Large Imperfection Research Articles

β-Ga2O3 bulk single crystals grown by a casting method

A novel casting method was developed to grow β-Ga2O3 bulk single crystals without using a seed crystal. After separation from the crucible and processing, 2-inch diameter single crystal β-Ga2O3 ingots with (100) plane could be obtained and no large imperfection were observed. The 10 × 10 mm2 β-Ga2O3 single crystals samples with different crystal orientation have good crystal quality with full width at half maximum less than 50″, surface roughness less than 0.5 nm and defect density at the magnitude of 104 cm−2. On the basis of the experimental phenomena, a numerical simulation model was proposed to explain the crystal growth process in the casting method.

Nonlinear Finite Element Analysis and Comparison of In‐Plane Strength of Circular and Parabolic Arched I‐Section Cellular Steel Beam

The advancement in steel fabrication technology extends the structural and constructional advantages of cellular steel beams into arched cellular steel structure members. However, less attention is given to understanding the in‐plane and out‐of‐plane structural behavior and performance of arched cellular steel beams. This article presents a numerical study using the finite element package ABAQUS to investigate the effect of arch axis geometry (circular and parabolic) and the impact of end support types on the in‐plane inelastic buckling strength and buckling mode of I‐section arched cellular steel beams. In the nonlinear finite element analysis of the model material nonlinearity, a second‐order effect due to large deformation and initial geometric imperfection was incorporated in predicting inelastic buckling load and buckling mode. Furthermore, finite element analysis results were verified by comparing them to the existing experimental work. Test models covering shallow to deep arches of subtended angle in a range of 45–180 were investigated under uniformly distributed vertical loads and mid‐span point loads. It was found that nonlinear finite element results fairly replicate the experimental work in predicting inelastic buckling load and post‐buckling behavior. From the parametric investigation, it was found that deep parabolic arched cellular steel beams are structurally more efficient than their equivalent circular arched cellular steel beams. Pinned in‐plane and free out‐of‐plane end support conditions result in a reduced inelastic ultimate buckling load capacity of arched cellular steel members when compared to other possible end support types. The geometry of an arch axis has no noticeable impact on the buckling mode of arched cellular steel beams.

The effect of calcination temperature on the photophysical and mechanical properties of copper iodide (5 mol%)–doped hydroxyapatite

Nanocomposite consisting of 5 mol% crystalline CuI-doped hydroxyapatite (HA) was prepared for the first time by facile chemical method and calcined at different temperatures such as 300 °C, 500 °C, 700 °C and 900 °C. In this study, HA played a role as the matrix and CuI was the reinforcement. The effect of calcination temperature on XRD pattern, TEM, SEM, BET, FTIR, luminescence intensity, photoluminescence quantum yield (PLQY), fluorescence lifetime, charge mobility measurements, electronic speckle pattern interferometry and mechanical properties were investigated. The modified Scherrer equation of the composites showed that the size of the particles increased with increasing calcination temperature from 66.64 to 87.20 nm. The photoluminescence intensity of CuI (5 mol%)/HA was quenched at room temperature, while the represented constant decay time for the calcined compound was increased at 700 °C. Furthermore, the CIE coordinates were shown 0.39333, 0.18493 for CuI (5 mol%)/HA calcined at 700 °C. The charge mobility values of the nanocomposites were extracted by space-charge limited current (SCLC) method and the range of effective mobility was from 3.645 × 10−4 to 6.697 × 10−4 cm2V−1s−1. Mechanical properties were fully discussed via ASTM-E9 standard and CuI (5 mol%)/HA calcined at 900 °C was in better range than other compounds, the σyc and hardness values were reported 7.32 Mpa and 40.81 HV respectively. Speckle interferometry was used to demonstrate that there was no large imperfection in the surface of each sample. The components were very sensitive to the calcination temperatures. In other words, the combination of CuI (5 mol%)/HA showed that the replacement of Cu ions with Ca was helpful to improve the photophysical and mechanical properties.

Flutter of geometrical imperfect functionally graded carbon nanotubes doubly curved shells

In this paper, flutter of geometrical imperfect functionally graded carbon nanotubes (FG-CNTs) doubly curved shell subjected to a supersonic flow is investigated. For this purpose, the imperfect doubly curved shell is reinforced by four different carbon nanotubes (CNTs) distributions in the thickness direction. The Hill’s elastic moduli are used to obtain the effective material properties of FG-CNTs doubly curved shell. The piston aerodynamic theory and von Karman geometrical nonlinearity terms are used to study large deflection flutter analysis of FG-CNTs imperfect shell. The effect of different parameters including large deflection, geometrical imperfection and CNTs volume fraction on critical flutter pressure of doubly curved shells are studied. According to the results, distributions with poor CNTs in the middle of thickness are more efficient in improving critical flutter pressure. Additionally, the effect of shell imperfection on flutter pressure is more considerable than CNTs volume fraction and distributions.

On the imperfection sensitivity and design of tori-spherical shells under external pressure

Tori-spherical shells are often used as enclosures of pressure vessels in ocean and civil engineering. When subjected to external pressure, these thin-walled shells are prone to buckling. The corresponding critical buckling pressure heavily depends on deviations from the ideal shell shape, but also the yield strength as well as the knuckle radius.This article summarizes and analyzes all known experimental results for tori-spherical shells under external pressure. A detailed numerical elastic-plastic buckling analysis of a tori-spherical bulkhead is presented including details regarding non-linear material model, finite-element modeling and solver settings.In addition, a wide variety of empirical design and numerical geometric imperfection approaches for tori-spheres are presented, applied and validated. Among the geometric imperfection approaches are realistic measured geometric imperfections, dimple imperfections, flat patch imperfections and reduced stiffness methods. Large scale parametric imperfection amplitude analyzes are performed in order to determine which imperfection concept delivers in general the best fit to experimental results.New design factors for different tori-spherical shell geometry configurations are consequently developed and validated with experimental results. The new design factors lead to significantly improved critical load estimations in comparison to lower-bounds obtained empirically.

Failure Behavior of Double-Layer-Domes Subjected to Impact

The dynamic failure behavior of double-layer-domes subjected to impact is studied numerically through the nonlinear finite element software LS-DYNA. The parameters considered in this work include the mass, velocity, and size of impactor, impact direction, roof weigh, geometric imperfection, rise-to-span ratio, and depth of dome. The dynamic time-history response and energy conversion of the structure are utilized to distinguish between the failure mechanism types. For the cases studied, it is found that failure of the structures falls into one of the three categories: (1) local shear failure, (2) partial progressive failure, and (3) full progressive failure. Non-failure case dominates the dome response when the kinetic energy of the impactor is small enough, and the structure can convert most of the kinetic energy into the strain energy, thereby absorbing the impact. Local shear failure occurs in a double-layer-dome when an impactor with very high kinetic energy strikes the dome. For an impactor striking with a mass of 5 to 300[Formula: see text]ton and a velocity of 50 to 120[Formula: see text]m/s, the double-layer-dome studied will suffer from partial progressive failure. Varying mass and velocity of the impactor in the range of 1 to 300[Formula: see text]ton and 200 to 400[Formula: see text]m/s, respectively, results in a tendency of the dome to exhibit local shear failure. Although impact direction does not cause a change in the failure mechanism type, there is a reduction in the severity of failure of the system as the impact angle increases. Roof weight has no dominant effect on the failure mechanism of the double-layer-dome. A small initial member imperfection with amplitude 0.001[Formula: see text] does not change the progressive failure type. A large member imperfection of 0.01[Formula: see text] triggers member buckling and leads to local shear failure of the dome. Except for some loading cases, the change in the rise to span ratio and depth of the dome does not seriously affect the failure mode.

Elastic thin shells with large axisymmetric imperfection: from bifurcation to snap-through buckling

Elastic thin shells are well-known for their highly unstable post-buckling, a response that exhausts their pressure bearing capacity and leads to catastrophic collapse. This paper examines elastic thin shells with a large axisymmetric imperfection that can escape the classical bifurcation of perfect spherical shells. We employ a shell theory formulation with exact expressions of the middle surface strains, curvature changes, and live pressure along with validating experiments and numerical simulations. The results show that a large axisymmetric imperfection in the form of a circular arc can induce snap-through buckling followed by a stable post-buckling that offers increasing resistance to pressure over a large change in volume. In addition, a sensitivity analysis on the role of defect geometry and shell radius to thickness ratio reveals the emergence of four buckling modes. For small imperfections, bifurcation buckling (mode 1) is dominant and resembles the typical dimple-like mode of perfect spherical shells. For larger imperfections, the shell attains the maximum pressure at the snap-through buckling where strain localization appears either within the imperfection (mode 2) or just below (mode 3). In the fourth mode, snap-through buckling precedes the attainment of the maximum pressure following a post-buckling path characterized by a large change of volume that makes the shell harder and stronger. These findings show that harnessing defect geometry and shell radius to thickness ratio can be effective in programming the post-buckling characteristics and transition between buckling modes, thus offering potential routes for the design of soft metamaterials with application to soft robotics and other sectors.

Effect of static load on vibro-acoustic behaviour of clamped plates with geometric imperfections

The effect of static load on the vibro-acoustic behaviour of clamped rectangular plates with various geometric imperfections is further investigated in this paper. An effective method applying static load on the plate subjected to dynamic excitations is proposed in the experiment. The Von Karman nonlinear incremental strain-displacement relationship is utilized to describe the large deflection and initial geometric imperfection. Based on the assumed mode method and Hamilton's principle, the nonlinear vibration governing equations of an imperfect plate considering the added effect in the experimental implementation are formulated. Firstly, the nonlinear static deflection is solved iteratively. Then the tangent stiffness matrix is utilized to calculate the linear vibration at the equivalent static position. The acoustic radiation can be derived hereof by Rayleigh integral. The theoretical, numerical and experimental results coincide well. The results show that the natural frequencies of the imperfect plate are higher than those of the original flat one. Under static load, different from the flat plate which is stiffened, the imperfection may lead to either stiffening or softening of the plate depending on the imperfection shape and the static load direction. And the vibro-acoustic characteristics are affected accordingly. It is noted that when the imperfection gets larger, snap-through may occur under static pressure. Furthermore, comparison of vibration characteristics among different load locations with the same static load is also discussed.

Анализ содержания и состояния противопожарной безопасности лесного хозяйства

The article has studied the main points of fire safety of forest in Russia. The order of actions of the relevant services and the people behavior during the fire season. Examining this issue, the author revealed shortcomings and vulnerabilities of large fire prevention system and imperfection of the legislative side of the issue and stated their reasons.

Surface stress effects on the nonlinear postbuckling characteristics of geometrically imperfect cylindrical nanoshells subjected to torsional load

The prime aim of the current investigation is to predict the nonlinear torsional buckling and postbuckling behavior of geometrically imperfect cylindrical nanoshells including surface stress effects. To this end, the size-dependent governing differential equations of cylindrical nanoshell based on von Karman–Donnell-type of kinematic nonlinearity are derived using a combination of Gurtin–Murdoch elasticity theory and the classical shell theory, and employing the principle of virtual work. Subsequently, by considering the transverse displacement and Airy stress function as independent variables, a boundary layer theory is put to use which takes surface stress effects into account in conjunction with the nonlinear prebuckling deformations, large postbuckling deflections and initial geometric imperfection. Finally, an efficient solution methodology based on a two-stepped singular perturbation technique is conducted to obtain the size-dependent postbuckling equilibrium paths of nanoshells. It is revealed that after the minimum point of postbuckling load, by increasing the value of applied torsional load, the difference between postbuckling load-deflection curves corresponding to the perfect and imperfect nanoshells tends to decrease.

Large-amplitude vibration of imperfect angle-ply laminated rectangular plates for various materials

This paper deals with the solution of modified-Duffing ordinary differential equation for large-amplitude vibration of imperfect angle-ply rectangular composite plates. The boundary condition is simply supported and in-plane movable. The initial condition for the vibration is an initial vibration amplitude. This vibration problem is solved numerically by Runge-Kutta method. The effect of plate imperfection is studied and proved that a typical backbone curve will show up in case of a relatively large imperfection. Three different composite materials are then chosen to reveal the influence of young’s modulus ratio. Four fiber volumes are assumed to study its effect on the vibration mode. It turns out that either increasing the fiber strength or increasing the fiber volume in a composite will lead to an increase of its overall strength. And this will further trigger the plate vibration to behave more nonlinearly.

Accurate backbone curves for large-amplitude vibrations of imperfect rectangular plate with viscous damping

This paper deals with the solution of modified-Duffing ordinary differential equation for large-amplitude vibrations of imperfect rectangular plate with viscous damping. Lindstedt's perturbation technique and Runge-Kutta method are applied. The results for both methods are presented and compared for a validity check. It is proved that Lindstedt's perturbation technique only works accurately for a small range of vibration amplitude. For a structure with a sufficiently large geometric imperfection, the well-known softenspring to harden-spring transforming backbone curve is confirmed and better developed. Although the softening to hardening behavior occurs twice in one backbone curve, the turning points share the same vibration frequency. Yet the amplitude for turning points varies due to the existence of imperfection. Moreover, the effect of damping ratio on vibration mode and vibration amplitude is studied. The usual nonlinear vibration tends to behave more linearly under the effect of large damping.

Edge-defined metric buckling of temperature-responsive hydrogel ribbons and rings

We report the temperature-responsive buckling of ribbon-like hydrogel thin films based on photo-crosslinkable copolymers of poly(N-isopropyl acrylamide) (PNIPAM) with pendent benzophenone units. Due to the finite resolution of the photo-lithographic patterning method—here dominated by the convergence of light from the illumination source—nominally homogeneous layers are always surrounded by a more highly swelling border with a lateral size scale similar to the film thickness. As one of the in-plane dimensions of the gel sheet is reduced to only several times its thickness, this edge effect serves as a sufficiently large imperfection to drive buckling of the otherwise metrically flat ribbon. Due to the symmetric geometry, the resulting geometry has essentially constant curvature of the mid-line of the ribbon, with a radius of curvature defined by its thickness and width. In this manner, we prepare thermally responsive overcurved rings that buckle into more highly coiled configurations as they swell, due to the mismatch in metric curvature relative to the geometric shape of the object. We consider the conditions for unfrustrated coiling of both circular and polygonal rings in terms of the number of self-crossings made upon wrapping the surface of a sphere, and demonstrate the fabrication of ‘self-cinching unknots’, i.e. coiled ribbons that can fasten themselves onto other objects upon deswelling, due to topological constraints.

Effects of grain-scale heterogeneity on surface roughness and sheet metal necking

Abstract Strain localization of sheet metals subjected to plane-strain stretching was simulated by finite-element analysis based on a crystal plasticity model. The ratio of specimen thickness to grain size, denoted by Ng, is varied from 1 to 70, and its influence on the evolution of surface roughness and the occurrence of sheet necking is investigated. Roughening of the free surface of the specimen is induced by the grain-scale strain heterogeneity associated with local grain misorientation. The magnitude of surface roughness depends mainly on the grain size and is less sensitive to Ng. As Ng decreases while maintaining the thickness, the magnitude of surface roughness becomes large with respect to the thickness. As a result, large geometrical imperfection is generated. Therefore, the formability of sheet metal is reduced as Ng decreases. Such an effect is found to be particularly considerable when Ng is less than 30. It is also found that the localization mode shifts from a sharp shear banding mode to a localized thinning mode as Ng increases.

Initial imperfection influence on the buckling load of closed elastic isotropic shallow conical shells

The influence of periodical imperfections on the buckling load value of shallow elastic closed conical shells undergoing external pressure was investigated by numerical analysis. Results are compared with experimental data. It is established that initial imperfections significantly influence the buckling pressure value only for large imperfection amplitude (an order of magnitude more than the shell thickness). The existence is established of the effect of a ‘static resonance’.

Advanced postbuckling and imperfection sensitivity of the elastic-plastic Shanley–Hutchinson model column

The postbuckling behavior and imperfection sensitivity of the Shanley‐Hutchinson plastic model column introduced by Hutchinson in 1973 are examined. The study covers the initial, buckled state and the advanced postbuckling regime of the geometrically perfect realization as well as its sensitivity to geometric imperfections. In Section 1, which is concerned with the perfect structure, a new, simple explicit upper bound for all solutions to the problem is found when the tangent modulus at bifurcation vanishes compared to the linear elastic (unloading) modulus. The difference between the upper bound and the solution to an actual problem is determined by an asymptotic expansion involving hyperbolic trial functions (instead of polynomials) which fulfill general boundary conditions at bifurcation and infinity. The method provides an accurate estimate of the maximum load even if it occurs in an advanced postbuckling state. Finally, it is shown that the maximum load is often considerably larger than the bifurcation load. Section 2 presents a new asymptotic expansion which is utilized to study the imperfection sensitivity of the Shanley‐Hutchinson elastic-plastic model column. The method is mainly characterized by three novel features. Firstly, unlike other expansions which are performed around one or maybe two points, ours takes the total postbuckling path of the geometrically perfect structure as its basis, that is, the equilibrium of an imperfect path is written as the postbuckling path of the perfect structure plus an asymptotic contribution. Secondly, the expansion parameter is chosen as the buckling mode amplitude minus its value at initiation of elastic unloading. In this connection, the asymptotic expansion of initiating elastic unloading to the lowest order given by Hutchinson serves as a kind of boundary value for the asymptotic expression. Thirdly, a new and more suitable set of base functions is introduced to enhance the accuracy of the asymptotic expansion for large imperfection levels without compromising the asymptotic behavior for small imperfections. If an asymptotically exact postbuckling solution for the perfect structure around the maximum load has been obtained by some method, be it numerical or asymptotic, then the prediction of the imperfection sensitivity is asymptotically correct.

Nonlinear dynamic stability of composite laminated plates

Catastrophe theory was applied to the investigation of nonlinear dynamic stability of composite laminated plates. The influence of large deflection, initial imperfection, support conditions and ply-angle of the fibers were considered. The catastrophic models and the critical conditions of dynamic buckling of composite laminated plates are obtained.

Species-area curve for land snails on Kikai Island in geological time

Abstract Historical changes in the coastline of Kikai Island of the Ryukyu Islands in the southeast part of Japan were estimated by using a numerical simulation based on a glacio-hydro-isostasy model. Temporal changes in the area of the island during the last 40 Kyr were compared with temporal changes in species diversity in fossil land snails of the island. The species number in the past was theoretically estimated by the area of Kikai Island in the past and a species-area relationship among the modern land snail fauna of the Ryukyu Islands. The theoretical species numbers are very close to the actual ones. This suggests that the change in island area is the main cause of the change in species diversity in Kikai Island. In addition, we discuss causes other than the area, such as island elevation, distance to the nearest large island, climate change, human activity, and imperfection of fossil data. We also discuss the change in Fisher's alpha and body size against the change in the area.

Dynamic buckling and post-buckling of imperfect columns under fluid–solid interaction

Abstract Dynamic buckling and post-buckling properties of simply supported imperfect columns under axial fluid–solid interaction are experimentally and numerically investigated in this study. By observing the elastic–plastic responses of imperfect columns, three critical criteria are defined for the columns with prescribed imperfection, namely, the dynamic buckling criterion, the dynamic yielding criterion and the plastic collapse criterion. The relevant critical impulses are determined for each column. The dynamic buckling and collapse mechanism, and the effects of dynamic load duration and initial imperfection of column on the elastic–plastic dynamic buckling and post-buckling properties are examined. The results indicate that, for columns with small imperfection, dynamic buckling will occur with the increase of the fluid–solid impulse. For columns with large imperfection, however, their failure is dominated by the flexural responses. The dynamic buckling and post-buckling characteristics of columns under fluid–solid interaction are also compared and discussed with respect to those of columns under solid–solid impacts. It is found that they are different from those of columns subjected to either impulsive impact or impact owing to suddenly applied load.

Analytical-Experimental Correlation for a Stiffened Composite Panel Loaded in Axial Compression

A combined analytical and experimental study of a blade-stiffened composite panel subjected to axial compression was conducted. The study e rst examined the effects of the differences between a simple model used to design the panel and the actual experimental conditions. It was found that the large imperfection used in the design process compensated for the simplifying assumptions of the design model, and the experimental failure load was only 10% higher than the design load. Next, e nite element analyses wereperformed in order to correlateanalytical and experimental results. The buckling loads from e nite element analyses agreed well with the experimental failure loads. However, substantial differences were found in the out-of-plane displacements of the panel. Finite element simulations of nonuniform load introduction with general contact dee nitions improved correlation between the measured and predicted out-of-plane deformations.