Sheet Thickness Ratio Research Articles

Spray characteristics of liquid-liquid Pintle injector

Liquid-liquid cross flow Pintle injector studies are of renewed interest due to their flow control characteristics. In Pintle Injectors, the interaction is between a thin annular sheet and radial jets of liquid. The cause of breakup of this liquid element and the formation of the spray are effectively brought out in this study. The spray pattern is investigated for different momentum ratio and its influence on the droplet formation and size distribution is demonstrated. Two configurations of Pintle injector were subjected to cold flow trails, ie., Type-I and Type-II. Laser shadowgraphy investigation was carried out on two momentum ratios of ξ = 1 and ξ = 0.7 for Type-I injector. The geometry of liquid before the formation of the spray is a hollow conical sheet. Radial impinging jets generate wave instabilities on the surface of the conical sheet. Instabilities grow in amplitude and the amplitude growth is a function of Weber number and λ/a (wavelength to sheet thickness ratio). Lower momentum ratio flows lead to better atomization as compared to higher momentum ratio flows. The D32 values obtained are 840 μm and 650 μm for ξ = 1 and ξ = 0.7 respectively. The influence of liquid sheet thickness and Weber number on the instability waves generated and the droplet size distribution is understood. The sheet thickness for the two cases of ξ = 1 and ξ = 0.7 were estimated by applying inviscid solution theory and the sheet thickness are 172 μm and 65 μm respectively. Type-II injector was designed based on the analysis of the Type-I injector test results. The annular gap in Type-II injector was reduced to 95 μm to achieve smaller sheet thickness and increased Weber number as compared to Type-I injector. Atomization of the liquid sheet is improved to a greater extend in Type-II injector, with droplet sizes of the order of 100 μm.

Nonlinear vibration of sandwich plates with FG-GRC face sheets in thermal environments

Present investigation deals with the nonlinear vibration of a sandwich plate with a homogeneous core and graphene-reinforced composite (GRC) face sheets supported by an elastic foundation under thermal environmental conditions. The material properties of GRC face sheets are assumed to be piece-wise functionally graded by changing the volume fraction of graphene in the thickness direction. The material properties of both the homogeneous core and the GRC face sheets are assumed to be temperature-dependent, and are estimated by the extended Halpin-Tsai micromechanical model. Reddy’s higher order shear deformation plate theory and the von Kármán-type kinematic nonlinearity are used to derive the motion equations which account for the plate-foundation interaction and the thermal effects. The nonlinear vibration solutions for the sandwich plate can be obtained by using a two-step perturbation technique. The effects of distribution type of reinforcements, core-to-face sheet thickness ratio, temperature variation, foundation stiffness and in-plane boundary conditions on the nonlinear vibration characteristics of sandwich plates with piece-wise functionally graded GRC face sheets are discussed in detail.

Tensile capacity of self-piercing rivet connections in thin-walled steel structures

The paper presents an experimental investigation on the tensile behavior and strength of self-piercing rivet (SPR) connections used in cold-formed thin-walled steel structures. The sheet thickness ratio, the sheet combination type, and the rivet length were analyzed for their effects on the tensile performance of SPR connections. The research also studied the feasibility of the existing calculation method of SPR connections and the other design methods of self-tapping screw connections for the SPRs investigated herein. Based on the test results and analyses, a new design method for the tensile capacity was proposed. The test results showed that the sheet thickness ratio, the sheet combination type, and the rivet length were the key factors controlling the failure mode and the tensile capacity of SPR connections. The proposed design method for the tensile capacity of SPR connections considers those primary factors as well as the different failure modes.

Nonlinear Transient Response of Functionally Graded Material Sandwich Doubly Curved Shallow Shell Using New Displacement Field

In this paper, the nonlinear transient dynamic response of functionally graded material (FGM) sandwich doubly curved shell with homogenous isotropic material core and functionally graded face sheet is analyzed using a new displacement field on the basis of Reddy’s third-order shear theory for the first time. The equivalent material properties for the FGM face sheet are assumed to obey the rule of simple power law function in the thickness direction. Based on Reddy’s theory of higher shear deformation, a new displacement field is developed by introducing the secant function into transverse displacement. Four coupled nonlinear differential equations are obtained by applying Hamilton’s principle and Galerkin method. It is assumed that the FGM sandwich doubly curved shell is subjected to step loading, air-blast loading, triangular loading, and sinusoidal loading, respectively. On the basis of double-precision variable-coefficient ordinary differential equation solver, a new program code in FORTRAN software is developed to solve the nonlinear transient dynamics of the system. The influences of core thickness, volume fraction, core-to-face sheet thickness ratio, width-to-thickness ratio and blast type on the transient response of the shell are discussed in detail through numerical simulation.

Effect of physical and geometrical parameters on low-velocity impact response of sandwich beams with carbon nanotube reinforced face sheets

The response of sandwich beam with carbon nanotube (CNT) reinforced composite face sheets and soft core when subjected to the action of an impacting mass is analysed theoretically. Contact force between the impactor and the beam is obtained using the conventional Hertz law. The field equations are derived via the Ritz based applied to the total energy of the system. The solution is obtained in the time domain by implementing the well-known Runge–Kutta method. After examining the validity of the present solution, the effects of distribution of CNTs, nanotube volume fraction, core-to-face sheet thickness ratio, initial velocity of the impactor and the impactor mass are studied in detail. Finally, it is concluded that, the highest peak contact force and the lowest indentation of the top face sheet belong to the sandwich beam with V-distribution figure of face sheet, followed by the uniformly distributed and Λ-ones, respectively. Keywords: Carbon nanotube fibers, sandwich beam, soft core.

Vibration response of viscoelastic sandwich plate with magnetorheological fluid core and functionally graded-piezoelectric nanocomposite face sheets

In this research, vibration analysis of a viscoelastic sandwich plate rested on a visco-Pasternak foundation is investigated. Sandwich plate consists of a magnetorheological (MR) fluid core and viscoelastic nanocomposite face sheets which include piezoelectric matrix and functionally graded carbon nanotubes (FG-CNTs) fiber. Core and face sheets are affected by applying magnetic and electric fields, respectively. The elastic medium is simulated by a visco-Pasternak model which is considered in terms of the effects of springiness, shear and damping of foundation. At first, the constitutive equations of sandwich plate are expressed by employing the geometric continuity conditions. Then, the equations of motion are derived by applying the energy method and Hamilton’s principle and an appropriate analytical approach is proposed to solve them. This approach can be considered as the different boundary conditions. Finally, the influences of various parameters such as the type of MR material, core to face sheets thickness ratio, volume fractions and symmetric distributions of CNTs in face sheets, magnetic and electric fields, viscoelastic constant of face sheets and elastic medium on the dimensionless natural frequencies of sandwich plate are studied. The results show that increasing core-to-face sheet thickness ratio leads to a decrease in the natural frequencies because the MR fluid core is softer than nanocomposite face sheets. Thus, the MR fluid core acts like a damper. Also, the loss factor of the MR fluid core decreases with increasing magnetic field intensity, and consequently, the natural frequency grows. In addition, increasing the volume fraction of CNTs causes the stiffness of the structure to increase. The results of this research can be utilized to realize applicable semi-active devices with controllable stiffness.

Thermal buckling analysis of functionally graded carbon nanotube-reinforced composite sandwich beams

Thermo-mechanical buckling of sandwich beams with a stiff core and face sheets made of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) within the framework of Timoshenko beam theory is presented. The material properties of FG-CNTRC are supposed to vary continuously in the thickness direction and are estimated through the rule of mixture. Also the properties of these materials should be considered temperature dependent. The governing equations and boundary conditions are derived by using Hamilton's principle and solved using an efficient technique called the Differential Transform Method (DTM) to achieve the critical buckling of the sandwich beam in uniform thermal environment. A detailed parametric study is guided to investigate the effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, and clamped-clamped, simply-simply and clamped-simply end supports on the critical buckling behavior of sandwich beams with FG-CNTRC face sheets. Numerical results for comparison of sandwich beams with uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) face sheets with those with FG-CNTRC face sheets are also presented.

Geometrically nonlinear analysis of sandwich beams under low velocity impact: analytical and experimental investigation

Nonlinear low velocity impact response of sandwich beam with laminated composite face sheets and soft core is studied based on Extended High Order Sandwich Panel Theory (EHSAPT). The face sheets follow the Third order shear deformation beam theory (TSDT) that has hitherto not reported in conventional EHSAPT. Besides, the two dimensional elasticity is used for the core. The nonlinear Von Karman type relations for strains of face sheets and the core are adopted. Contact force between the impactor and the beam is obtained using the modified Hertz law. The field equations are derived via the Ritz based applied to the total energy of the system. The solution is obtained in the time domain by implementing the well-known Runge-Kutta method. The effects of boundary conditions, core-to-face sheet thickness ratio, initial velocity of the impactor, the impactor mass and position of the impactor are studied in detail. It is found that each of these parameters have significant effect on the impact characteristics which should be considered. Finally, some low velocity impact tests have been carried out by Drop Hammer Testing Machine. The contact force histories predicted by EHSAPT are in good agreement with that obtained by experimental results.

Laser edge forming to increase the bending radius in hemming

Hemming can be used, for example, to join dissimilar materials which cannot be welded by conventional laser or arc based processes. A critical value in hemming is the ratio of outer sheet bending radius and outer sheet thickness because cracks can occur in outer sheets with low ductility due to a small bending radius. In this study, a novel approach is introduced for increasing the bending radius by laser based edge forming. The laser beam melts the edge of the inner sheet prior to the hemming process. In laser edge forming, the edge thickness increases due to the surface tension of the melt. The edge cross-section has typically a nearly circular shape after solidification. Two laser beam irradiation strategies were investigated. In case of the first strategy, a defocused laser beam was applied. The second strategy combined a focused laser beam resulting in the formation of a vapor capillary (keyhole) with sinusoidal beam oscillation transversal to the sheet edge. The results show that the position of the cylindrical edge cross-section according to the sheet plane could be affected by the applied irradiation strategy. The needed laser power was significantly lower when using a focused laser beam due to the deep penetration effect. The potential of the laser edge forming technique for crack-free hemming processes was demonstrated with 1 mm thick aluminum alloy sheets by carrying out stripe tests.

Indentation of rigidly supported sandwich beams with core gradation

Sandwich structures with optimized foam core have received considerable attention. The objective of this study is to investigate the indentation of sandwich beams with a two-layer core gradation. An analytical model is developed to predict the large indentation deflections of sandwich beams with two-layer metal foam cores subjected to the concentrated loading. Analytical predictions are compared with finite element simulations and good agreement is obtained. The effects of face sheet strength, core strength, and thickness ratio on the initial failure load of sandwich beams with core gradation are discussed in detail. The results show that through variation of the core thickness ratio and core strength ratio, the failure mode of sandwich beams could be controlled. Meanwhile, the load-carrying and energy absorption capacity of the sandwich beams can also be improved. This work is useful in the core design of the sandwich structures.

Postbuckling of sandwich plates with graphene-reinforced composite face sheets in thermal environments

Abstract Present investigation deals with the buckling and postbuckling behavior of a sandwich plate with a homogeneous core and graphene-reinforced composite (GRC) face sheets resting on an elastic foundation in thermal environments. The material properties of GRC face sheets are assumed to be piece-wise functionally graded by changing the volume fraction of graphene in the thickness direction. The material properties of both the homogeneous core layer and the GRC face sheets are assumed to be temperature-dependent, and are estimated by the extended Halpin-Tsai micromechanical model. The higher order shear deformation plate theory and the von Karman-type kinematic nonlinearity are used to derive the governing equations which account for the plate-foundation interaction and the thermal effects. The buckling loads and the postbuckling equilibrium paths are obtained by using a two-step perturbation technique. The impacts of the distribution type of reinforcements, core-to-face sheet thickness ratio, plate aspect ratio, temperature variation, foundation stiffness and in-plane boundary conditions on the postbuckling behavior of sandwich plates with functionally graded GRC face sheets are studied in detail.

Thermo-mechanical analysis of carbon nanotube-reinforced composite sandwich beams

In this paper Timoshenko beam theory is employed to investigate the vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) Beams with a stiff core in thermal environment. The material characteristic of carbon nanotubes (CNT) are supposed to change in the thickness direction in a functionally graded form. They can also be calculated through a micromechanical model where the CNT efficiency parameter is determined by matching the elastic modulus of CNTRCs calculated from the rule of mixture with those gained from the molecular dynamics simulations. The differential transform method (DTM) which is established upon the Taylor series expansion is one of the effective mathematical techniques employed to the differential governing equations of sandwich beams. Effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, different thermal environment and various boundary conditions on the free vibration characteristics of FG-CNTRC sandwich beams are studied. It is observed that vibration response of FG-CNTRC sandwich beams is prominently influenced by these parameters.

Investigations on remote laser beam welding of dissimilar joints of aluminum alloys and steel with varying sheet thicknesses for car body construction

For lightweight construction, different steel and aluminum materials with various thicknesses can be welded together, depending on the dimensions and the individual functions of the workpiece. Specifically for frame and body construction, remote laser beam welding has been established as a suitable and efficient joining method for similar material seams for several years. In contrast to joining similar materials, thermal joining of steel and aluminum alloys includes different technological challenges due to the formation of hard and brittle intermetallic phases, which decreases the strength and the formability of the dissimilar joints. In the context of these requirements, the presented results show, besides the influence of different steel materials, particularly the influence of different sheet thicknesses and thickness ratios on the appropriate process parameters for remote laser beam welded lap joints of steel and aluminum alloys, respectively. Different thickness ratios, process parameters, and material properties affect the geometrical formation of the weld seam regarding penetration depth tE and weld width b, which mainly influences the composition of the molten bath and accordingly the transmittable forces. Within the scope of the presented investigations, dissimilar joints of the steel materials such as HX220LAD+Z100, 22MnB5+AS150, and 1.4301 as well as the aluminum alloy such as AA6016-T4 are characterized. Among others, the influences of the energy per unit length, material grade, and sheet thickness ratio on the achievable strengths were analyzed. The characterization of the dissimilar joints includes tensile shear tests and metallographic analyses, depending on the energy per unit length.

Free Vibration of a Thick Sandwich Plate Using Higher Order Shear Deformation Theory and DQM for Different Boundary Conditions

In this paper, the effect of different boundary conditions on the free vibration analysis response of a sandwich plate is presented using the higher order shear deformation theory. The face sheets are orthotropic laminated composites that follow the first order shear deformation theory (FSDT) based on the Rissners-Mindlin (RM) kinematics field. The motion equations are derived considering the continuity boundary conditions between the layers based on the energy method and Hamilton's principle. The frequency and mode shapes of the structure are obtained using the differential quadrature method (DQM). The effects of different parameters such as the face sheet-to-core stiffness ratio, the boundary conditions, and the core-to-face sheet thickness ratio on the frequency of the sandwich plate are shown. Moreover, the numerical results indicate that the frequency of the CCCC and CFFF sandwich plates predict the higher and lower frequency, respectively.

Free vibration analysis of sandwich beams with honeycomb-corrugation hybrid cores

The vibration performance of sandwich beams with honeycomb-corrugation hybrid cores was investigated in this paper. The method of homogenization was employed to obtain the equivalent macroscopic stiffness of honeycomb-corrugation hybrid cores. Finite element methods and modal analysis techniques have been used to predict their vibration characteristics (i.e. their natural frequencies and mode shapes). It is shown that in most cases the predictions by using the equivalent homogenization model (2D model) agree well with the experimental and three-dimensional finite element calculated results. For sandwich beams with corrugated cores, the filling honeycomb not only enhances their flexural rigidity and increases their natural frequency of higher orders, but also more or less eliminates the anisotropy of the structural stiffness and suppresses the local modes of vibration. In addition, considering mass efficiency, a dimensionless frequency parameter was proposed. It was found that the frequency parameter has different sensitivity to the geometry parameters, i.e. the slenderness ratio of corrugated member, the face sheet thickness ratio and the relative density of filling honeycomb.

Vibration of thermally postbuckled sandwich plates with nanotube-reinforced composite face sheets resting on elastic foundations

This paper investigates the small- and large-amplitude vibrations of thermally postbuckled sandwich plates with carbon nanotube-reinforced composite (CNTRC) face sheets resting on elastic foundations. Two types of CNTRC face sheets, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The material properties of FG-CNTRCs are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The material properties of both CNTRC face sheets and homogeneous core layer are assumed to be temperature-dependent. The motion equations are derived based on a higher order shear deformation plate theory. The nonlinearity effect is taken into account in the sense of von Kármán nonlinear kinematic assumption. The plate-foundation interaction and the initial deflection caused by thermal postbuckling are also included. The numerical illustrations concern small- and large-amplitude vibration characteristics of thermally postbuckled sandwich plates with CNTRC face sheets under uniform temperature field. The effects of CNT volume fraction and distribution pattern of face sheets, the core-to-face sheet thickness ratio as well as foundation stiffness on the vibration characteristics of sandwich plates are examined in detail.

Low velocity impact response of sandwich beams with soft cores and carbon nanotube reinforced face sheets based on Extended High Order Sandwich Panel Theory

Response of sandwich beam with carbon nanotube reinforced composite (CNTRC) face sheets and soft core subjected to the action of an impacting mass based on the Extended High Order Sandwich Panel Theory (EHSAPT) is first analyzed. Distribution of fibers through the thickness of the face sheets could be uniform or functionally graded (FG). Contact force between the impactor and the beam is obtained using the conventional Hertz law. The field equations are derived via the Ritz based applied to the total energy of the system. The solution is obtained in the time domain by implementing the well-known Runge–Kutta method. After examining the validity of the present solution, the effects of distribution of Carbon Nanotubes (CNTs), nanotube volume fraction, core-to-face sheet thickness ratio, initial velocity of the impactor and the impactor mass are studied in detail. Finally, it is concluded that, the highest peak contact force and the lowest indentation of the top face sheet belong to the sandwich beam with V distribution figure of face sheet, followed by the UD and Λ-ones, respectively. Also, numerical results reveal that employing FG-CNTs in face sheets has a prominent role on impact response of the sandwich panel with soft core.

Nonlinear thermomechanical response of pressure-loaded doubly curved functionally graded material sandwich panels in thermal environments including tangential edge constraints

This paper investigates the nonlinear response of doubly curved functionally graded material sandwich panels resting on elastic foundations, exposed to thermal environments and subjected to uniform external pressure. The material properties of both face sheets and core layer are assumed to be temperature dependent, and effective material properties of functionally graded material layers are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Formulations are based on first-order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations, and tangential edge constraints into consideration. Approximate solutions are assumed to satisfy simply supported boundary conditions and Galerkin procedure is applied to derive expressions of buckling loads and nonlinear load–deflection relation. The effects of material, geometry and foundation parameters, face sheet thickness ratio, initial geometrical imperfection, thermal environments and degree of tangential restraint of edges on the snap-through instability, and nonlinear response of spherical and cylindrical functionally graded material sandwich panels are analyzed and discussed in detail.

Theoretical investigation on vibration frequency of sandwich plate with PFRC core and piezomagnetic face sheets under variable in-plane load

This research investigated the vibration frequency of sandwich plate made of piezoelectric fiber reinforced composite core (PFRC) and face sheets of piezomagnetic materials. The effective electroelastic constants for PFRC materials are obtained by the micromechanical approach. The resting medium of sandwich plate is modeled by Pasternak foundation including normal and shear modulus. Besides, sandwich plate is subjected to linearly varying normal stresses that change by load factor. The coupled equations of motion are derived using first order shear deformation theory (FSDT) and energy method. These equations are solved by differential quadrature method (DQM) for simply supported boundary condition. A detailed numerical study is carried out based on piezoelectricity theory to indicate the significant effect of load factor, volume fraction of fibers, modulus of elastic foundation, core-to-face sheet thickness ratio and composite materials on dimensionless frequency of sandwich plate. These findings can be used to aerospace, building and automotive industries.

Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory

ABSTRACTThis article proposes a higher-order shear deformation beam theory for free vibration analysis of functionally graded carbon nanotube-reinforced composite sandwich beams in a thermal environment. The temperature-dependent material properties of functionally graded carbon nanotube-reinforced composite beams are supposed to vary continuously in the thickness direction and are estimated through the rule of mixture. The governing equations and boundary conditions are derived by using Hamilton's principle, and the Navier solution procedure is used to achieve the natural frequencies of the sandwich beam in a thermal environment. A parametric study is led to carry out the effects of carbon nanotube volume fractions, slenderness ratio, and core-to-face sheet thickness ratio on free vibration behavior of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets. Numerical results are also presented in order to compare the behavior of sandwich beams including uniformly distributed carbon nanotube-reinforced composite face sheets to those including functionally graded carbon nanotube-reinforced composite face sheets.