temperature dependent, volume fractions of constituents are graded in the thickness direction according to a power law, and effective properties of porous FGM are estimated according to a modified rule of mixture. Porosities are evenly or unevenly distributed within the shell. Mathematical formulations are based on a first-order shear deformation theory taking into account geometrical nonlinearity and elasticity of in-plane restraints of edges. Two-term deflection and a multiterm stress function are assumed to satisfy simply supported boundary conditions. The Galerkin method and an iteration procedure are employed to evaluate critical buckling temperatures and trace temperature-deflection paths in the postbuckling region. The two-term solution of deflection is a significant suggestion for nonlinear buckling analysis of shear deformable cylindrical shells in general and thermal postbuckling analysis of porous FGM cylindrical shells in particular. This two-term solution includes inherent uniform deflection at the prebuckling state and overcomes mathematically tremendous difficulty in using three-term deflection for shear deformable cylindrical shells. Besides this innovative approach, the obtained results are of great interest for many engineering applications. Unlike the case of mechanical loads, porosities have beneficial influences on the stability of thermally loaded FGM cylindrical shells.

The dynamic response of cylindrical shell and square plate with pre-formed holes under blast loading

The dynamic response of cylindrical shells and square plate with pre-formed holes under blast loading was studied by numerical simulation. The numerical model was calibrated by the experimental data of square plates with pre-formed holes. The dynamic responses and deformation of cylindrical shells with pre-formed holes subjected to blast loading was investigated by the same numerical model. The structure response process has been divided into four specific stages which has been discussed systematically. According to the comparison of structure response process, stress concentration between these two structures under blast loading, it is concluded that the square plates have a better performance than that of cylindrical shell with or without pre-formed holes and the influence of pre-formed holes on blast-resisting of square plate is bigger than that of cylindrical shell. In addition, the global and local deformation characteristics are mainly result from the space configuration and pre-formed holes, respectively.

Challenges of Fully-Coupled High-Fidelity Ditching Simulations

An important element of the process of aircraft certification is the demonstration of the crashworthiness of the structure in the event of an emergency landing on water, also referred to as ditching. Novel numerical simulation methods, that incorporate the interaction between fluid and structure, open up a promising way to model ditching in full scale. This study focuses on two main issues of high-fidelity ditching simulations: the development of a suitable fluid-structure coupling framework and the generation of the structural model of the aircraft. The first issue is addressed by implementing a partitioned coupling approach, which combines a finite volume hydrodynamic fluid solver as well as a finite element structural solver. The developed framework is validated by means of two ditching-like experiments, which consider the drop test of a rigid cylinder and a deformable cylindrical shell. The results of the validation studies indicate that an alternative to the standard Dirichlet-Neumann partitioning approach is needed if a strong added-mass effect is present. For the full-scale simulation of aircraft ditching, structural models become more complex and have to account for damage. Due to its high localization, the damage creates large differences in model scale and usually entails severe non-linearities in the model. To address the issue of increasing computational effort for such models, the process of developing a multi-scale model for the simulation of the failure of fuselage frames is presented.

A shear deformable cylindrical shell model based on couple stress theory

In this paper, formulation of the thin cylindrical shell via the modified couple stress theory by taking account of shear deformation and rotary inertia is obtained. To do this, the study developed the first shear deformable cylindrical shell theory by considering the size effects via the couple stress theory and the equations of motion of shell with classical and non-classical boundary conditions were extracted through Hamilton’s principle. In the end, as an example, free vibrations of the single-walled carbon nanotube (SWCNT) were investigated. Here, the SWCNT was modeled as a simply supported shell, and the Navier procedure was used to solve the vibration problem. The results of the new model were compared with those of the classical theory, pointing to the conclusion that the classical model is a special case of the modified couple stress theory. The findings also demonstrate that the rigidity of the nano-shell in the modified couple stress theory compared with that in the classical theory is greater, resulting in the increase in natural frequencies. In addition, the effect of the material length scale parameter on the vibrations of the nano-shell in different lengths and thickness was investigated.

Free vibration analysis of four-unknown shear deformable functionally graded cylindrical microshells based on the strain gradient elasticity theory

In this paper, we present a four-unknown shear deformation theory and then develop a shear deformable functionally graded cylindrical microshell model using the strain gradient elasticity theory. Unlike the existing shear deformable cylindrical shell models, the present one contains four independent displacement functions only and introduces three material length scale parameters. In addition, the trapezoidal shape factor (1+z/R) of a shell element is taken into account in the expressions of classical and non-classical stresses to obtain the accurate stress-resultants over the thickness. The material properties of the microshell are estimated through the Mori–Tanaka homogenization technique. By using Hamilton’s principle, the equations of motion and boundary conditions are obtained. Closed-form solutions are derived for the free vibration problem of cylindrical microshells with simply supported ends and fixed ends respectively. Comparison studies are performed to establish the validity of the derived formulation. Finally, some illustrative examples are presented to investigate the influences of the material length scale parameter, gradient index, thickness-to-radius ratio, thickness-to-length ratio and boundary conditions on the vibration characteristics of cylindrical microshells. Numerical results indicate that both the frequency and higher-order mode shapes exhibit significant size-dependence when the thickness of the microshell approaches to the material length scale parameter.

Elasticity and geometry: a computational model of the Heineke–Mikulicz strictureplasty

Crohn's disease is a challenging inflammatory process with a propensity for focal gastro-intestinal tract inflammation and stricture. Surgically, Crohn's is often treated with resection. However, a subtype of diffuse disease with multiple strictures is treated by strictureplasty procedures in hope of avoiding short-gut syndrome. Prior work by Pocivavsek et al. defined the geometry of a Heineke-Mikulicz strictureplasty. Here, we bring this analysis one step closer to clinical and biological relevance by calculating the mechanical stresses and strains that the strictureplasty deformation generates on a model intestinal wall. The small bowel is simulated as a linearly elastic isotropic deformable cylindrical shell using finite element modeling. Data show a divergence in elastic response between the anti-mesenteric and mesenteric halves. The anti-mesenteric surface shows a bending dominated elastic response that correlates with the prior purely geometric analysis. However, the mesenteric half is not a neutral bystander during strictureplasty formation, as geometric arguments predict. Strong in-plane stretching strains develop in a rim around the image of the transverse closure, which may impact local perfusion and serve as sites of disease recurrence. Lastly, nearly all the deformation energy is stored in the central vertex stitch, placing this part at highest risk of dehiscence. This study enhances our understanding of mechanical response in complex nonlinear cylindrical geometries like the surgically manipulated intestinal tract. The developed framework serves as a platform for future addition of more complex clinically relevant parameters to our model, including real tissue properties, anisotropy, blood supply modeling, and patient deriver anatomic factors.

The Deformation of Cylindrical Shells Subjected to Radial Loads Using Mixed Formulation and Analytic Solutions

The objective of this work is to contribute with a simple and reliable numerical tool for the stress analysis of cylindrical vessels subjected to generalized forces using a mixed formulation. Variational techniques coupled with functional analysis are used to obtain an optimized solution for the shell displacement and further stress field evaluation using a combination of unknown analytic functions with Fourier expansions. A large cylindrical shell subjected to pinching loads is considered. These elements are intended to provide accurate modelling of the initially circular pipes response. Because of this behaviour, the bend's cross-section abandons its original roundness, turning into an oval or noncircular configuration. In addition, the initially plane cross-section, tends to deform out of its own plane. These two deformation patterns are termed ovalization and warping, respectively. In this work the results for the radial displacement and section ovalization are analysed where the solution has six terms for an acceptable accuracy. The transverse displacement presents important dependence on the shell thickness vs radius, where in the case of thin shells the ovalization is restricted to a local area and this is the case analysed. The proposed method leads to accurate results with low complex input data. The conclusions of this work are that the definition of the load system and boundary conditions are easily processed as the method has pre-defined possibilities for each load case or edge boundary conditions. An analytic solution is obtained and a low number of terms in the Fourier series show good accuracy as can be seen by a comparison with finite element methods.

Nonlocal shear deformable shell model for torsional buckling and postbuckling of microtubules in thermal environments

Buckling and postbuckling analysis is presented for microtubules subjected to torsion in thermal environments. The microtubule is modeled as a nonlocal shear deformable cylindrical shell which contains small scale effects. The governing equations are based on a higher order shear deformation theory. The thermal effects are included and the material properties are assumed to be temperature-dependent. The small scale parameter e0a is estimated by matching the buckling twist angle of microtubules obtained from the nonlocal shear deformable shell model with the existing result. The results show that the small scale effect plays an important role in the postbuckling of microtubules.

Experimental investigation of the effect of electric discharges of large length in water on the energy of deformation of a cylindrical shell

The influence of the length of a high-voltage discharge channel in water on the plastic deformation of a concentric cylindrical shell has been experimentally studied. Electric discharges induced by micro-conductors in water with channel lengths up to 420 mm have been realized for the first time, and their electrical characteristics have been measured. The effect of the discharge channel length on the efficiency of plastic deformation of a cylindrical shell has been determined.

Effect of boundary conditions of cylindrical shells on stabilisation of tube compression by viscous pressure forming

As a result of compression instability, buckling and wrinkling easily occur in the tube‐compression process, especially for thin‐walled parts, which restricts the application of tube compression. Investigation of the effects of boundary conditions of cylindrical shells on the stabilisation of tube compression by viscous pressure forming (VPF) is very important. In this article, the stress of the cylindrical shell under different boundary conditions is examined. Subsequently, using the ANSYS Academic Research code for elastic–plastic deformation of cylindrical shells under different boundary conditions, the distributions of stress and strain and the post‐buckling paths for the cylindrical shell are investigated. The results show that wrinkling in the tube‐compression process by VPF can be removed when the ends of the cylindrical shells are confined. Finally, the finite element results are compared with the experimental results and confirm the validity of the technique and its use for design purposes.

The Influences of Constitutive Models on the Collapses of OFHC Copper Cylindrical Shells under Impact Compression

An axial collapse test of Oxygen-Free High-Conductivity copper (OFHC) cylindrical specimen subjected to impact against a steel plane target at the velocity range between 64 m/s and 165 m/s was performed on a single gas gun. The deformation process of the OFHC cylindrical shell in the specimen was a sequence of the thermovisco-plastic wave propagation between target plate and the structural plate. The experimental results were simulated numerically by use of LS-DYNA. The influences of OFHC constitutive models on the deformations of OFHC cylindrical shells were shown in the paper. It seems that the Johnson－Cook(J-C) constitutive model gave a better prediction of the shape of the OFHC cylindrical shell in such an impact test. The deformation of cylindrical shell is sensitive to the work-hardening coefficient. The energy absorption behaviors of the OFHC cylindrical shells were also investigated. The energy absorption capability of the shells influenced by their geometries were also shown in the paper.

Nonlinear vibration of microtubules in living cells

Large amplitude flexural vibration behavior is presented for microtubules (MTs) embedded in an elastic matrix of cytoplasm. The microtubule is modeled as a nonlocal shear deformable cylindrical shell which contains small scale effect. The surrounding elastic medium is modeled as a two-parameter elastic foundation. Formulations are based on higher order shear deformation shell theory with a von Kármán-Donnell-type of kinematic nonlinearity. The thermal effect is also included and the material properties are assumed to be temperature-dependent. The small scale parameter e 0 a is estimated by matching the fundamental frequencies from existing results with the numerical results obtained from the nonlocal shear deformable shell model. The numerical results show that the fundamental frequencies of MTs are very sensitive to the small scale parameter e 0 a. The results reveal that the small scale parameter e 0 a reduces the natural frequencies of MTs, but the effect of the small scale parameter on the nonlinear vibration response is relatively weaker when compared to the effect of the small scale parameter on the postbuckling response of MTs.

Nonlocal shear deformable shell model for thermal postbuckling of axially compressed double-walled carbon nanotubes

An investigation is reported of the thermal buckling and postbuckling of axially compressed double-walled carbon nanotubes (CNTs) subjected to a uniform temperature rise. The double-walled carbon nanotube is modeled as a nonlocal shear deformable cylindrical shell, which contains small-scale effects and van der Waals interaction forces. The governing equations are based on higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and include thermal effects. Temperature-dependent material properties, which come from molecular dynamics (MD) simulations, and an initial point defect, which is simulated as a dimple on the tube wall, are both taken into account. The small-scale parameter, e 0 a, is estimated by matching the buckling temperature of CNTs observed from the MD simulation results with the numerical results obtained from the nonlocal shear deformable shell model. The numerical illustrations concern the thermal postbuckling response of perfect and imperfect, single- and double-walled CNTs with different values of compressive load ratio. The results show that buckling temperature and postbuckling behavior of nanotubes are very sensitive to the small-scale parameter. The results reveal that temperature-dependent material properties have a significant effect on the thermal postbuckling behavior of both single- and double-walled CNTs.

Nonlocal Shear Deformable Shell Model for Post-Buckling of Axially Compressed Double-Walled Carbon Nanotubes Embedded in an Elastic Matrix

Buckling and post-buckling analysis is presented for axially compressed double-walled carbon nanotubes (CNTs) embedded in an elastic matrix in thermal environments. The double-walled carbon nanotube is modeled as a nonlocal shear deformable cylindrical shell, which contains small scale effects and van der Waals interaction forces. The surrounding elastic medium is modeled as a tensionless Pasternak foundation. The post-buckling analysis is based on a higher order shear deformation shell theory with the von Kármán–Donnell-type of kinematic nonlinearity. The thermal effects are also included and the material properties are assumed to be temperature-dependent and are obtained from molecular dynamics (MD) simulations. The nonlinear prebuckling deformations of the shell and the initial local point defect, which is simulated as a dimple on the tube wall, are both taken into account. A singular perturbation technique is employed to determine the post-buckling response of the tubes and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the tube and the elastic medium. The small scale parameter e0a is estimated by matching the buckling loads of CNTs observed from the MD simulation results with the numerical results obtained from the nonlocal shear deformable shell model. Numerical solutions are presented to show the post-buckling behavior of CNTs surrounded by an elastic medium of conventional and tensionless Pasternak foundations. The results show that buckling and post-buckling behavior of CNTs is very sensitive to the small scale parameter e0a. The results reveal that the unilateral constraint has a significant effect on the post-buckling response of CNTs when the foundation stiffness is sufficiently large.

Buckling and postbuckling of radially loaded microtubules by nonlocal shear deformable shell model

This paper presents an investigation on the buckling and postbuckling of microtubules (MTs) subjected to a uniform external radial pressure in thermal environments. The microtubule is modeled as a nonlocal shear deformable cylindrical shell which contains small scale effects. The governing equations are based on higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and include the extension-twist and flexural-twist couplings. The thermal effects are also included and the material properties are assumed to be temperature-dependent. A singular perturbation technique is employed to determine the buckling pressure and postbuckling equilibrium paths. The small scale parameter e 0 a is estimated by matching the buckling pressure of MTs measured from the experiments with the numerical results obtained from the nonlocal shear deformable shell model. The numerical results show that buckling pressure and postbuckling behavior of MTs are very sensitive to the small scale parameter e 0 a. The results reveal that the 13_3 microtubule has a stable postbuckling path, whereas the 13_2 microtubule has an unstable postbuckling behavior due to the presence of skew angles.

Nonlocal shear deformable shell model for postbuckling of axially compressed microtubules embedded in an elastic medium

Buckling and postbuckling analysis is presented for axially compressed microtubules (MTs) embedded in an elastic matrix of cytoplasm. The microtubule is modeled as a nonlocal shear deformable cylindrical shell which contains small scale effects. The surrounding elastic medium is modeled as a Pasternak foundation. The governing equations are based on higher order shear deformation shell theory with a von Kármán-Donnell-type of kinematic nonlinearity and include the extension-twist and flexural-twist couplings. The thermal effects are also included and the material properties are assumed to be temperature-dependent. The small scale parameter e (0) a is estimated by matching the buckling load from their vibrational behavior of MTs with the numerical results obtained from the nonlocal shear deformable shell model. The numerical results show that buckling load and postbuckling behavior of MTs are very sensitive to the small scale parameter e (0) a. The results reveal that the MTs under axial compressive loading condition have an unstable postbuckling path, and the lateral constraint has a significant effect on the postbuckling response of a microtubule when the foundation stiffness is sufficiently large.

Torsional buckling and postbuckling of double-walled carbon nanotubes by nonlocal shear deformable shell model

Abstract This paper presents an investigation on the buckling and postbuckling of double-walled carbon nanotubes (CNTs) subjected to torsion in thermal environments. The double-walled carbon nanotube is modeled as a nonlocal shear deformable cylindrical shell which contains small scale effects and van der Waals interaction forces. The governing equations are based on higher order shear deformation shell theory with a von Karman–Donnell-type of kinematic nonlinearity and include the extension-twist and flexural-twist couplings. The thermal effects are also included and the material properties are assumed to be temperature-dependent and are obtained from molecular dynamics (MD) simulations. The small scale parameter e 0 a is estimated by matching the buckling torque of CNTs observed from the MD simulation results with the numerical results obtained from the nonlocal shear deformable shell model. The results show that buckling torque and postbuckling behavior of CNTs are very sensitive to the small scale parameter e 0 a . The results reveal that the size-dependent and temperature-dependent material properties have a significant effect on the torsional buckling and postbuckling behavior of both single-walled and double-walled CNTs.

Analysis of Nonlinear Bulging of Liquid-Filled Cylindrical Shells Under Local Dynamic Loading

Consideration is given to a nonlinear problem on the nonstationary deformation of cylindrical shells filled with a perfect incompressible liquid and subjected to radial pulse loading distributed along a part of the lateral surface