Shape Imperfections Research Articles

Materials for x-ray refractive lenses minimizing wavefront distortions

Abstract

Upheaval buckling of surface-laid offshore pipeline

Offshore pipelines operating under high pressure and temperature are subjected to upheaval buckling. Pipeline behaviour in upheaval buckling depends on a number of factors including the shape of pipeline imperfection, installation stresses, loading types, seabed sediment behaviour and the flexural stiffness of the pipe. Current method of predicting upheaval buckling is based on simplified shapes of pipeline imperfection developed for idealized seabed conditions. To account for the effect of internal pressure, the pressure load is represented using an equivalent temperature. However, the applicability of these idealizations on the prediction of upheaval buckling has not been well-investigated. In this paper, the three-dimensional finite element modelling technique is used to investigate the applicability of idealized shapes and their effects on the upheaval buckling of pipeline for a seabed condition at offshore Newfoundland in Canada. The finite element model is then used to conduct a parametric study to investigate the effects of installation stress, loading types, seabed parameters and the flexural stiffness of the pipe. Finally, a design chart is developed to determine the optimum height of seabed features to manage pipeline stability against upheaval buckling under different temperature and pressure loadings.

Shape and Size of Initial Geometrical Imperfections of Structural Glass Members

Abstract In this paper measuring and determining of initial geometrical imperfections of set of glass members are presented. Measured specimens had the different dimensions and different composition – monolithic glass or laminated glass using different types of interlayer foils and glass panes. The shape of initial overall bow was measured using different methods and results were statistically evaluated and compared with allowable values defined in standards.

Influence of imperfections on the stability of beams with intermediate flexible supports

For the prediction of the ultimate load of beams and columns, respectively susceptible to lateral torsional buckling and flexural buckling, numerical FEM-calculations including geometric imperfections and residual stresses (so-called “GMNIA analyses”), are becoming more commonly employed and recognized. In these analyses, the shape of the geometric imperfections is often based on the 1st buckling mode, seen as the worst case for these members.In this paper, the buckling behaviour of beams and columns with additional intermediate flexible supports is studied and illustrated, using additional spring elements with systematically varied stiffness.As expected, a decrease of the spring stiffness always leads to a reduced elastic critical buckling load. Nevertheless, when assuming geometric imperfections based on the 1st buckling mode, this may lead to a higher ultimate load than for the system with rigid intermediate supports, when identical imperfection amplitudes are used. These interesting results are presented and analyzed for two simple cases, in order to clearly show the main effects. These cases are: 1.) Columns under compression with additional flexible support at midspan; 2.) Beams under bending with additional flexible supports of the compressed flange only. For the latter case, a parametric study was performed, varying the number of intermediate supports and stiffness of the lateral supports.

Korn inequalities for shells with zero Gaussian curvature

We consider shells with zero Gaussian curvature, namely shells with one principal curvature zero and the other one having a constant sign. Our particular interests are shells that are diffeomorphic to a circular cylindrical shell with zero principal longitudinal curvature and positive circumferential curvature, including, for example, cylindrical and conical shells with arbitrary convex cross sections. We prove that the best constant in the first Korn inequality scales like thickness to the power 3/2 for a wide range of boundary conditions at the thin edges of the shell. Our methodology is to prove, for each of the three mutually orthogonal two-dimensional cross-sections of the shell, a “first-and-a-half Korn inequality”—a hybrid between the classical first and second Korn inequalities. These three two-dimensional inequalities assemble into a three-dimensional one, which, in turn, implies the asymptotically sharp first Korn inequality for the shell. This work is a part of mathematically rigorous analysis of extreme sensitivity of the buckling load of axially compressed cylindrical shells to shape imperfections.

Experimental compressive strength analyses of high tensile steel thin-walled stiffened panels with a large lightening opening

This work investigates the compressive load carrying capability of experimentally tested reinforced steel panels with a large lightening opening. A series of experiments have been carried out on reinforced panels with circular and elongated circular opening of different sizes. The effect of different opening shapes, different opening sizes as well as different initial imperfection shapes and amplitudes, on the loading carrying capacity are studied. The resultant collapse modes are presented and both initial and post-collapse shapes are analysed and the sequential occurrence of the post-collapse deformation shapes have been analysed. The experimental results of force-vertical/lateral displacements relationships, strain energy density and stress-strain relationships are presented and analysed. Finally, the experimental results have been compared with other experimental ones for unstiffened plates with elongated circular opening subjected to uniaxial compressive load.

Composite spheroidal shells under external pressure

ABSTRACTBuckling, collapse, and first ply failure pressures have been obtained for a range of spheroidal FRP shells under static external pressures. Comparisons of the load carrying capacities are made for like geometries. It is shown that some prolate ellipsoids can be stronger, for up to 70% than the equivalent spheres. The effect of boundary conditions in the equatorial plane on the buckling strength is assessed for the diameter-to-wall- thickness ratio ranging from 100 to 500. Regions where the strength (FPF) rather than asymmetric bifurcation control the failure have been identified. Small perturbations in ply orientations, ±5°, have been introduced in order to assess their influence on the buckling strength. Both symmetric and asymmetric stacking with respect to the mid-plane have been analyzed (including random stacking).Initial shape imperfection positioned at the apex of a hemispherical head has been examined. The latter aimed at assessing the sensitivity of buckling pressure to deviations from perfect geometry. Results have been obtained for the lower bound approach based on the local flattening using the increased-radius. Imperfections in ellipsoids have also been studied. Axisymmetric modeling of all shells was used throughout in this study. Only the upper half of shells was modeled, and the issue of boundary conditions at the equatorial plane was also explored.

Sizing strategy for stringer and orthogrid stiffened shells under axial compression

ABSTRACTThin-walled stiffened shell structures are used in primary structures of space launcher vehicles. These structures are prone to buckling and thus fail due to a loss of structural stability. Generally, it has to be distinguished between two major modes of instability for stiffened shell structures: a global buckling of the entire structure and a local buckling of skin fields, longitudinal and circumferential stiffeners. Due to the large number of variables when designing stiffened shell structures, their preliminary design is a demanding task. To allow an efficient preliminary design, sizing strategies can be developed. For this purpose, analytical methods, which allow to assess the local and global instability of stiffened shell structures, are employed. In this article, sizing strategies based on efficient analytical methods are introduced and applied to identify suitable designs of stringer stiffened and orthogrid stiffened shell structures. To study the imperfection sensitivity of stringer and orthogrid stiffened shell structures, numerical computations are performed using the single perturbation load approach and mode shape imperfections. Finally, weight strength curves are derived for stringer and orthogrid stiffened shell structures.

Statistical Analysis of the Influence of Imperfect Texture Shape and Dimensional Uncertainty on Surface Texture Performance

This paper investigates the effects of imperfect texture shape and dimensional uncertainty on the surface texture performance (load-carrying capacity and coefficient of friction) by adopting numerical experiments, statistical models, and artificial neural network. The imperfect texture shape is regarded as a polygon, and the uncertain geometrical dimensions include the dimple diameter, the area density, and the dimple depth. Results reveal that the most critical geometric parameters that influence the friction force are manufacturing errors associated with the texture’s area density. With respect to the load-carrying capacity and the coefficient of friction, manufacturing errors associated with the dimple diameter are more influential than those of the dimple depth and the area density. It is shown that insofar as the optimization of surface texture performance is concerned, the imperfect texture shape and the dimensional uncertainty associated with the laser texturing with three-sigma performance level are harmless, but manufacturing errors with the one-sigma level can dramatically reduce the load-carrying capacity and increase the coefficient of friction. Specifically, when the dimensions of the area density, the dimple depth, and the dimple diameter are set as 30%, $5.5~\mu \text{m}$ , and $100~\mu \text{m}$ , respectively, the imperfect texture shape at the three-sigma level can achieve higher performance than lower levels of control of machining precision.

Influence of Small Added Mass on Splitting Flexural Frequency Spectrum of Circular Ring with Initial Imperfection of Shape

The paper presents the results of the research into the problem of vibration of the infinitely long circular cylindrical shell, which has a symmetrical initial shape imperfection. The infinitely long shell is viewed as the ring of a single width in situations of planar deformation. It was discovered that the effect of splitting the bending spectrum frequency of the isolated ring not only occurs when the number of waves of asymmetric imperfection coincides with the number of waves of dynamic deformations, but also where the number of imperfections is twice as big as the number of the forming waves. This conclusion is correct provided that the number of waves of shape imperfection is even. An opportunity to remove the splitting frequency of the bending spectrum of a thin imperfect circular ring by acceding to it little linear mass is studied. The research has shown that neither the selection of attaching point of added mass nor its size allow discarding the unwanted in terms of a dynamic strength and reliability of the constructions, effect of staggering frequency. During the research a range of qualitative effects caused by the ring having inevitable deviations from the perfect geometrical form were identified.

Nonlinear stability analysis of a radially retractable hybrid grid shell in the closed position

The buckling capacity of a radially retractable hybrid grid shell in the closed position was investigated in this paper. The geometrically non-linear elastic buckling and elasto-plastic buckling analyses of the hybrid structure were carried out. A parametric study was done to investigate the effects rise-to-span ratio, beam section, area and pre-stress of cables, on the failure load. Also, the influence of the shape and scale of imperfections on the elasto-plastic buckling loads was discussed. The results show that the critical buckling load is reduced by taking account of material non-linearity. Furthermore, increasing the rise-tospan ratio or the cross-section area of steel beams notably improves the stability of the structure. However, the cross section area and pre-stress of cables pose negligible effect on the structural stability. It can also be found that the hybrid structure is highly sensitive to geometric imperfection which will considerably reduce the failure load. The proper shape and scale of the imperfection are also important.

Post-buckling Behaviour of Imperfect Cylindrical Panels Subjected to Axial Compressive Load: Experimental vs.Theoretical

Post-buckling behavior of imperfect, laminated composite cylindrical panels subjected to axial compressive load has been investigated by using an equilibrium path approach which uses an arc-length method. Influence of the eigen imperfection shapes and its relative magnitude on the post-buckling behavior of the cylindrical panels with different Rt ratios is briefly discussed for different unidirectional lay-up sequences of interest with all the sides considered as simply supported boundary configuration. The confidence gained on the numerical approach is further extended to correlate (or validate) with the experimental post-buckling behavior of various glass-polyester laminated composite cylindrical panels considered in this investigation

Влияние несовершенств формы на колебания кольцевого резонатора волнового твердотельного гироскопа

Влияние несовершенств формы на колебания кольцевого резонатора волнового твердотельного гироскопа

Tunable Blocker-Tolerant On-Chip Radio-Frequency Front-End Filter With Dual Adaptive Transmission Zeros for Software-Defined Radio Applications

This paper presents a tunable active bandpass filter (BPF) with adjustable transmission zeros (TZs) close to the passband for software-defined radio (SDR) applications. The RF front-end frequency selectivity is enhanced by the creation of TZs that also improve the out-of-band (OOB) input-referred third-order intercept point (IIP3). The filter is based on two-path signal cancellation and consists of a tunable BPF in parallel with two tunable bandstop filters. This combination ensures the correct amplitude and phase relationships across a wide tuning range to create adjustable TZs without sacrificing the gain of the passband. This paper presents in detail the design considerations and guidelines, as well as analysis of the filter performance in the presence of nonidealities such as parasitics and imperfect clock signal shape. The proposed filter is implemented with high- $Q~N$ -path filter blocks in a 65-nm CMOS process. The passband of the filter is tunable from 0.1 to 1.4 GHz with a 3-dB bandwidth of 9.8–10.2 MHz, a gain of 21.5–24 dB, a noise figure of 3–4.2 dB, and a total power consumption of 50–73 mW. TZs are created on both sides of the passband with a minimal offset of 25 MHz and are tunable across a 20-MHz range with up to a 60-dB rejection. The measured blocker 1-dB compression point is 8 dBm and the OOB IIP3 is 23 dBm. The reported filter provides a promising on-chip filtering solution for multistandard multifrequency SDR applications with improved interference mitigation capabilities.

Effects of imperfection shapes on buckling of conical shells under compression

This paper describes a systematic numerical investigation into the nonlinear elastic behavior of conical shells, with various types of initial imperfections, subject to a uniformly distributed axial compression. Three different patterns of imperfections, including first axisymmetric linear bifurcation mode, first non-axisymmetric linear bifurcation mode, and weld depression are studied using geometrically nonlinear finite element analysis. Effects of each imperfection shape and tapering angle on imperfection sensitivity curves are investigated and the lower bound curve is determined. Finally, an empirical lower bound relation is proposed for hand calculation in the buckling design of conical shells.

Bearing Capacity of Aluminum Bars with Built-Up Cross Section and Glued or Welded Connections

The paper is focused on numerical analysis and experimental test of aluminum bars with glued and welded connections between separate members. The connection properties were tested experimentally. The numerical analysis were conducted for the beam and shell model of the structure. The shape and magnitude of initial geometric imperfection was taken into account.

Effects of Geometric Imperfections on the Bracing Performance of Cross Beams during Construction of Composite Bridges

Steel girders require stability controls for different construction stages before the lateral-torsional support from the concrete deck occurs. The load-carrying capacity of bridge girders and bracing forces generated in their bracings are very sensitive to the girders' initial imperfections in terms of both the magnitude and distribution along the span. Relatively little knowledge is available in this matter; however, decisions on the worst shape of imperfections that gives a conservative resistance and/or maximizes the bracings forces is often not an easy task in practice. The present paper reports the test results (in terms of the load-carrying capacities and bracing forces) of a large-scale bridge of twin I-girder type in which the location of the intermediate cross beam was varied across the depth of the main girders. Moreover, extensive numerical investigations were performed to study the effects of some relevant shape of imperfections on both the load-carrying capacities of the studied bridges and the magnitude of bracing forces generated in the cross beams that were involved. The test results showed that the load-carrying capacity of steel girders can exceed their lowest theoretical eigenvalue because of the presence of initial imperfections. In the finite-element analyses of the studied bridge cases, in some cases, the girders followed their shape of geometric imperfections and reached a load value that was greater than the lowest eigenvalue of the systems.

The complete bifurcation structure of nonlinear boundary problem for cylindrical panel subjected to uniform external pressure

The present paper presents the complete bifurcation structure of nonlinear boundary problem of thin-walled systems for cylindrical panel subjected to uniform external pressure. We examine various boundary conditions on straight edges (free, simply supported, rigidly clamped edges, edges with prescribed fixed joint conditions); curvilinear edges are simply supported. To construct solutions of the boundary problem in question and to trace equilibrium paths, we employ the non-linear extended Kantorovich method in conjunction with a conventional path-tracing technique. The structure has bifurcation paths associated with symmetric, skew-symmetric, asymmetric, and snap-through deformed shapes that provides a basis for analysis of the worst shape imperfections.

Slender steel columns: How they are affected by imperfections and bracing stiffness

Finite-element programs can be used for designing columns and their bracing systems. It is well known, however, that the output obtained from such programs is highly dependent upon the input (such as imperfections and stiffness properties). In the present study, the effects of imperfections on the predicted strength and stiffness requirements of steel columns and of their bracing systems are investigated. Two different systems are analyzed: 1) a braced non-sway column and 2) a braced sway column. It was found that a poor choice of the shape of the initial imperfections can provide unrealistic results in terms of both the buckling load on the columns and the predicted reactions of the bracings. It was also found that superimposing different imperfection shapes can contribute to obtaining realistic and trustworthy results. Furthermore, it was shown that the shapes of the initial imperfections that lead to the lowest buckling load and those that result in the strongest bracing forces, are generally not the same.

High transmission Ni compound refractive lens for high energy X-rays.

We present a new planar Ni compound refractive lens for high energy X-rays (116 keV). The lens is composed of identical plano-concave elements with longitudinal parabolic grooves manufactured by a punch technique. In order to increase the lens transmission, the thickness of the single lens at the parabolic groove vertex was reduced to less than 5 μm and the radius of curvature was reduced to about 20 μm. The small radius of curvature allowed us to reduce the number of single elements needed to get the focal length of 3 m to 54 single lenses. The gain parameter has been significantly improved compared to the previous lenses due to higher transmission, but the focused beam size and its gain are not as good as expected, mostly due to the aberrations caused by the lens shape imperfections.