Viscoelasticity and high buckling stress of dense carbon nanotube brushes

We report on the mechanical behavior of a dense brush of small-diameter (1–3 nm) non-catalytic multiwall (2–4 walls) carbon nanotubes (CNTs), with ~10 times higher density than CNT brushes produced by other methods. Under compression with spherical indenters of different radii, these highly dense CNT brushes exhibit a higher modulus (~17–20 GPa) and orders of magnitude higher resistance to buckling than vapor phase deposited CNT brushes or carbon walls. We also demonstrate the viscoelastic behavior, caused by the increased influence of the van der Waals’ forces in these highly dense CNT brushes, showing their promise for energy-absorbing coatings.

Mechanical properties of sheet metal under forming conditions

In the bulge test, a sheet metal specimen is clamped over a circular hole in a die and formed into a bulge by the hydraulic pressure on one side of the specirnen. As the unsupported part of the specimen is deformed in this way, its area is increased, in other words, the material is generally stretched and its thickness generally decreased. The stresses causing this stretching action are the membrane stresses in the shell generated by the hydraulic pressure, in the same way as the rubber in a toy balloon is stretched by the membrane stresses caused by the air inside it. The bulge test is a widely used sheet metal test, to determine the "formability" of sheet materials. Research on this forming process (2)-(15)* has hitherto been almost exclusively confined to predicting the behaviour of the bulged specimen through the constitutive equations (stresses and strains in relation to displacements and shapes) and empirical work hardening characteristics of the material as determined in the tension test. In the present study the approach is reversed; the stresses and strains in the specimen are measured and determined from the geometry of the deformed shell. Thus, the bulge test can be used for determining the stress-strain relationship in the material under actual conditions in sheet metal forming processes. When sheet materials are formed by fluid pressure, the work-piece assumes an approximately spherical shape, The exact nature and magnitude of the deviation from the perfect sphere can be defined and measured by an index called prolateness. The distribution of prolateness throughout the workpiece at any particular stage of the forming process is of fundamental significance, because it determines the variation of the stress ratio on which the mode of deformation depends. It is found. that, before the process becomes unstable in sheet metal, the workpiece is exactly spherical only at the pole and at an annular ring. Between the pole and this annular ring the workpiece is more pointed than a sphere, and outside this ring, it is flatter than a sphere. In the forming of sheet materials, the stresses and hence the incremental strains, are closely related to the curvatures of the workpiece. This relationship between geometry and state of stress can be formulated quantitatively through prolateness. The determination of the magnitudes of prolateness, however, requires special techniques. The success of the experimental work is due to the technique of measuring the profile inclination of the meridional section very accurately. A travelling microscope, workshop protractor and surface plate are used for measurements of circumferential and meridional tangential strains. The curvatures can be calculated from geometry. If, however, the shape of the workpiece is expressed in terms of the current radial (r) and axial ( L) coordinates, it is very difficult to calculate the curvatures within an adequate degree of accuracy, owing to the double differentiation involved. In this project, a first differentiation is, in effect, by-passed by measuring the profile inclination directly and the second differentiation is performed in a round-about way, as explained in later chapters. The variations of the stresses in the workpiece thus observed have not, to the knowledge of the author, been reported experimentally. The static strength of shells to withstand fluid pressure and their buckling strength under concentrated loads, both depend on the distribution of the thickness. Thickness distribution can be controlled to a limited extent by changing the work hardening characteristics of the work material and by imposing constraints. A technique is provided in this thesis for determining accurately the stress distribution, on which the strains associated with thinning depend. Whether a problem of controlled thickness distribution is tackled by theory, or by experiments, or by both combined, the analysis in this thesis supplies the theoretical framework and some useful experimental techniques for the research applied to particular problems. The improvement of formability by allowing draw-in can also be analysed with the same theoretical and experimental techniques. Results on stress-strain relationships are usually represented by single stress-strain curves plotted either between one stress and one strain (as in the tension or compression tests) or between the effective stress and effective strain, as in tests on tubular specimens under combined tension, torsion and internal pressure. In this study, the triaxial stresses and strains are plotted simultaneously in triangular coordinates. Thus, both stress and strain are represented by vectors and the relationship between them by the relationship between two vector functions. From the results so obtained, conclusions are drawn on both the behaviour and the properties of the material in the bulge test. The stress ratios are generally equal to the strain-rate ratios (stress vectors collinear with incremental strain vectors) and the work-hardening characteristics, which apply only to the particular strain paths are deduced. Plastic instability of the material is generally considered to have been reached when the oil pressure has attained its maximum value so that further deformation occurs under a constant or lower pressure. It is found that the instability regime of deformation has already occurred long before the maximum pressure is attained. Thus, a new concept of instability is proposed, and for this criterion, instability can occur for any type of pressure growth curves.

Failure analysis of cold-formed steel sections

The purlin-sheeting system has been the subject of numerous theoretical and experimental investigations over the past 30 years, but the complexity of the problem has led to great difficulty in developing a sound and general model. The primary aim of the thesis is to investigate the failure behaviours of cold-formed zed and channel sections for use in purlin-sheeting systems. Both the energy method and finite strip method are used to develop an approach to investigate cold-formed zed and channel section beams with partial-lateral restraint from the metal sheeting when subjected to a uniformly distributed transverse load. The stress analysis of cold-formed zed and channel section beams with partially-lateral restraint from the metal sheeting when subjected to a uniformly distributed transverse load is investigated firstly by using the analytical model based on the energy method in which the restraint actions of the sheeting are modelled by using two springs representing the translational and rotational restraints. The numerical results have showed that the two springs have significantly different influences on the stresses of the beams. The influence of the two springs has also been found to depend on the anti-sag bar and the position of the loading line. A novel method is presented for analysing the elastic local buckling behaviour of cold-formed zed and channel section beams with partial-lateral restraint from metal sheeting when subjected to a uniformly distributed transverse load, which is carried out by inputting the cross sectional stresses with the largest compressive stress into the finite strip analysis. By using the presented novel method, individual influences of warning stress, partially lateral restraints from the sheeting and the dimensions of the cross section and position of the loading line on the buckling behaviour are investigated.

Global optimisation of cold-formed steel sections

In this thesis, standard algorithms are used to carry out the optimisation of cold-formed steel purlins such as zed, channel and sigma sections, which are assumed to be simply supported and subjected to a gravity load. For zed, channel and sigma section, the local buckling, distortional buckling and lateral-torsional buckling are considered respectively herein. Currently, the local buckling is based on the BS 5950-5:1998 and EN 1993-1-3:2006. The distortional buckling is calculated by the direct strength method employing the elastic distortional buckling which is calculated by three available approaches such as Hancock (1995), Schafer and Pekoz (1998), Yu (2005). In the optimisation program, the lateral-torsional buckling based on BS 5950-5:1998, AISI and analytical model of Li (2004) are investigated. For the optimisation program, the programming codes are written for optimisation of channel, zed and sigma beam. The full study has been coded into a computer-based analysis program (MATLAB).

Structural behaviour of glass reinforced plastics

The aim of this research is to promote the use of G.R.P. as a structural material. In the past, the use of G.R.P. has been confined to non-load carrying applications. Such uses are still rapidly increasing but in addition significant changes have been made during the last decade in the development of semi-structural and now even fully structural applications. Glass-reinforced plastic is characterized by a high strength but a relatively low modulus of elasticity. For this reasona G.R.P. structure can expect to show large deformations as a result of which the individual structural members will fail under load due to a loss of stability rather than approaching the ultimate strength of the material. For this reason the selection of the geometrical shapes of G.R.P. structural elements is considered to be an important factor in designing G.R.P. structures. The first chapter of this thesis deals with a general review of the theoretical and experimental methods used to describe the structural properties of G.R.P. The research programme includes five stages dealing with the structural behaviour of G.R.P. The first stage (Chapter 2) begins with selecting and designing an optimum box beam cross-section which gives the maximum flexural and torsional rigidity. The second stage of investigation (Chapter 3) deals with beam to beam connections. A joint was designed and manufactured with different types of fasteners used to connect two beam units. A suitable fastener was selected and the research extended to cover the behaviour of long span beams using multiple joints. The third part of the investigation includes a study of the behaviour of box beams subjected to combined bending, shear and torsion. A special torque rig was developed to perform the tests. Creep deformation of 6 m span G.R.P. was investigated as the fourth stage under a range of loading conditions. As a result of the phenomenon of post buckling behaviour exhibited in the compression flange during testing of box beams during earlier stages of the investigation it was decided to consider this phenomenon in more detail in the final stage of the investigation. G.R.P. plates with different fibre orientation were subjected to uniaxial compression and tested up to failure. In all stages of the investigation theoretical predictions and experimental results were compared and generally good correlation between theory and experimental data was observed.

Web strength of rolled steel joists

This work is concerned with the behaviour of thin webbed rolled steel joists or universal beams when they are subjected to concentrated loads applied to the flanges. The prime concern is the effect of high direct stresses causing web failure in a small region of the beam. The review shows that although many tests have been carried out on rolled steel beams and built up girders, no series of tests has restricted the number of variables involved to enable firm conclusions to be drawn. The results of 100 tests on several different rolled steel universal beam sections having various types of loading conditions are presented. The majority of the beams are tested by loading with two opposite loads, thus eliminating the effects of bending and shear, except for a small number of beams which are tested simply supported on varying spans. The test results are first compared with the present design standard (BS 449) and it is shown that the British Standard is very conservative for most of the loading conditions included in the tests but is unsafe for others. Three possible failure modes are then considered, overall elastic buckling of the web, flexural yielding of the web due to large out of plane deflexions and local crushing of the material at the junction of the web and the root fillets. Each mode is considered theoretically and developed to establish the main variables, thus enabling a comparison to be made with the test results. It is shown that all three failure modes have a particular relevance for individual loading conditions, but that determining the failure load given the beam size and the loading conditions is very difficult in certain instances. Finally it is shown that there are some empirical relationships between the failure loads and the type of loading for various beam serial sizes.

The structural properties of glassfibre reinforced plastics

The research work described in this thesis is concerned with the development of glassfibre reinforced plastics for structural uses in Civil Engineering construction. The first stage was primarily concerned with the design of GRP lamintes with structura1 properties and method of manufacture suitable for use with relatively large structural components. A cold setting, pressure moulding technique was developed which proved to be efficient in reducing the void content in the composite and minimising the exothermic effect due to curing. The effect of fibre content and fibre arrangement on strength and stiffness of the cornposite was studied and the maximum amount of' fibre content that could be reached by the adopted type of moulding technique was determined. The second stage of the project was concerned with the introduction of steel-wire "sheets" into the GRP cornposites, to take advantage of the high modulus of steel wire to improve the GRP stiffness and to reduce deformation. The experimental observations agreed reasonably well with theoretical predictions in both first and second stages of the work. The third stage was concerned with studying the stability of GRP flat rectangular plates subjected to uniaxial compression or pure shear, to simulate compression flanges or shear webs respectively. The investigation was concentrated on the effect of fibre arrangement in the plate on buckling load. The effect of the introduction of steel-wire sheets on the plate stability in compression was also investigated. The boundary conditions were chosen to be close to those usually assumed in built-up box-sections for both compression flanges and webs. The orthotropic plate and the mid-plane symmetric were used successfully in predicting the buckling load theoretically. In determining the buckling load experimentally, two methods were used. The Southwell plot method and electrical strain gauge method. The latter proved to be more reliable in predicting the buckling load than the former, especially for plates under uniaxial compression. Sample design charts for GRP plates that yield and buckle simultaneously under compression are also presented in the thesis. The final stage of the work dealt with the design and test of GRP beams. The investigation began by finding the optimum cross-section for a GRP beam. The cross-section which was developed was a thin walled corrugated section which showed higher stiffness than other cross-sections for the same cross-sectional area (i.e. box, I, and rectangular sections). A cold setting, hand layings technique was used in manufacturing these beams wbich were of nine types depending on the type of glass reinforcement employed and the arrangement of layers in the beam. The simple bending theory was used in the beam design and proved to be satisfactory in predicting the stresses and deflections. A factor of safety of 4 was chosen for design purposes and considered to be suitable for long term use under static load. Because of its relatively low modulus, GRP beams allowable deflection was limited to 1/120th of the span which was found to be adequate for design purposes. A general discussion of the behaviour of GRP composites and their place relative to the more conventional structural material was also presented in the thesis.

Failure of steel gusset plates

This thesis examines the parameters associated with the failure of triangular steel gusset plates. Eighty two results are presented investigating the position of the applied load, the gusset plate height to length ratio, size, thickness, internal angle and the removal of the inside corner. The thickness of the loaded plate and its influence on the gusset plates failure is also investigated. Twenty two similar gusset plates were tested to investigate the welds connecting the gusset plate to the adjacent loaded and support edges. The experimental results are compared with existing methods, none of which cover all the variables tested. Some methods do not consider buckling and most of those that do are inadequate. Most of the methods do not accurately take account of the load position. An alternative method based on experimental observations is presented for design purposes. The method covers any combination of the variables tested. To test assumptions made in the theoretical work forty seven strut tests took place to investigate buckling characteristics and fifteen special gusset plates were also tested. The gusset plates were found to fail in an elastic-plastic buckling manner. A gusset plate has a specific moment of resistance capacity about it’s inside corner and the ultimate load that can be applied is dependent upon the position of the load relative to the supported edge. There is an optimum height to length ratio for strength and any increase in the internal angle from 90 degrees produces little change in moment capacity. The removal of small portions of the inside corner of a gusset plate has little effect upon its moment capacity. The loaded plate does not provide any significant moment of resistance to the applied load at failure. The main functions of the loaded and supported edge welds is to prevent the gusset plate from slipping from between the plates.

Computer simulation for tube-making by the cold roll-forming process

The conventional design of forming rolls depends heavily on the individual skill of roll designers which is based on intuition and knowledge gained from previous work. Roll design is normally a trial an error procedure, however with the progress of computer technology, CAD/CAM systems for the cold roll-forming industry have been developed. Generally, however, these CAD systems can only provide a flower pattern based on the knowledge obtained from previously successful flower patterns. In the production of ERW (Electric Resistance Welded) tube and pipe, the need for a theoretical simulation of the roll-forming process, which can not only predict the occurrence of the edge buckling but also obtain the optimum forming condition, has been recognised. A new simulation system named "CADFORM" has been devised that can carry out the consistent forming simulation for this tube-making process. The CADFORM system applied an elastic-plastic stress-strain analysis and evaluate edge buckling by using a simplified model of the forming process. The results can also be visualised graphically. The calculated longitudinal strain is obtained by considering the deformation of lateral elements and takes into account the reduction in strains due to the fin-pass roll. These calculated strains correspond quite well with the experimental results. Using the calculated strains, the stresses in the strip can be estimated. The addition of the fin-pass roll reduction significantly reduces the longitudinal compressive stress and therefore effectively suppresses edge buckling. If the calculated longitudinal stress is controlled, by altering the forming flower pattern so it does not exceed the buckling stress within the material, then the occurrence of edge buckling can be avoided. CADFORM predicts the occurrence of edge buckling of the strip in tube-making and uses this information to suggest an appropriate flower pattern and forming conditions which will suppress the occurrence of the edge buckling.

Structural optimization

The non-linear programming algorithms for the minimum weight design of structural frames are presented in this thesis. The first, which is applied to rigidly jointed and pin jointed plane frames subject to deflexion constraints, consists of a search in a feasible design space. Successive trial designs are developed so that the feasibility and the optimality of the designs are improved simultaneously. It is found that this method is restricted lo the design of structures with few unknown variables. The second non-linear programming algorithm is presented .in a general form. This consists of two types of search, one improving feasibility and the other optimality. The method speeds up the 'feasible direction' approach by obtaining a constant weight direction vector that is influenced by dominating constraints. For pin jointed plane and space frames this method is used to obtain a 'minimum weight' design which satisfies restrictions on stresses and deflexions. The matrix force method enables the design requirements to be expressed in a general form and the design problem is automatically formulated within the computer. Examples are given to explain the method and the design criteria are extended to include member buckling. Fundamental theorems are proposed and proved to confirm that structures are inter-related. These theorems are applicable to linear elastic structures and facilitate the prediction of the behaviour of one structure from the results of analysing another, more general, or related structure. It becomes possible to evaluate the significance of each member in the behaviour of a structure and the problem of minimum weight design is extended to include shape. A method is proposed to design structures of optimum shape with stress and deflexion limitations. Finally a detailed investigation is carried out into the design of structures to study the factors that influence their shape.

Reply: 'Myopic foveoschisis: An ectatic retinopathy, not a schisis'

Full text: We thank Tsilimbaris et al1 for their comments on the appropriateness of the term ‘myopic foveoschisis’ to describe the condition that is characterized by the separation of neural retina layers associated with high myopia and posterior staphyloma. They have proposed the term ‘myopic ectatic retinopathy’ as a more literal and functionally more accurate descriptor of the condition to avoid the use of the word ‘schisis’, which may be misleading because it is also used to describe other conditions where there is separation of neural retina layers without the presence of staphyloma.2 Using the word ‘ectatic’ for this condition would imply that we are fairly certain about the pathogenesis and mechanistic factors that underlie its development and progression. However, this is not the case, unfortunately, as our review of the literature has shown. There are several theories ranging from vitreous traction to sclerosing changes of retinal vessels to progression of staphylomas as possible etiological factors. Therefore, it is likely to be multifactorial in nature—hence the success reported with different procedures that address either the vitreous traction factor using vitrectomy, peel plus tamponade or the scleral ectasia factor using posterior buckling techniques. In the absence of a good understanding of underlying pathogenesis, it is probably best to use purely descriptive names rather than mechanistic terms. The use of descriptive terms, even though similar, do not necessarily cause confusion as long as they are widely accepted as differentiating terminology, for example, postoperative pseudophakic cystoid macular edema (Irvine–Gass syndrome) vs cystoid macular edema associated with posterior uveitis in a phakic patient. The introduction of too many mechanistic or pathogenetic terms in the absence of clear understating of etiology can in fact cause more confusion, for example, serous chorioretinopathy vs central serous retinopathy vs serous choroidopathy. The confinement to broad descriptive terms can enhance communication and reduce confusion without committing to any presumption about etiology until it is better understood. This approach is probably best illustrated by the recent advances in the understanding of mactel21, a condition initially described and classified, using descriptive nomenclature, by Don Gass as bilateral, idiopathic acquired juxtafoveolar telangiectasis (Group2A) and as distinctly different from unilateral, congenital parafoveolar telangiectasis (Group 1A; Gass,3 pp 504–506 vs 127–128). Finally, it is worthy to note that for myopic foveoschisis associated with a staphyloma that is associated with outer layer macular detachment, Don Gass also descriptively included the additional observation (before the advent of OCT) that the retinal profile was concave rather than convex in shape, thereby differentiating it from rhegmatogenous detachments with recruitment of subretinal fluid that is associated with posteriorly located breaks and macular holes in myopic eyes. References 1.Tsilimbaris MK, Vavvas DG, Bechrakis NE. Myopic foveoschisis: an ectatic retinopathy, not aschisis. Eye 2016; 30: 328–329. 2.Powner MB, Gillies MC, Tretiach M, Scott A, Guymer RH, Hageman GS et al. Perifoveal müller cell depletion in a case of macular telangiectasia type 2. Ophthalmology 2010; 117(12): 2407–2416. 3.Gass DM. Stereoscopic Atlas of Macular Diseases: Diagnosis and Treatment, 4th edn. Mosby-Yearbook: St. Louis, 1997.