Instability Of Shells Research Articles

Study on Evolution Characteristics and Instability Model of Overburden Stress Shell with the Longwall Mining along Strike

Roof fracture is one of the main reasons for dynamic disaster in working face. During the process of long wall mining, due to the continuous fracture and collapse of roof, a stress shell composed of high stress is formed around the surrounding rock of the stope. The gravity of the overlying rock is transferred to the coal body around the stope through the stress shell. With the advancing of the working face, the stress shell has undergone the dynamic evolution process of the initial shell, extension shell, and flat shell. Based on the theory of shell and plate, the mechanical model of elliptical thin rock plate is constructed. The stress and bending moment distribution expressions of elliptic structure are obtained under two boundary conditions: the surrounding fixed-supported edges and simply supported edges. The results show that cracks begin to appear at the middle point of the semimajor axis and propagate along both ends of the semimajor axis. Then the fracture begins at the end of the semiminor axis, and the crack extends along the arc direction, forming an “X-O” type fracture. Finally, the mechanical nature of the stress shell instability is the result of the tensile fracture of the bedrock at the top of the shell.

The effect of uncertainty sources on the dynamic instability of CNT-reinforced porous cylindrical shells integrated with piezoelectric layers under electro-mechanical loadings

In the present study, the influence of the propagation of different uncertainty sources on the dynamic stability of a sandwich carbon nanotube-reinforced (CNT) cylindrical shell under a pulse axial load is investigated. The core of the cylindrical shell is composed of a porous metal matrix reinforced with CNTs. The core is surrounded by piezoelectric layers. Five distributions of CNT reinforcements in the shell thickness are considered in this study. Moreover, it is assumed that the shell rests on an elastic foundation. Two dynamic curves and the Chebyshev model are combined to examine the dynamic stability probability of functionally-graded carbon nanotube-reinforced cylindrical shells surrounded by piezoelectric layers (FG-CNT-P). The stability of the shell is investigated under both mechanical dynamic load and electrical potential. The effective material properties of the functionally graded carbon nanotube shells are estimated through a micromechanical model based on the extended rule of mixture. The virtual work method based on Sanders’ nonlinear theory and the higher-order shear deformation theory is used to derive the dynamic equilibrium equations of the CNT cylindrical shells surrounded by piezoelectric layers and an elastic medium. The Fourier differential quadrature method is used to solve these equations. The analysis results are presented in terms of the probabilistic density functions (PDFs) of the buckling loads of the composite shells. Accordingly, the probabilistic distributions of the buckling loads of the shells corresponding to the first three modes of buckling are overlapping. Hence, the first mode of buckling determined in a deterministic study may not always be the dominant failure mode of the structure. Consequently, a great attention is paid to this phenomenon and the effects of different factors on it. Finally, the sensitivities of the critical loads of the FG-CNT-P cylindrical shells to different sources of uncertainty are assessed through a sensitivity analysis.

Dynamic Instability of Shallow Shells Interacting with a Three-Dimensional Potential Gas Flow

To study the interaction of a vibrating shallow shell with a three-dimensional subsonic gas flow, we deduce a system of hypersingular integral equations for the aerodynamic derivatives of the pressure drop. This system of equations is convenient for the solution of the problems of aeroelasticity. We solve the system of hypersingular integral equations by using a numerical approach based on the discrete vortex method. To model vibrations of shallow shells, we deduce a system of ordinary differential equations with the help of the assumed-mode method. We also perform the numerical investigation of dynamic instability of the equilibrium state of a shallow shell in the subsonic gas flow.

Instability-driven shape forming of fiber reinforced polymer frames

Thin fiber reinforced polymer (FRP) composites are widely implemented in adaptive and morphing structures. However, realization of the necessary complex 3-dimensional FRP structures requires the use of expensive molds thereby limiting the design space and flexibility. Using the elastic strain energy of pre-stretched membranes holds potential for addressing this challenge. In this work, a novel manufacturing technique for fabricating 3-dimensional FRP structures moldlessly is presented where pre-stretched membranes are used to drive out-of-plane buckling instabilities of FRP composite shells. To explore the potential of this approach, a simple square frame design is investigated. An analytical model based on high deformation beam buckling theory is developed for understanding the parameters driving the out-of-plane behavior of these structures. Experimental and finite element results are used for model validation and reveal excellent agreement, with errors less than 10% over a large portion of the design space. Analytical and finite element models demonstrate that the out-of-plane deformation can be tailored by varying the structure’s geometric and material parameters. A new design space for FRP composite laminates is characterized, enabling highly flexible design. The manufacturing and modeling techniques can be extended to other geometries for the realization and analysis of arbitrarily complex surfaces.

Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

The application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure (P) – inflation (lambda or v) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

Buckling analysis of ring stiffened thin cylindrical shell under external pressure

Submarine pressure hulls, fire-tube boilers, vacuum tanks, oil well casings, submersibles, underground pipelines, tunnels, rocket motor casing, etc., are some of the examples of thin cylindrical shell structures which collapse due to buckling under uniform pressure. To enhance the buckling strength of bare cylindrical shells, one of the best solutions is to stiffen them with ring stiffeners. In this work in order to predict the shell instability failure mode (SIFM) and general instability failure mode (GIFM) FE models are generated and analysed using buckling analysis of general-purpose FE software ANSYS. The numerical results obtained using FE analysis are compared with published analytical and experimental results. Hence in the present study efforts are taken to develop FE models to predict global and shell instability failure modes of externally ring stiffened cylindrical shells by using linear FE analysis. It is proposed to use full/half bare cylindrical shell FE models (L/R ratio upto 200) to determine SIFM and FE models with shell281- Beam189 (for stiffeners) can be used to determine GIFM. The developed FE models are validated by comparing numerical results with experimental results published by Seleim and Roorda [25]. By using both proposed FE models it is possible to predict the failure modes namely SIFM and GIFM, comparing their values of critical buckling pressures. The lower pressure value can indicate the possible failure mode.

Dynamic instability analysis of general shells reinforced with polymeric matrix and carbon fibers using a coupled IG-SFSM formulation

In the present article, the dynamic instability of shells subjected to periodic in-plane and external pressure loadings in thermal environment is considered. The considered shells are made of laminated composite of carbon fibers and the reinforced polymeric matrix by randomly oriented carbon-nanotubes (CNTs) which is functionally distributed in each layer. Consequently, the considered material is made of three phases of fiber/polymer/CNT. The extended governing equilibrium and compatibility equations are solved by a coupled formulation which combines the isogeometric analysis (IGA) and finite element method (FEM) in two orthogonal direction of the parametric space. Since the proposed coupled IGA-FE method is developed in form of the finite strip (FS) elements, it is named isogeometric B-spline finite strip method (IG-SFSM). In order to perform the parametric studies, the effects of various geometrical and mechanical properties, boundary conditions and temperatures are considered. The obtained results show that IG-SFSM is an applicable method for dynamic instability assessment of the shells which can reduce the computational efforts comparing to the other prevalent methods such as FEM and element-free family, and also reduce the restrictions and shortcomings of the standard IGA methods.

Influence of Stress Loading Path on the Limit of Plastic Wrinkling and Instability of Plates and Shells

Influence of Stress Loading Path on the Limit of Plastic Wrinkling and Instability of Plates and Shells

Robustness of Empirical Vibration Correlation Techniques for Predicting the Instability of Unstiffened Cylindrical Composite Shells in Axial Compression.

Thin-walled carbon fiber reinforced plastic (CFRP) shells are increasingly used in aerospace industry. Such shells are prone to the loss of stability under compressive loads. Furthermore, the instability onset of monocoque shells exhibits a pronounced imperfection sensitivity. The vibration correlation technique (VCT) is being developed as a nondestructive test method for evaluation of the buckling load of the shells. In this study, accuracy and robustness of an existing and a modified VCT method are evaluated. With this aim, more than 20 thin-walled unstiffened CFRP shells have been produced and tested. The results obtained suggest that the vibration response under loads exceeding 0.25 of the linear buckling load needs to be characterized for a successful application of the VCT. Then the largest unconservative discrepancy of prediction by the modified VCT method amounted to ca. 22% of the critical load. Applying loads exceeding 0.9 of the buckling load reduced the average relative discrepancy to 6.4%.

Turbulence and Energetic Particles in Radiative Shock Waves in the Cygnus Loop. II. Development of Postshock Turbulence

Abstract Radiative shock waves in the Cygnus Loop and other supernova remnants show different morphologies in [O iii] and Hα emission. We use HST spectra and narrowband images to study the development of turbulence in the cooling region behind a shock on the west limb of the Cygnus Loop. We refine our earlier estimates of shock parameters that were based upon ground-based spectra, including ram pressure, vorticity, and magnetic field strength. We apply several techniques, including Fourier power spectra and the Rolling Hough Transform, to quantify the shape of the rippled shock front as viewed in different emission lines. We assess the relative importance of thermal instabilities, the thin shell instability, upstream density variations, and upstream magnetic field variations in producing the observed structure.

A robust and computationally efficient finite element framework for coupled electromechanics

Electro-active polymers (EAPs) are increasingly becoming popular materials for actuators, sensors, and energy harvesters. To simulate the complex behaviour of actuators under coupled loads, particularly in the realm of soft robotics, biomedical engineering and energy harvesting, finite element simulations are proving to be an indispensable tool. In this work, we present a novel finite element framework for the simulation of coupled static and dynamic electromechanical interactions in electro-active polymeric materials. To model the incompressible nature of EAPs, a two-field mixed displacement–pressure formulation which, unlike the commonly-used mixed three-field and F-bar formulations, is applicable for both nearly and fully incompressible materials, is employed. For the spatial discretisation, innovative quadratic Bézier triangular and tetrahedral elements are used. The governing equations for the coupled electromechanical problem are solved using a monolithic scheme; for elastodynamics simulations, a state-of-the-art implicit time integration is adapted. The accuracy and the computational efficiency of the proposed framework are demonstrated by studying several benchmark examples in computational electromechanics which include simulations of a spherical gripper in elastostatics and a dielectric pump in elastodynamics. Such complex simulations clearly depict the advantages of the proposed finite element framework over the Q1/P0 and Q1-F-bar elements. Furthermore, the superiority of the proposed framework in accurately capturing complex coupled electromechanical interactions in thin electro-active polymeric shells is demonstrated by studying a thin helical actuator under different excitation frequencies and by reproducing buckling instabilities in thin semi-cylindrical and semi-spherical shells. With the ability to simulate various elastostatics and elastodynamics phenomena using a single finite element framework for bulk as well as thin dielectric elastomers while using coarse structured or unstructured meshes that can be readily generated using existing mesh generators, this novel framework offers a robust, accurate, and computationally efficient numerical framework for computational electromechanics.

Predicting delayed instabilities in viscoelastic solids.

Determining the stability of a viscoelastic structure is a difficult task. Seemingly stable conformations of viscoelastic structures may gradually creep until their stability is lost, while a discernible creeping in viscoelastic solids does not necessarily lead to instability. In lieu of theoretical predictive tools for viscoelastic instabilities, we are presently limited to numerical simulation to predict future stability. In this work, we describe viscoelastic solids through a temporally evolving instantaneous reference metric with respect to which elastic strains are measured. We show that for incompressible viscoelastic solids, this transparent and intuitive description allows to reduce the question of future stability to static calculations. We demonstrate the predictive power of the approach by elucidating the subtle mechanism of delayed instability in thin elastomeric shells, showing quantitative agreement with experiments.

Massive core/star formation triggered by cloud–cloud collision: Effect of magnetic field

Abstract We study the effect of magnetic field on massive dense core formation in colliding unequal molecular clouds by performing magnetohydrodynamic simulations with sub-parsec resolution (0.015 pc) that can resolve the molecular cores. Initial clouds with the typical gas density of the molecular clouds are immersed in various uniform magnetic fields. The turbulent magnetic fields in the clouds consistent with the observation by Crutcher et al. (2010, ApJ, 725, 466) are generated by the internal turbulent gas motion before the collision, if the uniform magnetic field strength is 4.0 μG. The collision speed of 10 km s−1 is adopted, which is much larger than the sound speeds and the Alfvén speeds of the clouds. We identify gas clumps with gas densities greater than 5 × 10−20 g cm−3 as the dense cores and trace them throughout the simulations to investigate their mass evolution and gravitational boundness. We show that a greater number of massive, gravitationally bound cores are formed in the strong magnetic field (4.0 μG) models than the weak magnetic field (0.1 μG) models. This is partly because the strong magnetic field suppresses the spatial shifts of the shocked layer that should be caused by the nonlinear thin shell instability. The spatial shifts promote the formation of low-mass dense cores in the weak magnetic field models. The strong magnetic fields also support low-mass dense cores against gravitational collapse. We show that the numbers of massive, gravitationally bound cores formed in the strong magnetic field models are much larger than in the isolated, non-colliding cloud models, which are simulated for comparison. We discuss the implications of our numerical results on massive star formation.

Shape morphing in molecular cloud-cloud collision affected by coherent instabilities

This paper presents the results of numerical simulation of Molecular Cloud-Cloud Collision in the under the head-on and glancing impacts. The calculations are performed according to different colliding scenarios between two dissimilar (by size, displacement and inner distribution of matter) spherical clouds. The aim is to study the matter compression in clumps and filaments formed, the generation of vortex coherent structures in new formations imbalanced after the collision and to analyze the influence of emergent instabilities on clouds morphing. In-house Eulerian code is used to perform a numerical experiment on high-performance computers. Nebula shaping and the compression oscillations in a shock core depend on initial impulse of colliding molecular clouds. The article gives a morphological analysis of gas redistribution by density under local compression in a bow-shock layer and filaments which are generated. The mechanism of perturbations to matter turbulization, fragmentation and disruption of new formations is revealed. Strong shock compression pulsations generated in the gas core and waved rarefactions in the interstellar medium are interpreted as possible Nonlinear Thin Shell Instability and Kelvin–Helmholtz Instability aftereffect.

Coupling effects and thin-shell corrections for surface instabilities of cylindrical fluid shells.

We show that when linear azimuthal perturbations on the surfaces of a fluid shell are regrouped according to α^{m}, they can be divided into Bell model terms, coupling terms, and the newly identified thin-shell correction terms, where α is the ratio of R_{out} to R_{in}, and m is the mode number of a given unstable mode on the surfaces. It is also revealed that α^{m} is a convenient index variable of coupling effects, with which we show that the evolution of instability is composed of three stages, i.e., strongly coupled stage, transition stage, and uncoupled stage. Roughly, when α^{m}<6, the fluid shell is in the strongly coupled stage, where both coupling effects and the newly identified thin-shell corrections play important roles. Strong feed through is expected to be observed. Theuncoupled stage is reached at α^{m}∼36, where Bell's model of independent surface holds. In between is the transition stage, where mode competitions on the two surfaces are expected to be observed. These results afford an intuitive picture which is easy to use in guiding the design of experiments. They may also help to quickly grasp major features of instability experiments of this kind.

Instability of Conical Shells with Multiple Dimples under Axial Compression

Thin-walled conical shells are primary structures in offshore application. Presence of imperfection can considerably reduce the load carrying capacity of such structures when in use. This study examines the buckling behavior of axially compressed imperfect steel cones using the multiple perturbation load analysis (MPLA). This is both a numerical and experimental study. Eight conical shell test models were manufactured in pairs and collapsed under axial compression: two perfect, and the remaining six with MPLA imperfection amplitude, A, of 0.56, 1.12 and 1.68 having two equally-spaced dimples on each cones. Experimental test results for all the conical shell models and the accompanying numerical predictions are given in this paper. Repeatability of experimental data was good. The errors within each pair were 3%, 13%, 1% and 0%. In addition, there was a good comparison between experimental and numerical data. The ratio of experimental to numerical buckling loads varies from 0.91 to 1.13.

Nonlinear Limit Cycle Oscillation and Flutter Analysis of Clamped Curved Plates

This Paper studies the instability (flutter) and poststability limit cycle oscillations of elastic shallow shells in a supersonic gas flow. In a previous paper by the authors, a nonlinear dynamic aeroelastic analysis of streamwise square curved plates was made to compare with the experimental results of Anderson. In the present Paper, computational results are presented for a much larger range of several parameters, which are important for flutter and limit cycle oscillations including both spanwise and streamwise curved plates with various aspect ratios, various boundary conditions, and the effects of static pressure and in-plane mechanical loadings. No previous study has included such a wide range of parameters and parameter values. Von Kármán shallow shell theory, a modal expansion along with the Galerkin method, and the piston theory aerodynamic model for supersonic/hypersonic flow are employed to obtain these results.

Synthesis and Electrochemical Characterization of Silk Fibroin Micro/Nano Particles

In this study, the dynamic instability of three-layered cylindrical shells containing a functionally graded (FG) interlayer subjected to static and time dependent periodic axial compressive loads are investigated. The governing relations, modified Donnell type dynamic stability and deformation compatibility equations are derived. The governing equations are reduced Mathieu–Hill equation by using Galerkin׳s method and the expressions for boundaries of unstable regions of three-layered cylindrical shell with an FG interlayer are found. Finally, the effects of variations of volume fractions of FG interlayer and shell characteristics on the magnitudes of boundaries of unstable regions are studied numerically.

Shell instability analysis by using mixed interpolation

In this paper, buckling and post-buckling behavior of plates and shells are investigated. An efficient triangular shell element having six nodes is employed in this study. To consider large deflection and rotation, total Lagrangian formulation is utilized. The authors employ mixed interpolation for strain fields to deviate shear and membrane locking phenomena. The effects of different types of boundary conditions and geometry properties of plates and shells are studied. An almost complete literature review is also provided to show the progress of researches about the current topics. Various states of buckling including bifurcation and snap-through are assessed in different problems. In this study, the popular benchmarks of shell structures are analyzed to show the accuracy and capability of element. In addition, some new benchmarks which can be used by other researchers are also introduced and solved. Further, a comparison study between the proposed element and NLDKGQ element in OpenSees software is implemented for some complex curved shell structures.

Effects of LESA in Three-dimensional Supernova Simulations with Multidimensional and Ray-by-ray-plus Neutrino Transport

Abstract A set of eight self-consistent, time-dependent supernova (SN) simulations in three spatial dimensions (3D) for 9 and 20 M ⊙ progenitors is evaluated for the presence of dipolar asymmetries of the electron lepton-number emission as discovered by Tamborra et al. and termed lepton-number emission self-sustained asymmetry (LESA). The simulations were performed with the Aenus–Alcar neutrino/hydrodynamics code, which treats the energy- and velocity-dependent transport of neutrinos of all flavors by a two-moment scheme with algebraic M1 closure. For each of the progenitors, results with fully multidimensional (FMD) neutrino transport and with ray-by-ray-plus (RbR+) approximation are considered for two different grid resolutions. While the 9 M ⊙ models develop explosions, the 20 M ⊙ progenitor does not explode with the employed version of simplified neutrino opacities. In all 3D models we observe the growth of substantial dipole amplitudes of the lepton-number (electron neutrino minus antineutrino) flux with stable or slowly time-evolving direction and overall properties fully consistent with the LESA phenomenon. Models with RbR+ transport develop LESA dipoles somewhat faster and with temporarily higher amplitudes, but the FMD calculations exhibit cleaner hemispheric asymmetries with a far more dominant dipole. In contrast, the RbR+ results display much wider multipole spectra of the neutrino emission anisotropies with significant power also in the quadrupole and higher-order modes. Our results disprove speculations that LESA is a numerical artifact of RbR+ transport. We also discuss LESA as a consequence of a dipolar convection flow inside of the nascent neutron star and establish, tentatively, a connection to Chandrasekhar’s linear theory of thermal instability in spherical shells.