Dimensionless Geometric Parameters Research Articles

Dynamic instability region analysis of sandwich piezoelectric nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal strain gradient theory

In this research, the dynamic instability region (DIR) of the sandwich nano-beams are investigated based on nonlocal strain gradient elasticity theory (NSGET) and various higher order shear deformation beam theories (HSDBTs). The sandwich piezoelectric nano-beam is including a homogenous core and face-sheets reinforced with functionally graded (FG) carbon nanotubes (CNTs). In present study, three patterns of CNTs are employed in order to reinforce the top and bottom face-sheets of the beam. In addition, different higher-order shear deformation beam theories such as trigonometric shear deformation beam theory (TSDBT), exponential shear deformation beam theory (ESDBT), hyperbolic shear deformation beam theory (HSDBT), and Aydogdu shear deformation beam theory (ASDBT) are considered to extract the governing equations for different boundary conditions. The beam is subjected to thermal and electrical loads while is resting on Visco-Pasternak foundation. Hamilton principle is used to derive the governing equations of motion based on various shear deformation theories. In order to analysis of the dynamic instability behaviors, the linear governing equations of motion are solved using differential quadrature method (DQM). After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various shear deformation theories, nonlocal parameter, strain gradient parameter, the volume fraction of the CNTs, various distributions of the CNTs, different boundary conditions, dimensionless geometric parameters, Visco-Pasternak foundation parameters, applied voltage and temperature change on the dynamic instability characteristics of sandwich piezoelectric nano-beam.

Performance and prediction of large deformation contractile shape memory alloy knitted actuators

Compliant, large deformation actuating functional fabrics are essential to next-generation wearables, aerospace structures, and medical devices as they excel at traditional mechanical performance metrics while being soft and pliable. Actuating functional fabrics have been implemented from a variety of multifunctional material systems and fabric manufacturing techniques. A specifically intriguing combination of material system and fabric manufacturing technique are contractile shape memory alloy (SMA) knitted actuators, which generate recoverable actuation deformations of up to 50%, provide actuation forces on the magnitude of 1 N–10 N, are biocompatible, and actuate in response to thermal stimuli. However, the prediction of the knitted functional fabric actuator performance is inherently difficult due to the complex geometry of knitted architectures and the nonlinear material behavior of most multifunctional fibers. This paper presents an empirical model of the contractile SMA knitted actuator performance based on the definition of a dimensionless geometric parameter, the knit index (ik). An experimental study of the contractile SMA knitted actuator quasi-static uniaxial thermo-mechanical performance validates the knit index and the wire diameter as the smallest set of performance-predicting geometric parameters. An empirical model is formulated for the prediction of the contractile SMA knitted actuator performance based on geometric inputs (forward design) and the recommendation of geometric parameters that accomplish specific performance metrics (inverse design). The process of describing and predicting the performance with dimensionless geometric parameters is a step to understanding the mechanics of contractile SMA knitted actuators, has merit for the design of other actuating functional fabrics, and propels the creation of novel wearables, medical devices, and aerospace structures with large actuation deformations.

CONTACT PROBLEM FOR A TWO-LAYERED CYLINDER

Introduction. The investigation of the contact problems for cylindrical bodies is urgent due to the engineering contact strength analysis on shafts, cores and pipe-lines. In the present paper, a new contact problem of elastostatics on the interaction between a rigid band and an infinite two-layered cylinder, which consists of an internal continuous cylinder and an outer hollow one, with a frictionless contact between the cylinders, is studied. The outer cylindrical band of finite length is press fitted. By using a Fourier integral transformation, the problem is reduced to an integral equation with respect to the unknown contact pressure.Materials and Methods. Different combinations of linearly elastic materials of the composite cylinder are considered. Asymptotics of the symbol function of the integral equation kernel at zero and infinity is analyzed. This plays an important role for the application of the analytical solution methods. A key dimensionless geometric parameter is introduced, and a singular asymptotic technique is employed to solve the integral equation.Research Results. On the basis of the symbol function properties, a special easily factorable approximation being applicable in a wide variation range of the problem parameters is suggested. The Monte-Carlo method is used to determine the approximation parameters. The asymptotic formulas are derived both for the contact pressure, and for its integral characteristic. Calculations are made for different materials and for various relative thickness of the cylindrical layer including thin-walled layers.Discussion and Conclusions. The asymptotic solutions are effective for relatively wide bands when the contact zone length is bigger than the diameter of the composite cylinder. It is significant that the method is applicable also for those cases when the outer cylindrical layer is treated as a cylindrical shell. The asymptotic solutions can be recommended to engineers for the contact strength analysis of the elastic barrels with a flexible coating of another material.

Influence of electric brush‐plating voltage on hydrophobic behaviour of a cauliflower‐like Ni coating surface

The effect of the plating voltage on the surface roughness, morphology, chemical composition and wettability of the Ni coatings was investigated by means of Laser scanning confocal microscopy, scanning electronic microscope, X-ray diffraction, energy-dispersive spectroscopy, and water contact angle measurements. The results indicate that the evolution of surface morphology on Ni coatings prepared by brush-plating depends strongly on the variation of plating voltage. The microstructure characterization shows that the typical hierarchical cauliflower-like structures was formed uniformly on the as-prepared Ni coatings. The combination of the porous morphology and hierarchical cauliflower-like structures plays a crucial role in improving the hydrophobic property. In absence of surface chemical modification, the Ni coatings exhibit an excellent hydrophobicity and have a high contact angle of 141 degree. Based on the Cassie-Baxier models, the relationship of two dimensionless geometrical parameters and the wetting property of the Ni coatings were investigated. It was demonstrated that to obtain the stable Cassie hydrophobic state, the aspect ratio and the water contact angle on the basal surface should be as large as possible and the spacing factor should be limited within a specific range for given aspect ratio and water contact angle on the basal surface.

Parametric study on structural behavior of tubular K-joints under axial loading at fire-induced elevated temperatures

Present research used the results of 405 finite element (FE) analyses to study the effect of the joint geometry on the ultimate strength and initial stiffness of tubular K-joints subjected to axial loading at fire-induced elevated temperatures. The FE models were validated against the data available from experimental tests. Structural behavior under different temperatures (200 °C, 400 °C, 500 °C, and 700 °C) was investigated and compared to the behavior at ambient temperature (20 °C). Results showed that by increasing the temperature, the ultimate strength and initial stiffness may decrease drastically. On average, the reduction of ultimate strength is 5%, 19%, 51%, and 83% at 200 °C, 400 °C, 550 °C, and 700 °C, respectively. A parametric study was conducted to investigate the effect of dimensionless geometrical parameters (β, γ, θ, and τ) on the ultimate strength and initial stiffness. Afterwards, ultimate strength data extracted from the FE analyses was compared with the values calculated from the equations proposed by available design codes in which the ultimate strength of the joint at elevated temperatures is obtained by replacing the yield stress of the steel at ambient temperature with the corresponding value at elevated temperature. It was indicated that this method may not have acceptable accuracy for carbon steel K-joints under axial loading. Hence, a new design formula was developed, through nonlinear regression analyses, to determine the ultimate strength of K-joints subjected to balanced axial loads at elevated temperatures.

Quantitative research on the influence of particle size and filling thickness on aerogel glazing performance

Silica aerogel has attracted increasing interest in building glazing for energy efficiency owing to its light weight, ultra-low thermal conductivity and high visual transmittance. In this study, four types of aerogel granules with various average particle sizes (viz. 0.41, 1.03, 1.64 and 2.54 mm) were prepared by using a low-cost ambient pressure drying method. Three gaps between two pieces of glass (viz. 6, 9 and 12mm) were filled with aerogel granules, yielding 12 pieces of aerogel filling glazing. The light transmittance and reflectance of the aerogel glazing samples were experimentally measured by using a spectrometer. Based on the experimental results, the correlation between the light transmittance performance and the geometrical parameter of the aerogel glazing were established based on a proposed dimensionless geometrical parameter. It revealed that the visible light transmittance and the shading coefficient of the aerogel glazing had a positive correlation with the particle size and a negative correlation with the filling thickness. In addition, the filling thickness had a greater influence on the properties of aerogel glazing than the particle size. This opens new possibility for a multiple-objective evaluation of the aerogel glazing aiming at building energy efficiency.

Static strength of axially loaded tubular KT-joints at elevated temperatures: Study of geometrical effects and parametric formulation

This paper aims to study the structural behavior of tubular KT-joints subjected to axial loading at fire induced elevated temperatures. At first, a finite element (FE) model was developed and validated against the data available from experimental tests. Then, a set of 810 FE analyses were performed to study the influence of temperature and dimensionless geometrical parameters (β, γ, θ, and τ) on the ultimate strength and initial stiffness. The joints were analyzed under two types of axial loading and five different temperatures (20 °C, 200 °C, 400 °C, 550 °C, and 700 °C). Up to now, there has not been any design formula available for determining the ultimate strength of KT-joints at elevated temperatures. Hence, after parametric study, a new equation was developed through nonlinear regression analyses, for calculating the ultimate strength of KT-joints subjected to axial loading at elevated temperatures.

Stress concentration factor distribution of inclined brace in multiplanar offshore tubular double kt joints

The majority of tubular joints commonly found in offshore structures are in the form of multi-planar tubular joints, but very few investigations have been reported due to the complexity and high cost involved. The majority of research have been focused on the study of stress distribution at certain position such as saddle and crown points, and the hot spot stress (HSS) at other position along the weld toe of brace/chord intersection have been ignored. In this paper a 60° two-planar double KT (DKT) tubular joint is modelled as a finite element model from an offshore jacket platform. The effect of dimensionless geometrical parameters on the geometrically stress distribution and SCF distribution along the weld toe of inclined brace in axially loaded on the joint are investigated. Non-dimensional parameters that are varied include β, τ, γ and θ. Validation of the finite element model shown a good agreement to the global structural analysis results. The results of parametric studies show that the increase of the β leads to decrease of SCF. While the increase of the τ, γ and θ leads to increase of SCF. The peak SCF mostly occurs at the outer saddle point. The effect of parameters β, γ and θ on the SCF are greater than the effect of parameters τ.

Topological defects in two-dimensional liquid crystals confined by a box.

When a spatially uniform system that displays a liquid-crystal ordering on a two-dimensional surface is confined inside a rectangular box, the liquid crystal direction field develops inhomogeneous textures accompanied by topological defects because of the geometric frustrations. We show that the rich variety of nematic textures and defect patterns found in recent experimental and theoretical studies can be classified by the solutions of the rather fundamental, extended Onsager model. This is critically examined based on the determined free energies of different defect states, as functions of a few relevant, dimensionless geometric parameters.

Free vibration analysis of a piezoelectric curved sandwich nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal elasticity theories

In this study, the free vibration responses of piezoelectric sandwich curved nano-beams resting on Winkler-Pasternak foundation are investigated based on the nonlocal elasticity theory and various higher-order shear deformation theories. The sandwich curved nano-beam includes a homogenous piezoelectric core and two face-sheets reinforced with functionally graded carbon nano-tubes (CNTs). Three various patterns of CNTs are employed in this analysis to distribute CNTs along to height of the nano-beam. The structure is subjected to a two-dimensional electric potential. In addition, different higher-order shear deformation beam theories (HOSDBTs), such as trigonometric shear deformation beam theory (TSDBT), exponential shear deformation beam theory (ESDBT), hyperbolic shear deformation beam theory (HSDBT), and Aydogdu shear deformation beam theory (ASDBT), are considered to extract the governing equations for different boundary conditions. The Hamilton principle is used to derive the governing equations of motion, based on various shear deformation theories. In order to analyse the vibration behaviors, the linear governing equations of motion are solved using the differential quadrature method (DQM). The comprehensive numerical results are presented to investigate the influence of important parameters, such as various shear deformation theories, nonlocal parameter, the volume fraction of the CNTs, various distributions of the CNTs, different boundary conditions, the external electric field and dimensionless geometric parameters, on the vibration characteristics of a piezoelectric curved sandwich nano-beam.

Optimization of geometrical parameter for V-type alpha Stirling engine based on dimensionless analysis

This paper aims to study the effect of mechanism and geometrical parameters on the shaft work of alpha-type Stirling engine with V-cylinder arrangement and find the appropriate value of geometrical parameters to get the maximum value of shaft work output. The equation of motions of both expansion and compression pistons and the variations of volumes and pressures inside the cylinders are expressed in dimensionless forms. Schmidt analysis and Senft’s shaft work theory are used to build dimensionless thermodynamic models in order to derive dimensionless shaft work and optimal geometrical parameters for achieving the maximum efficiency

Stress Concentration Factor of A Two-Planar Double KT Tubular Joint due to In-Plane Bending Loading in Steel Offshore Structures

The purpose of this study is to investigate the proper Stress Concentration Factor (SCF) of a 60° two-planar DKT tubular joint of a tripod wellhead offshore structure. So far, calculation of SCF for a multi-plane tubular joint was based on the formulation for the simple/uniplanar tubular joints that yield in over/under prediction of the SCF of the joint. This situation in turn decreasing the accuracy of fatigue life prediction of the structures. The SCF is one of the most important parameters in the tubular joint fatigue analysis. The tubular joint is modelled as finite element models with bending loads acting on the braces that cover a wide range of dimensionless geometrical parameters (β, τ, γ). The effect of such parameters on the SCF distribution along the weld toe of braces and chord on the joint are investigated. Validation of the finite element model has shown good agreement to the global structural analysis results. The results of parametric studies show that the peak SCF mostly occurs at around crown 2 point of the outer central brace. The increase of the β leads to decrease the SCF. While the increase of the τ and γ leads to increase the SCF. The effect of parameter β and γ on the SCF are greater than the effect of parameter τ.

Free Bending Vibrations of Rotating Disks With A Concentric Hole

Dynamic behavior of rotating annular disks is the main focus of this study. Solution of governing differential equations of the system is obtained by Galerkin method that includes proposing an approximate function for displacement that satisfies the boundary conditions. Two displacement functions are selected for the solution and the boundary conditions are imposed to obtained the natural frequencies of the rotating disk. It is investigated how the dynamic behavior is affected by the rotation speed of the disk in details and the results are visualized using Campbell diagrams which are drawn using dimensionless geometric parameters. Also the solution method are validated using the results of the related studies in the literature.

Mechanical Properties of 3D Isotropic Anti‐Tetrachiral Metastructure

Chiral metastructures consisting of ring (polygonal or cubic) nodes and elastic bending ligaments exhibit excellent design flexibility for compliant structures. In this paper, based on rigid cubic node rotation and the kinematic geometrical relations of a three‐dimensional (3D) isotropic anti‐tetrachiral structure, an analytical expression for the modulus of the 3D isotropic anti‐tetrachiral structure is derived from strain energy analysis. The nylon powder Selected Laser Sintering (SLS) additive manufacturing technique is employed for fabricating two types of 3D isotropic anti‐tetrachiral specimens with different geometrical parameters; then comparison between experiments, finite element analysis (FEA), and theoretical studies is performed for verifying the analytical formula. The mechanical properties of 3D isotropic anti‐tetrachiral structures can be tuned with two independent dimensionless geometrical parameters. The proposed 3D anti‐tetrachiral structures can be employed for designing advanced structures against impact damages, realizing flexibility of industrial components, and optimizing the vibration attenuation abilities of engineering structures.

Estimating discharge coefficient of stepped spillways under nappe and skimming flow regime using data driven approaches

An important step toward spillways design always involves appropriate determination of the discharge coefficient. Since existing equations are incapable of estimating the discharge coefficient of stepped spillway accurately, other approaches such as data driven techniques can be employed as an alternative which are useful in modeling processes when the physical knowledge is limited. For this purpose, Gene Expression Programming (GEP) and Support Vector Machine (SVM) as data driven methods were applied for the modeling discharge coefficient of the stepped spillways using data derived from physical models and original experiments under nappe and skimming flow regimes. The input parameters included different dimensionless geometric and hydraulic parameters of napped and skimming regimes data. The obtained results indicated that the applied methods have a high capability in the modeling of discharge coefficient for the stepped spillways. The model comprised of four input parameters used for modeling of the discharge coefficient in nappe flow showed more accurate results (%RMSE = 0.042, 0.328 and R2 = 0.966, 0.961 for the SVM and GEP models, respectively). In skimming flow data, the model with five input parameters produced RMSE = 0.015, 0.357 and R2 = 0.987, 0.979 in SVM and GEP, respectively. A comparison of the GEP and SVM results with the obtained results from the Multiple Linear Regression (MLR) showed that the performance of the linear model (i.e., MLR) was not suitable because the phenomenon of discharge coefficient is inherently complex and nonlinear. The results of sensitivity analysis for both proposed methods showed that the Fr1 and H/y1 parameters in nappe flow and Fr1 and Re parameters in skimming flow had the most important influence on modeling of the stepped spillways discharge coefficient. The results also revealed that the SVM relatively surpassed the GEP in the modeling of discharge coefficient. Nevertheless, the utilization of GEP model is highly recommended due to the high performance and extracting of simple, explicit equation by it.

Stress concentration factors (SCFs) of bulge formed K-joints under balanced axial loads

A novel stiffened joint called bulge formed joint was put forward. Compared with the unstiffened joint, an additional bulge plate is utilized to connect the chord and braces. Based on the finite element (FE) and experimental method, stress concentration factors (SCFs) were investigated for both a bulge formed K-joints and the corresponding unstiffened joint. By the verification of experimental data, the FE models were used to investigate the SCFs of the bulge formed joints. The maximum SCF of the bulge formed K-joint under balanced axial loads is located at the position φ=105°, which is close to but not exactly the saddle. The SCFs around the intersection weld can decrease remarkably compared with the unstiffened joint by the change of geometrical parameters of the bulge plate. Then 2117 FE analyses were conducted to investigate the geometrical effects on SCFs of the bulge formed joint. These dimensionless geometrical parameters include τs, η1, η2, θ, β, γ, τ, among which, the first three parameters are typical of the bulge formed joints, while the others are same as the definitions in the unstiffened joints. Finally, a set of SCF parametric formulas were obtained by nonlinear regression analyses.

Improvement of PVT air-cooling by the integration of a chimney tower (CT/PVT)

In this work, a bi-dimensional numerical simulation of the turbulent natural convection for cooling of the solar panel in a new concept of hybrid photovoltaic/thermal solar collector by integration of a chimney tower has been analysed. The hydrodynamic flow field is governed by the Navier–Stokes equations in the fluid region, thermal field by the energy equation. The standard k-ε turbulence model is used for describing the turbulent fluctuations of velocities and scalar quantities. The Influences of the dimensionless geometric parameters, such as the collector diameter ratio (Dc∗), the absorber length (La∗) and the chimney tower diameter ratio and the chimney tower height (Dt∗, Ht∗) on the flow features and heat transfer rate are presented. The obtained results show that the optimum dimensionless geometrical parameters of the new hybrid system proposed (La∗=0.625, Dc∗=3, Ht∗=0.625, and Dt∗=2) produce an improvement in the heat transfer rate of 78.13% compared to the base case, for Ra=5×106. Correlations of the average Nusselt numbers are obtained and discussed.

Segmented thermoelectric generator: exponential area variation in leg

Summary The innovative design of segmented thermoelectric generator with exponential area variation is introduced. Thermal efficiency and power output are assessed for various values of the design parameter (a = (L/x) ln[Aa/A(x)], where Aa is constant, and a is the dimensionless geometric parameter, L is the pin length, and A(x) is the pin cross-sectional area), external load parameter (RL/R0, ratio of external electrical resistance to reference electrical resistance), and temperature parameter (θ = Tlow/Thigh, ratio of cold junction temperature to high junction temperature). The device efficiency obtained is validated through the previous experimental data for various hot and cold junction temperature differences. The findings reveal that thermal efficiency resulted from the current study agrees well with the experimental data. The innovative design of the segmented thermoelectric generator with exponentially decaying pin configuration enhances the thermal efficiency and output power as compared with the device having a single material pin configuration. Increasing temperature ratio results in the reduction in the thermal efficiency and the output power of thermoelectric generator. In addition, lowering the external load parameter improves the thermal efficiency and the output power of the thermoelectric device. The design parameter that maximizes the thermal efficiency of the thermoelectric generator does not maximize the device output power.

In Plane Mechanical Properties of Tetrachiral and Antitetrachiral Hybrid Metastructures

A novel tetrachiral and antitetrachiral hybrid metastructure is proposed, and its in-plane mechanical properties are studied through strain energy analysis. Based on rigid ring rotation assumption, the analytical expression for the in-plane modulus of anisotropic tetrachiral and antitetrachiral hybrid metastructure is derived, and in-plane tensile experimental test and finite element simulation are performed and compared with the theoretical models. The corresponding in-plane anisotropic mechanical properties can be tuned with three independent dimensionless geometrical parameters, and effects of dimensionless geometrical parameters on the in-plane mechanical properties are studied systematically. Finally, an innovative tetrachiral and antitetrachiral hybrid metastructure stent is designed, and its mechanical behaviors under uniaxial tensile loading are investigated. It is found that the designed tetrachiral and antitetrachiral hybrid stent shows negative Poisson ratio properties, and the axial and circumferential deformation can be controlled through adjusting the spacing of unit cell along axial and circumferential directions.

Thermal buckling analysis of functionally graded cylindrical shells

Thermal buckling behavior of cylindrical shell made of functionally graded material (FGM) is studied. The material constituents are composed of ceramic and metal. The material properties across the shell thickness are assumed to be graded according to a simple power law distribution in terms of the volume fraction rule of mixtures. Based on the Donnell shell theory, a system of dimensionless partial differential equations of buckling in terms of displacement components is derived. The method of separation of variables is used to transform the governing equations to ordinary differential equations (ODEs). A shooting method is used to search for the numerical solutions of the differential equations under two types of boundary conditions. Effects of the power law index, the dimensionless geometrical parameters, and the temperature ratio on the critical buckling temperature are discussed in detail.