Stability analysis of linear thin shells

Shell structure is widely used in engineering area. The purpose of this dissertation is to show the behavior of a thin shell under external load, especially for long cylindrical shell under compressive load, I analyzed not only for linear elastic problem and also for buckling problem, and by using finite element analysis it shows that the imperfection of a cylinder could affect the critical load which means the buckling capability of this cylinder. For linear elastic problem, I compared the theoretical results with the results got from Straus7 and Abaqus, and the results are really close. For the buckling problem I did the same: compared the theoretical and Abaqus results, the error is less than 1%, but in reality, it’s not possible to reach the theoretical buckling capability due to the imperfection of the cylinder, so I put different imperfection for the cylinder in Abaqus, and found out that with the increasing of the percentage of imperfection, the buckling capability decreases, for example 10% imperfection could decrease 40% of the buckling capability, and the outcome meet the buckling behavior in reality.

Nonlinear theories for thin shells,

"Contract Nonr 1866(02)."

Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling

We present an isogeometric thin shell formulation for multi-patches based on rational splines over hierarchical T-meshes (RHT-splines). Nitsche’s method is employed to efficiently couple the patches. The RHT-splines have the advantages of allowing a computationally feasible local refine- ment, are free from linear independence, possess high order continuity and satisfy the partition of unity and non-negativity, properties. In addition, C 1 continuity of the RHT-splines obviates to use of rotational degrees of freedom. The good performance of the present method is demonstrated by a number of numerical examples.

Analytical Investigations 0n Collapse of Cylindrical Submarine Shells

Submarine hull structure is a watertight envelope, under hydrostatic pressure when in operation. Stiffened cylindrical shells constitute the major portion of these submarine hulls and these thin shells under compression are susceptible to buckling failure. Normally loss of stability occurs at the limit point rather than at the bifurcation point and the stability analysis has to consider the change in geometry at each load step. Hence geometric nonlinear analysis of the shell forms becomes. a necessity. External hydrostatic pressure will follow the deformed configuration of the shell and hence follower force effect has to be accounted for. Computer codes have been developed based on all-cubic axisymmetric cylindrical shell finite element and discrete ring stiffener element for linear elastic, linear buckling and geometric nonIinear analysis of stiffened cylindrical shells. These analysis programs have the capability to treat hydrostatic pressure as a radial load and as a follower force. Analytical investigations are carried out on two attack submarine cylindrical hull models besides standard benchmark problems. In each case, the analysis has been carried out for interstiffener, interdeepframe and interbulkhead configurations. The shell stiffener attachment in each of this configuration has been represented by the simply supported-simply supported, clamped-clamped and fixed-fixed boundary conditions in this study. The results of the analytical investigations have been discussed and the observations and conclusions are described. Rotation restraint at the ends is influential for interstiffener and interbulkhead configurations and the significance of axial restraint becomes predominant in the interbulkhead configuration. The follower force effect of hydrostatic pressure is not significant in interstiffener and interdeepframe configurations where as it has very high detrimental effect on buckling pressure on interbulkhead configuration. The geometric nonlinear interbulkhead analysis incorporating follower force effect gives the critical value of buckling pressure and this analysis is recommended for the determination of collapse pressure of stiffened cylindrical submarine shells.

Awaking the vacuum with spheroidal shells

It has been shown that well-behaved spacetimes may induce the vacuum fluctuations of some nonminimally coupled free scalar fields to go through a phase of exponential growth. Here, we discuss this mechanism in the context of spheroidal thin shells emphasizing the consequences of deviations from spherical symmetry. © 2013 American Physical Society.

Evaluation of the Design of Komendant's Cycloidal, Thin Shell Roofs At the Kimbell Art Museum Using Finite Element Analysis

The analysis of Komendant's design of the Kimbell Art Museum was carried out in order to determine the effectiveness of the ring beams, edge beams and prestressing in the shells of the roof system. Finite element analysis was not available to Komendant or other engineers of the time to aid them in the design and analysis. Thus, the use of this tool helped to form a new perspective on the Kimbell Art Museum and analyze the engineer's work. In order to carry out the finite element analysis of Kimbell Art Museum, ADINA finite element analysis software was utilized. Eight finite element models (FEM-1 through FEM-8) of increasing complexity were created. The results of the most realistic model, FEM-8, which included ring beams, edge beams and prestressing, were compared to Komendant's calculations. The maximum deflection at the crown of the mid-span surface of -0.1739 in. in FEM-8 was found to be larger than Komendant's deflection in the design documents before the loss in prestressing force (-0.152 in.) but smaller than his prediction after the loss in prestressing force (-0.3814 in.). Komendant predicted a larger longitudinal stress of -903 psi at the crown (vs. -797 psi in FEM-8) and 37 psi at the edge (vs. -347 psi in FEM-8). Considering the strength of concrete of 5000 psi, the difference in results is not significant. From the analysis it was determined that both FEM-5, which included prestressing and fixed rings, and FEM-8 can be successfully and effectively implemented in practice. Prestressing was used in both models and thus served as the main contribution to efficiency. FEM-5 showed that ring and edge beams can be avoided, however an architect might find them more aesthetically appropriate than rigid walls.

Structural transformation of graphite by arc-discharge

The formation of novel structures by the passage of an electric current through graphite is described. These structures apparently consist of hollow three-dimensional graphitic shells bounded by curved and faceted planes, typically made up of two graphene layers. The curved structures were frequently decorated with nano-scale carbon particles, or short nanotubes. In some cases, nanotubes were found to be seamlessly connected to the thin shells, indicating that the formation of the shells and the nanotubes is intimately connected. Small nanotubes or nanoparticles were also sometimes found encapsulated inside the hollow structures, while fullerene-like particles were often seen attached to the outside surfaces. With their high surface areas and structural perfection, the new carbon structures may have applications as anodes of lithium ion batteries or as components of composite materials.

Ultrathin graphitic structures and carbon nanotubes in a purified synthetic graphite

A new class of carbon structure is reported, which consists of microscale graphitic shells bounded by curved and faceted planes containing two to five layers. These structures were originally found in a commercial graphite produced by the Acheson process, followed by a purification treatment. The particles, which could be several hundreds of nanometres in size, were frequently decorated with nanoscale carbon particles, or short nanotubes. In some cases, nanotubes were found to be seamlessly connected to the thin shells, indicating that the formation of the shells and that of the nanotubes are intimately connected. The structures are believed to form during a purification process which involves passing an electric current through the graphite in the presence of a reactive gas. In support of this, it is shown that similar particles can be produced in a standard carbon arc apparatus. With their extremely thin graphene walls and high surface areas, the new structures may have a range of useful properties.

Aspectos quânticos e clássicos da instabilidade de campos fundamentais em espaços-tempos astrofísicos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Thermal buckling of circular cylindrical and conical thin-walled shells

"Aeronautical Research Laboratory. Contract AF 33(616)-3885, Project no. 7(8-1367), Task no. 70524."

Stable isotope ratios in shells of marine organisms

Oxygen and carbon isotope analyses have been carried out on calcareous skeletons of important recent groups of organisms. Annual temperature ranges and distinct developmental stages can be reconstructed from single shells with the aid of the micro-sampling technique made possible by modern mass-spectrometers. This is in contrast to the results of earlier studies which used bulk sampIes. The skeletons analysed are from Bermuda, the Philippines, the Persian Gulf and the continental margin off Peru. In these environments, seasonal salinity ranges and thus annual variations in the isotopic composition of the water are small. In addition, environmental parameters are weIl documented in these areas. The recognition of seasonal isotopic variations is dependant on the type of calcification. Shells built up by carbonate deposition at the margin, such as molluscs, are suitable for isotopic studies. Analysis is more difficult where chambers are added at the margin of the shell but where older chambers are simultaneously covered by a thin veneer of carbonate e. g. in rotaliid foraminifera. Organisms such as calcareous algae or echinoderms that thicken existing calcareous parts as weIl as growing in length and breadth are the most difficult to analyse. All organisms analysed show temperature related oxygen-isotope fractionation. The most recent groups fractionate oxygen isotopes in accordance with established d18O temperature relationships (Tab. 18, Fig. 42). These groups are deep-sea foraminifera, planktonic foraminifera, serpulids, brachiopods, bryozoa, almost all molluscs, sea urchins, and fish (otoliths). A second group of organisms including the calcareous algae Padina, Acetabularia, and Penicillus, as weIl as barnacles, cause enrichment of the heavy isotope 18O. Finally, the calcareous algae Amphiroa, Cymopolia and Halimeda, the larger foraminifera, corals, starfish, and holothurians cause enrichment of the lighter isotope 16O. Organisms causing non-equilibrium fractionation also record seasonal temperature variations within their skeletons which are reflected in stable-oxygen-isotope patterns. With the exception of the green algae Halimeda and Penicillus, all organisms analysed show lower d13C values than calculated equilibrium values (Tab. 18, Fig. 42). Especially enriched with the lighter isotope 12C are animals such as hermatypic corals and larger foraminifera which exist in symbiosis with other organisms, but also ahermatypic corals, starfish, and holothurians. With increasing age of the organisms, seven different d13C trends were observed within the skeletons. 1) No d13C variations are observed in deep-sea foraminifera presumably due to relatively stable environmental conditions. 2) Lower d13C values occur in miliolid larger foraminifera and are possibly related to increased growth with increasing age of the foraminifera. 3) Higher values are found in planktonic foraminifera and rotaliid larger foraminifera and can be explained by a slowing down of growth with increasing age. 4) A sudden change to lower d13C values at a distinct shell size occurs in molluscs and is possibly caused by the first reproductive event. 5) A low-high-Iow cycle in calcareous algae is possibly caused by variations in the stage of calcification or growth. 6) A positive correlation between d18O and d13C values is found in some hermatypic corals, all ahermatypic corals, in the septa of Nautilus and in the otoliths of fish. In hermatypic corals from tropical areas, this correlation is the result of the inverse relationship between temperature and light caused by summer cloud cover; in other groups it is inferred to be due to metabolic processes. 7) A negative correlation between d18O and d13C values found in hermatypic corals from the subtropics is explained by the sympathetic relationship between temperature and light in these latitudes. These trends show that the carbon isotope fractionation is controlled by the biology of the respective carbonate producing organisms. Thus, the carbon isotope distribution can provide information on the symbiont-host relationship, on metabolic processes and calcification and growth stages during ontogenesis of calcareous marine organisms.

Finite element analysis of the statics of and vibrations in axisymmetric shells

The finite element process is now used almost routinely as a tool of engineering analysis. From early days, a significant effort has been devoted to developing simple, cost effective elements which adequately fulfill accuracy requirements. In this thesis we describe the development and application of one of the simplest elements available for the statics and dynamics of axisymmetric shells . A semi analytic truncated cone stiffness element has been formulated and implemented in a computer code: it has two nodes with five degrees of freedom at each node, circumferential variations in displacement field are described in terms of trigonometric series, transverse shear is accommodated by means of a penalty function and rotary inertia is allowed for. The element has been tested in a variety of applications in the statics and dynamics of axisymmetric shells subjected to a variety of boundary conditions. Good results have been obtained for thin and thick shell cases .

Practical calculations for uniform external pressure buckling in cylindrical shells with stepped walls

Metal cylindrical storage structures of significant size, such as silos and vertical-axis tanks, are almost always constructed from many short cylindrical shells of different thickness as the stress resultants on the wall progressively increase towards the base. The resulting increases in thickness are always made in step changes using metal sheets of uniform thickness because of the availability of such source materials. The result is a shell with a stepped wall with multiple discrete steps in thickness. Such shells are very susceptible to buckling under external pressure when empty or partially filled, but the buckling mode may involve only part of the shell height due to the changes in shell thickness. These changes must therefore be accounted for within the design process. A new method of determining the critical buckling resistance of such shells was recently developed, and although it has been shown to be valid, the methodology for its application in practical design has not been set out or shown. This paper therefore briefly describes the new method and demonstrates the manner in which it can be used to produce rapid, safe assessments of cylindrical shells with a wide range of patterns of wall thickness changes. The results are then suitable for direct introduction into such documents as the European standard on metal shells [1] and the ECCS Recommendations [2].