Wrinkling of pressurized elastic shells

We study the formation of localized structures formed by the point loading of an internally pressurized elastic shell. While unpressurized shells (such as a ping-pong ball) buckle into polygonal structures, we show that pressurized shells are subject to a wrinkling instability. We study wrinkling in depth, presenting scaling laws for the critical indentation at which wrinkling occurs and the number of wrinkles formed in terms of the internal pressurization and material properties of the shell. These results are validated by numerical simulations. We show that the evolution of the wrinkle length with increasing indentation can be understood for highly pressurized shells from membrane theory. These results suggest that the position and number of wrinkles may be used in combination to give simple methods for the estimation of the mechanical properties of highly pressurized shells.     

Moving loads on elastic cylindrical shells

This paper presents a theoretical analysis of the axially-symmetric, steady-state response of a linearly-elastic, homogeneous, infinitely-long, cylindrical shell, subjected to a ring load traveling at a constant velocity. The Fourier transform method in conjunction with the contour integral has been applied to obtain the steady-state response. A numerical illustration is given.     

Subcritical scattering from buried elastic shells

Buried objects have been largely undetectable by traditional high-frequency sonars due to their insignificant bottom penetration. Further, even a high grazing angle sonar approach is vastly limited by the coverage rate dictated by the finite water depth, making the detection and classification of buried objects using low frequency, subcritical sonar an interesting alternative. On the other hand, such a concept would require classification clues different from the traditional high-resolution imaging and shadows to maintain low false alarm rates. A potential alternative, even for buried targets, is classification based on the acoustic signatures of man-made elastic targets. However, the elastic responses of buried and proud targets are significantly different. The objective of this work is to identify, analyze, and explain some of the effects of the sediment and the proximity of the seabed interface on the scattering of sound from completely and partially buried elastic shells. The analysis was performed using focused array processing of data from the GOATS98 experiment carried out jointly by MIT and SACLANTCEN, and a new hybrid modeling capability combining a virtual source-or wave-field superposition-approach with an exact spectral integral representation of the Green's functions for a stratified ocean waveguide, incorporating all multiple scattering between the object and the seabed. Among the principal results is the demonstration of the significant role of structural circumferential waves in converting incident, evanescent waves into backscattered body waves, emanating to the receivers at supercritical grazing angles, in effect making the target appear closer to the sonar than predicted by traditional ray theory.     

Meniscus instability in a thin elastic film

A new kind of meniscus instability leading to the formation of stationary fingers with a well-defined spacing has been observed in experiments with elastomeric films confined between a plane rigid glass and a thin curved glass plate. The wavelength of the instability increases linearly with the thickness of the confined film, but it is remarkably insensitive to the compliance and the energetics of the system. However, lateral amplitude (length) of the fingers depends on the compliance of the system and on the radius of curvature of the glass plate. A simple linear stability analysis is used to explain the underlying physics and the key observed features of the instability.     

Free vibrations of elastic circular toroidal shells

In this paper, the free vibrations of elastic in vacuo circular toroidal shells under different boundary conditions are studied using the linear Sanders thin shell theory. Beam functions are used to describe the motion along the meridional direction whilst trigonometric functions are used to represent the deformation of the cross section. It is shown that both the natural frequencies and the mode shapes can be accurately predicted as long as the employed beam functions satisfy the boundary conditions at the ends of the shells. The dependence of the free vibration characteristics of an elastic toroidal shell upon boundary conditions and toroidal to cross-sectional radius ratio is also illustrated and explained in this paper.     

General theory of micropolar elastic thin shells

The paper formulates general hypotheses of micropolar elastic thin shells that are given asymptotic validation. Using these hypotheses and three-dimensional Cosserat (micropolar, asymmetric) theory of elasticity, general two-dimensional applied models of micropolar elastic thin shells with independent displacement and rotation fields, constrained rotation and low shear rigidity are constructed to suit dimensionless physical parameters of the shell material. The constructed micropolar shell models take into complete account transverse shear strain and related strain. Models of micropolar elastic thin plates and beams are particular cases of the constructed micropolar shell models. An axially symmetric stress-strain state problem of a hinged cylindrical micropolar shell is considered. Numerical analysis is used to demonstrate effective strength and rigidity characteristics of micropolar elastic shells.     

Model reduction for parametric instability analysis in shells conveying fluid

Flexible pipes conveying fluid are often subjected to parametric excitation due to time-periodic flow fluctuations. Such systems are known to exhibit complex instability phenomena such as divergence and coupled-mode flutter. Investigators have typically used weighted residual techniques, to reduce the continuous system model into a discrete model, based on approximation functions with global support, for carrying out stability analysis. While this approach is useful for straight pipes, modelling based on FEM is needed for the study of complicated piping systems, where the approximation functions used are local in support. However, the size of the problem is now significantly larger and for computationally efficient stability analysis, model reduction is necessary. In this paper, model reduction techniques are developed for the analysis of parametric instability in flexible pipes conveying fluids under a mean pressure. It is shown that only those linear transformations which leave the original eigenvalues of the linear time invariant system unchanged are admissible. The numerical technique developed by Friedmann and Hammond (Int. J. Numer. Methods Eng. Efficient 11 (1997) 1117) is used for the stability analysis. One of the key research issues is to establish criteria for deciding the basis vectors essential for an accurate stability analysis. This paper examines this issue in detail and proposes new guidelines for their selection.     

Melting and elastic shear instability of alkali halides

Ultrasonic data for the elastic moduli c_ij as functions of pressure and temperature are used to calculate critical temperatures T_cr(P = 0) and their initial pressure derivatives (?T_cr/?P)_P=0 for the elastic stability of the alkali halides with the rocksalt and CsCl structures. The stability criteria used for the two structures are c′ = ½(c₁₁ ? c₁₂) = 0 and c₄₄ = 0, respectively. The critical parameters T_cr(P = 0) and (?T_cr/?P)_P=0 exhibit remarkable correlations with the melting temperatures T_m(P = 0) and their initial pressure derivatives (?T_m/?P)_P=0, offering strong support to the existence of a connexion between shear instability and melting, as postulated by previous investigators. Critical parameters for the rocksalt oxides MgO, CaO, and SrO compare favourably with the critical and melting parameters for their fluoride analogues LiF, NaF and KF respectively.     

Contact instability in adhesion and debonding of thin elastic films

Based on experiments and 3D simulations, we show that a soft elastic film during adhesion and debonding from a rigid flat surface undergoes morphological transitions to pillars, labyrinths, and cavities, all of which have the same lateral pattern length scale, lambda close to lambda/H approximately 3 for thick films, H > 1 microm . The linear stability analysis and experiments show a new thin film regime where lambda/H approximately equal to 3 + 2pi(lambda/3 muH)1/4 (gamma is surface tension, mu is shear modulus) because of a significant surface energy penalty (for example, lambda/H approximately equal to 6 for H = 200 nm; mu = 1 MPa).     

有吸收流体介质中典型弹性壳体的共振散射

研究了环境流体有吸收时弹性球壳和圆柱壳的共振散射特性。利用严格弹性理论和分离变量法导出的经典简正级数解仍然成立。但是,散射形态函数要根据介质吸收而进行修正,否则将得到不合理的结果。重新定义了有吸收介质中的反向散射形态函数,计算了各种吸收条件下中空和有固体填充物的弹性球壳和圆柱壳的形态函数。结果表明,环境流体的吸收导致中频段的吻合共振显著减弱,但对壳内填充物的低频共振影响较小。     

Resonance scattering of sound by spheroidal elastic bodies and shells

The resonances of spheroidal elastic bodies (prolate and oblate) in the form of solid bodies and shells are determined using dynamic elasticity theory and Debye potentials. In addition to analytic solutions, results of computer calculations are presented for the angular characteristics and scattering cross sections of spheroidal elastic bodies.     

Resonance scattering of canonical elastic shells in absorbing fluid medium

Resonance scattering of elastic spherical shell and cylindrical shell while the surrounding fluid medium has absorption is studied. The normal mode solution derived using exact elastic theory and the separation of variables is still applicable. However, the scattering form function has to be modified for the absorbing medium, otherwise the unreasonable result would be obtained. The backscattering form function in the absorbing medium is redefined, and the form function of elastic spherical and cylindrical shell with vacuum or solid matter filled is calculated in various absorption conditions. The results show that the absorption of surrounding fluid leads to notable attenuation of the coincidence resonances in the mid-frequency, but it has a little influence on the low-frequency resonance scattering induced by the filler inside the shell.     

黏性流体中超细长弹性杆的动力学不稳定性

基于坐标基矢摄动的方法研究了黏性流体中超细长弹性杆动力学稳定性判据与失稳后的模态选择,推导出了黏性介质中超细长弹性杆Kirchoff动力学方程的一阶摄动表示,即线性的二阶偏微分方程组.以平面扭转DNA环为例,说明了以上结果的应用,得到了平面扭转DNA环的稳定性判据及其稳定的临界区域,讨论了其失稳后的模态选择及黏性阻力对其的影响.     

Driven self-assembly of hard nanoplates on soft elastic shells

The driven self-assembly behaviors of hard nanoplates on soft elastic shells are investigated by using molecular dynamics(MD) simulation method, and the driven self-assembly structures of adsorbed hard nanoplates depend on the shape of hard nanoplates and the bending energy of soft elastic shells. Three main structures for adsorbed hard nanoplates,including the ordered aggregation structures of hard nanoplates for elastic shells with a moderate bending energy, the collapsed structures for elastic shells with a low bending energy, and the disordered aggregation structures for hard shells,are observed. The self-assembly process of adsorbed hard nanoplates is driven by the surface tension of the elastic shell,and the shape of driven self-assembly structures is determined on the basis of the minimization of the second moment of mass distribution. Meanwhile, the deformations of elastic shells can be controlled by the number of adsorbed rods as well as the length of adsorbed rods. This investigation can help us understand the complexity of the driven self-assembly of hard nanoplates on elastic shells.