Corrugation Direction Research Articles

Lateral behavior and PFI model of sinusoidal corrugated steel plate shear walls

This study focused on the lateral behavior of sinusoidal corrugated steel plate shear walls (CoSPSWs), which consist of a steel boundary frame and sinusoidal corrugated infill wall plates. Firstly, eigenvalue buckling analyses were conducted on sinusoidal corrugated wall plates under pure shear, and local as well as global shear buckling stress formulas were proposed. Nonlinear pushover analyses were then conducted on sinusoidal corrugated steel plate shear walls with different corrugation configuration, corrugation direction as well as influences from gravity loads. The results show that the lateral behavior of sinusoidal corrugated wall plates is obviously affected by the corrugation configuration and gravity load effects, but not much by the corrugation direction. Based on the shear slenderness ratio, sinusoidal corrugated wall plates could be classified into stocky, moderate and slender walls, with lateral load-resisting mechanism corresponding to shear yielding, inelastic shear buckling, and elastic shear buckling followed by incomplete tension field action, respectively. CoSPSWs with stocky wall plates tend to have both good lateral capacity and ductility, CoSPSWs with moderate wall plates would still have good lateral capacity but lower ductility, and CoSPSWs with slender wall plates would have good ductility but lower lateral capacity. Shear strength formulas were proposed for horizontal corrugated wall plates, not affected by gravity loads due to accordion effects, as well as vertical corrugated wall plates considering the gravity load effects. Plate-frame interaction (PFI) models were also proposed for horizontal and vertical CoSPSWs considering the gravity load effects.

Conceptual design and application research of a corrugated flexible skin with high bending stiffness

AbstractIn this paper, sliding panels are used to increase the bending stiffness of the classic corrugated flexible skin, and the corresponding application procedure for aircraft structures is developed. After the conceptual design of the corrugated flexible skin with sliding panels is proposed, the analytical models to calculate the equivalent tensile and bending properties are investigated. At the same time, its flexibility in the corrugation direction and the load-bearing capacity (is proportional to the bending stiffness) in the direction perpendicular to corrugation are studied by numerical simulation and experiment. The application procedure is established based on geometric analysis and strain definition, and according to this procedure, the corrugated flexible skin with sliding panels is applied to the drooping leading edge to eliminate the gap on the upper skin. The results show that the corrugated flexible skin with sliding panels has more bending stiffness than the classic corrugated flexible skin in the direction perpendicular to corrugation while maintaining the deform ability in the corrugation direction, and the application procedure is effective and can be applied to other parts of the aircraft structure.

Chevron Angle Effect on Plate and Shell Heat Exchangers Measured with Particle Tracking Velocimetry

The effect of the Chevron angle on inner flow structures within plate and shell heat exchangers (PSHE) has been determined for low, intermediate, and high pressure drop channels. Local flow statistics within PSHE channels have been quantified by experiments at Reynolds number 3450 in transparent test sections with 15/15°, 15/45° and 45/45° Chevron angles with the aid of particle tracking velocimetry. Velocity vectors projected onto the channel frontal view derived by straightforward interpolations of consecutive positions of a particle trajectory have been found to yield the mean flow characteristics. Particle trajectories at low Chevron angles resemble longitudinal wavy flow, whereas they preferentially follow the corrugation direction in angles higher than 45°. For the 15/45° configuration, there is lack of symmetry regarding the vertical velocity component about the heat exchanger central plane. Flow recirculation characterizes the outlet, and its intensity increases with decreasing Chevron angles. The ratios of Fanning friction factors for 15/15° and 15/45°, and for 15/15° and 45/45° are 1.35 and 2.24, respectively. The non-uniform velocity field across the PSHE channel affects the Nusselt number homogeneity. For channels with 45/45° Chevron angles, it can be 80% higher than the average Nusselt number at the channel center, whereas it can be 80% lower near the channel boundaries.

Seismic behavior of corrugated double-skin composite wall (DSCW) with concrete-filled steel tubes: Experimental investigation

This paper presents the seismic behavior of corrugated double-skin composite wall (DSCW) with concrete-filled steel tube boundary elements. Fifteen 1/3-scale DSCW specimens, varying in shear span ratio, axial compression ratio, corrugation direction and shape, connector type and steel faceplate profile, were tested under cyclic loading. All specimens except W15 failed in flexural failure. The cyclic response of vertical corrugated DSCW was much better than that of horizontal corrugated DSCW. Compared to flat DSCW, corrugated DSCW, even with a 20% reduction in the concrete cross-sectional area, had considerably higher peak load, ductility ratio and energy dissipation. The setting of connectors slowed down the damage rate of the corrugated DSCW in the failure stage, and also significantly improved the peak load and ductility of the corrugated DSCW with λ = 1.5. Increasing the shear span ratio significantly reduced the peak load and initial stiffness of the DSCW, but did not affect the ductility and energy dissipation. The corrugated DSCW, failed in flexural-dominated mode, had excellent collapse resistance, achieving a drift ratio exceeding 2% and a ductility ratio greater than 3.3, and it was recommended to take n = 0.3 as the limit value of axial compression ratio of corrugated DSCW. Moreover, the average ratio of Pt/Pc was 1.082 with a mean absolute error of 0.068 and a root mean square error of 0.084, indicating that the calculated value of proposed formulas for calculating the lateral strength of vertical corrugated DSCW can reflect the measured data well.

Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation.

The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. This is why numerical analyses are becoming a common standard in this branch of manufacturing. Such trends cause either the use of advanced computational models that take into account the full 3D geometry of the flat and wavy layers of corrugated board, or the use of homogenization techniques to simplify the numerical model. The article presents theoretical considerations that extend the numerical homogenization technique already presented in our previous work. The proposed here homogenization procedure also takes into account the creasing and/or perforation of corrugated board (i.e., processes that undoubtedly weaken the stiffness and strength of the corrugated board locally). However, it is not always easy to estimate how exactly these processes affect the bending or torsional stiffness. What is known for sure is that the degradation of stiffness depends, among other things, on the type of cut, its shape, the depth of creasing as well as their position or direction in relation to the corrugation direction. The method proposed here can be successfully applied to model smeared degradation in a finite element or to define degraded interface stiffnesses on a crease line or a perforation line.

Determination of corrugated core sandwich panels elastic constant based on three different experimental methods and effect of structural integrity on flexural properties

This study deals with the investigation of flexural stiffness and transverse shear rigidity in the direction of corrugation of the integrated and non-integrated corrugated core sandwich panels with the rectangular core. The non-integrated sandwich panels were reinforced with conventional 2-D fabrics in which resin provides the bond between core and skins. The integrated sandwich panels were reinforced with 3-D weft knitted fabrics in which bonding of the core wall to skins was carried out by combined efforts of knitted loop and resin. Using weft knitting technical capabilities, samples of the integrated and non-integrated structures were manufactured with the uppermost degree of resemblance in terms of geometry and mass. Flexural stiffness and transverse shear rigidity of the structures based on the known and unknown facing modulus of ASTM D7250 standard and Nordstrand–Carlsson methods were calculated. The estimated elastic constants based on unknown facing modulus and the Nordstrand–Carlsson methods were found to be highly compatible. However, the unknown facing modulus method is prone to disclose the statistical significant differences between the elastic constants of the structures with fewer tests. Regarding the unknown facing modulus method, it was found that the flexural stiffness and transverse shear rigidity of the non-integrated structure in the direction of corrugation were higher than those of the integrated structure. Results also indicated that the load-carrying capacity in the direction of corrugation was significantly higher in case of the non-integrated rectangular core structure compared with that of the integrated structure.

The effect of core geometry on flexural stiffness and transverse shear rigidity of weight‐wise identical corrugated core sandwich panels reinforced with 3D flat spacer knitted fabric

AbstractThis article aims to evaluate the effect of core geometry on flexural stiffness and transverse shear rigidity of corrugated core sandwich panels both experimentally and numerically. Using vacuum‐assisted resin transfer molding (VARTM) method, three composite sandwich panels reinforced with 3D weft knitted spacer fabric with rectangular, hat‐type (trapezoidal) and triangular cross‐sectional geometries were produced. In order to eliminate weight variation among the produced sandwich panel samples, the unit cell dimensions, core wall to skin angle, and the yarn count used to knit the core wall were carefully chosen. Results pointed to existence of statistically significant difference between the load‐carrying capacity and transverse shear rigidity in the direction of corrugation of the structures. It was concluded that triangular and rectangular structures have the highest and lowest load‐carrying capacity, transverse shear rigidity, and core shear modulus in the direction of corrugation, respectively.

Compression Capacity of Corrugated Core Hybrid Composite Sandwich Structure

Improvement of mechanical properties of light-weight corrugated core sandwich structures is a big demand in aerospace applications. Among these applications, space vehicles which encounter pressure loads and severe aerodynamic heating during ascent and reentry. The open-cell corrugated core is useful for active cooling of the sandwich structures. In this work, hybrid composite structural members with fiberglass corrugated core and carbon fiber skin facings were manufactured using vacuum bag technique. Different specimen configurations with rectangular cross-section area have been subjected to the load in the longitudinal direction of the corrugation and examined by edgewise compression test. The proposed testing has been applied to take advantage of the highest inertia of the specimen in such orientation. The test provides a basis for estimating the load carrying capacity when these structure members are used as individual webs in the aircraft interiors. Also as the core sheet is turned by 90° to the regular load direction, this structure member is similar to the so-called honeycomb when ordered in parallel rows and hence it is appropriate for floor sandwiching. In contrary to a honeycomb, this core consists of fiberglass laminate and therefore higher compressive resistance is associated. The results exhibit high values of both stiffness and ultimate compression force in the corrugation direction. For the rectangular area and the open corrugated contour, specific properties relative to the weight are extremely high. Also, the results and graphs indicate that there must be at least three corrugated ligaments with a trapezoidal cross section of 0.5” height and 63o per cell to grantee stability under load and high absorbed energy in the non-linear stage as well.

Analytical investigation of composite sandwich beams filled with shape memory polymer corrugated core

Shape memory polymers (SMPs) are a class of smart materials which can recover their shape even after many shape changes in application of an external stimulus. In this paper, flexural behavior of a composite beam, constructed of a corrugated part filled with SMPs, is studied. This composite beam is applicable in sensor and actuator applications. Since the corrugated profiles display higher stiffness-to-mass ratio in the transverse to the corrugation direction, the beams with a corrugated part along the transverse direction are stiffer than ones with a corrugated part along the length. Employing a developed constitutive model for SMPs and the Euler–Bernoulli beam theory, the behavior of the composite beam is studied. Since the utilized constitutive model is in the integral form, the finite-difference-method is used for discretizing the equations. It is shown that load capacity is increased in both composite beams compared to a pure SMP beam. This bigger load capacity is obtained by a low decrease in shape fixity. In addition, for different corrugated shapes (trapezoidal, pseudo-sinusoidal and triangular) with the same SMP content, the beam response is obtained. Finally, the results of the constrained stress-recovery are obtained and the effects of mechanical properties on its behavior, are studied.

Effect of Corrugation Angle and Direction on the Performance of Corrugated Steel Plate Shear Walls

Corrugated steel plate shear wall (CSPSW) is one of the lateral resistance systems which consists mainly of steel frame (beam and column) with vertical or horizontal corrugated steel plate connected to the frame by weld, bolts or both. This type of steel shear wall characterized by low cost and short construction time with high strength, ductility, initial stiffness and excellent ability to dissipate energy. The aim of this paper is to evaluate the effect of corrugation angle and its direction on the performance of CSPSW under cyclic loading. The Finite element analysis was employed to achieve the research aim. The FE models were validated with experimental data available in the literature. Results reveal that the corrugation angle has a clear influence on initial stiffness, strength, ductility, and energy dissipation of CSPSW. The optimum performance of CSPSW can be obtained with angles of 30o for CSPSW with vertical corrugation and 20o for CSPSW with horizontal corrugation. The use of CSPSW with vertical corrugation provides higher strength, stiffness, and ductility compared to CSPSW with horizontal corrugation. Therefore, it is recommended to use CSPSW with vertical corrugation.

Numerical investigation of heat transfer and friction characteristics for turbulent flow in various corrugated tubes

Thermal and hydraulic characteristics of turbulent water flow in a transverse corrugated tube with various corrugation direction (inward/outward) and corrugation shape (triangle, curve, rectangle, and trapezoid) are numerically investigated. The axisymmetric model of corrugated tubes with 10 mm inner diameter was investigated by changing the geometrical parameters for Reynolds number ranging from 5000 to 61,000 and constant heat flux boundary condition. Structured, nonuniform grid system is applied. Momentum, continuity, and energy equations were treated by means of a finite volume method using the SIMPLE scheme with the k–ε turbulence model and enhanced wall treatment. The results reveal that corrugation direction and corrugation shape have perceptible effects upon the heat transfer in the form of Nusselt number ( Nu) and pressure drop in the form of friction factor (ƒ). The average Nu for (inward) trapezoidal, rectangular, curved, and triangular corrugation shapes are 52.61%, 50.12%, 47.82%, and 44.96%, respectively, higher than the smooth tube. The average Nu for (outward) trapezoidal, curved, triangular, and rectangular corrugation shapes are 48.31%, 45.72%, 41.23%, and 40.94%, respectively, which are higher than a smooth tube. The results reveal that both inward/outward curved and triangular roughness shape have the superior performance evaluation criterion than rectangular and trapezoidal. Turbulence kinetic energy contour shows the increase in heat transfer performance for all corrugated tubes compared with a smooth tube. Inward corrugated tube provides the highest turbulence kinetic energy along the tube length and, consequently, the highest heat transfer. In addition, inward corrugated tubes provide the highest values and homogeneity of the velocity distribution along the core of tubes.

Investigation of Stress Intensity Factor for Corrugated Plates with Different Profiles Using Extended Finite Element (XFEM)

Corrugated plates play very important role in variousengineering applications. The occurrence of crack in the body ofcorrugated plate might results in catastrophic failure. In thepresent paper there are different profiles of corrugated plates(trapezoidal, sinusoidal and triangle) that are studied. In eachprofile the stress intensity factor and shape factor werecalculated for various crack orientations, various corrugationangles and different curvature radius for the same profile. Theyare all subjected to different loading conditions using ExtendedFinite Element Method (XFEM).It is found the stress intensity factor when load applied parallelto corrugation direction is higher when load appliedperpendicular to corrugation direction. Also found that thestress intensity factor increase by 115% when curvature radiusincreases with the load applied perpendicular to corrugation.This study also found and explained that the stress intensityfactor increases slightly when the corrugation angle of the trianglecorrugated plate increases. In all cases studied, the trapezoidalthe corrugated plate shows the lower values of the stress intensity factorcompared to the sinusoidal and triangle corrugated plates.

Cyclic analyses of corrugated steel plate shear walls

SummaryCorrugated steel plate shear wall (CoSPSW), which consists of a steel boundary frame and a corrugated steel wall panel with the corrugation in the horizontal or vertical direction, is a new type of lateral load‐resisting system in the family of steel plate shear walls. Compared with the unstiffened special plate shear walls (SPSW), CoSPSW would have greater elastic buckling capacity and more resistance to the gravity loads transferred to the wall panel or neatly avoid them, depending on the corrugation direction. The main research contents of this paper is on the cyclic behavior of CoSPSWs and comparison with SPSWs. Nonlinear push‐over and cyclic analyses were conducted on a group of CoSPSW and SPSW models, and parametric studies were performed with different panel and frame configuration, as well as gravity load effects. It turns out that CoSPSWs with deep corrugation have higher lateral stiffness, lateral strength, and energy dissipation than SPSWs, whereas CoSPSWs with shallow corrugation have higher lateral stiffness and ductility, but lower lateral strength than SPSWs. For all cases investigated, CoSPSWs have stable hysteric curves with no almost pinching, and they are much less sensitive to the influence of gravity loads or weaker boundary frames, compared to SPSWs.

Bending and buckling of a metal seven-layer beam with crosswise corrugated main core – Comparative analysis with sandwich beam

The study is devoted to thin-walled simply supported sandwich beams: three and seven-layer beams. Seven-layer beams are composed of a trapezoidally crosswise corrugated main core and two three-layer facings with trapezoidally lengthwise corrugated cores. Essential difference between such a structure and classical three-layer beams consists in the fact that the facings are of three-layer structure too. Hence, the structure is a seven-layer beam, the layers of which are distinguished by different properties. The thin-walled beam with three trapezoidally corrugated cores is an innovatory orthotropic structure, not referred to in the literature. Characteristic feature of the beam consists in differentiation of shear effects in particular layers, according to the core corrugation direction. Deformation of the cross section of the beam depends on the direction too. An original mathematical model is formulated, which includes the hypothesis of deformation of the cross section of the beam, inclusive of the displacement and strain fields, and rigidities of the layers in particular directions. The adequate model of three-layer beam with steel foam core is also formulated. Basing on the principle of the total potential energy the equations of equilibrium are derived for three and seven-layer beams, respectively. Then the equations are analytically solved. In case of seven-layer beams the deflections and the critical axial force are determined for different values of the trapezoidal corrugation pitch of the main core. The results are compared with adequate for three-layer beam and presented in Tables. It is concluded that such seven-layer beam – plate band with three-layered facings is more resistant to the load than the classical three-layered beams of the same mass with regard to strength and stability. Additional effect of the research consists in generalization of classical theories of sandwich plates.

Study of Stress Intensity Factor in Corrugated Plate Using Extended Finite Element Method (XFEM)

The presence of crack with different lengths and locations in structure of corrugated plate is studied. XFEM is along with enrichment function based on partition of unity is used for the calculation of stresses due to the presence of crack. Stress intensity factors (KI) and relations for shape factors (C) are calculated for the four most common crack orientations and loading conditions. Results showed that crack in the flange with load perpendicular to corrugation direction yields higher values of KI and C in addition to wider spread of stress concentration contours than the web. When loading becomes parallel to corrugation direction, the stress intensity factor and C factor become remarkably less due to the corrugation stiffness. Third mode KIII is appeared in the fourth case in addition to the presence of the first mode KI due to 45o inclination of the web and applied load direction

Shape optimisation of composite corrugated morphing skins

Abstract One of the challenging parts of the morphing wing is the anisotropic skin, which must be flexible enough to allow the wing to change its shape and at the same time being stiff enough to withstand the aerodynamic loads. Composite corrugated skins have exceedingly anisotropic behaviour as they are stiff along the corrugation direction but flexible in transverse direction. Hence, elastomeric coated composite corrugated panels have been proposed as a candidate for application in morphing wings. This paper presents the shape optimisation of the corrugation with respect to better performance of the morphing skin and manufacturing constraints. The shape of the skin is optimised by minimising the in-plane stiffness and weight of the skin and maximising its flexural out-of-plane stiffness. The objective functions were obtained from homogenised model that depends on geometric and mechanical properties of the coated corrugated panel by means of finite element method for thin beams. A few methods of optimisation were considered: aggregated and genetic algorithm methods as representative of two major categories of multi-objective solving methods. A number of different approaches are proposed in order to solve the problem, such as corrugated skin with and without elastomer coating. The advantages of the new optimised shape of the corrugated skin over the typical shapes are discussed.

Characteristic and formation mechanism of matt surface of double-rolled copper foil

Copper foils for flexible printed circuit boards were prepared by double rolling, and the matt surface of double-rolled copper foil was characterized by atomic force microscope, scanning electron microscope, 3D optical interferometer, optical microscope and surface profiler. The morphology characteristics of matt surface were studied, and the formation mechanism of matt surface was discussed. The results showed that the matt surface of the double-rolled copper foil presented rough and relatively homogeneous morphology, and the morphologies of upper and lower matt surfaces were practically coincident. As the copper strips just entered into the deforming zone, the roughening of laminated surface occurred, but the roughness was relatively small. When the copper strips passed through the neutral plane, the roughness of the laminated surface increased significantly. In the backward slip zone, the initial micro-dimples between the two laminated surfaces were connected in the rolling direction, which led to the formation of larger and airtight dimples; when the copper strips moved toward the neutral plane and entered into the forward slip zone, the pressure of fluid in the airtight dimples increased rapidly, which enhanced the depths of the dimples; meanwhile, the depression corrugations with certain depth and larger width were formed on the laminated surface because of the dimple connection in the width direction. The copper foils with thickness of 36–54μm were fabricated by double rolling, and the Rz value of their matt surfaces was 1.0–1.3μm, which meet the requirements for directly using as adhesive surface of resin substrate, and therefore multiple roughening treatments during the traditional production process of flexible printed circuit board might be omitted. The formation mechanism of the matt surface of double-rolled copper foil proposed on the basis of the metal flow and deformation mechanics theory could explain the representative characteristics of the length direction of corrugations on matt surface being perpendicular to the rolling direction, several corrugations within a grain on the matt surface and the coincident morphologies of the upper and lower matt surfaces.

보강된 사다리꼴 주름판의 과도 응답 해석

In this paper, the transient response analysis of the trapezoidal corrugated plate subjected to the pulse load is investigated by the theoretical method. Three types of pulse loads are considered: stepped, isosceles triangular and right triangular pulse loads. The corrugated plates can be represented as an orthotropic plate. Both the effective extensional and flexural stiffness of this equivalent orthotropic plate are considered in the analysis. The plate is stiffened by concentric stiffeners perpendicular to the corrugation direction. The stiffening effect is represented by the discrete stiffener theory. This theoretical results are validated by those obtained from 3D finite element analysis based on shell elements. Some numerical results are presented to check the effect of the geometric properties.

Influences of Oblique Surface Corrugation on Boundary-Layer Instability

The influence of surface corrugation on the growth of Tollmien–Schlichting (TS) waves was examined experimentally in a zero-pressure-gradient boundary layer. Corrugations with various oblique angles were considered to see how the growth of two-dimensional (2D) TS waves was affected by the angle of surface corrugation. The results clearly showed that as the oblique angle increased, the destabilizing effect (which was pronounced for the 2D corrugation) gradually weakened and that when the corrugation direction was normal to the TS wave, the corrugation little influenced the growth of 2D TS wave though the wave underwent a spanwise distortion corresponding to the corrugation.

집중질량을 고려한 보강된 사다리꼴 주름판의 진동해석

In this paper, the vibration characteristics of the trapezoidal corrugated plate with axial stiffeners and lumped masses are investigated by the analytical method. The corrugated plate can be treated as an equivalent orthotropic plate as this plate has different flexure properties in two perpendicular directions; flexible in the corrugation direction and stiff in the transverse direction. The effective extensional and flexural stiffness of the equivalent plate are considered to obtain the precise solution in the analysis. The plate is stiffened by concentric stiffeners horizontally to the corrugation direction. The discrete stiffener theory is adopted to consider the position of stiffener. To demonstrate the validity of the proposed approach, the comparison is made with the results of 3D ANSYS finite element solutions. Some numerical results are presented to check the effect of the geometric properties.