Effects Of Various Boundary Conditions Research Articles

The Numerical Analysis of the non-contact type Spiral Springs

In the analysis of the non-contact type spiral springs, several theories about Archimedean spiral beam with limited boundary conditions have already been reported. In this paper, we introduced the theory which can freely select boundary conditions without restriction on spring shape. Then we analyzed the Archimedean spiral beam and Logarithmic spiral beam, which are typical spring shapes, and considered the effect of various boundary conditions, e.g. bending moment amount, deflection angle, etc. Since this theory is analyzed in polar coordinates, so various boundary conditions can be easily given for analysis. Additionally, we introduce applied FEM method with arc beam elements to analyze springs that are not ideal shapes. The simulation results by theorical method were in good agreement with the simulation results by FEM method. We made a spring and compared the simulation and the experiment. The simulation results were in good agreement with the experimental results. Finally, we introduce proposed methods to improve the spring performance.

Material Effect on Stress Behavioural Characteristics of Composite Rectangular Plate

A numerical study has been carried out to examine the effects of the material on stress behavioural characteristics of a rectangular plate with and without cutout for a conventional and composite material plate subjected to pressure loads using finite element method.Further, this paper addresses the effect of various boundary conditions applied to the plate. A comparison has been made between the conventional and composite material with and without the cutout. It is observed that the application of pressure loads and boundary conditions have a substantial influence on stress behavioural characteristics of a rectangular plate with and without cutout on both the materials. The results obtained from numerical simulation are compared and found that simulation results are in good agreement with the previous studies.

Effect of rod-to-grain angle on capacity and stiffness of axially and laterally loaded long threaded rods in timber joints

Long threaded rods have recently been widely used as a reinforcement of glued laminated timber in perpendicular to the grain direction. The recent research has thus focused mainly on the withdrawal properties of the threaded rods in the axial direction. Utilizing their large withdrawal stiffness and strength, the threaded rods can also effectively be used as connectors in moment resisting timber joints. Yet, in joints, the threaded rods are often imposed to a non-axial loading, due to inclination of the rod axis to the grain as well as loading direction different from the rod axis. No design models are currently available for the combined axial and lateral loading of the threaded rods. In the present work, the effects of the rod-to-grain and load-to-rod angles on capacity and stiffness of the threaded rods are investigated by use of experiments and finite element models. Based on those, analytical expressions for determining stiffness and capacity of axially and laterally loaded threaded rods are proposed, intended as a basis for practical joint design. Furthermore, effect of various boundary conditions applied at the rod-ends is studied.

Prediction of the Stress–Strain Behavior of Open-Cell Aluminum Foam under Compressive Loading and the Effects of Various RVE Boundary Conditions

The prediction of the mechanical behavior of metallic foams with realistic microstructure and the effects of various boundary conditions on the mechanical behavior is an important and challenging issue in modeling representative volume elements (RVEs). A numerical investigation is conducted to determine the effects of various boundary conditions and cell wall cross sections on the compressive mechanical properties of aluminum foam, including the stiffness, plateau stress and onset strain of densification. The open-cell AA6101-T6 aluminum foam Duocel is used in the analyses in this study. Geometrical characteristics including the cell size, foam relative density, and cross-sectional shape and thickness of the cell walls are extracted from images of the foam. Then, the obtained foam microstructure is analyzed as a 2D model. The ligaments are modeled as shear deformable beams with elastic-plastic material behavior. To prevent interpenetration of the nodes and walls inside the cells with large deformations, self-contact-type frictionless interaction is stipulated between the internal surfaces. Sensitivity analyses are performed using several boundary conditions and cells wall cross-sectional shapes. The predicted results from the finite element analyses are compared with the experimental results. Finally, the most appropriate boundary conditions, leading to more consistent results with the experimental data, are introduced.

Cooling beyond the boundary value in supercritical fluids under vibration.

Supercritical fluids when subjected to simultaneous quench and vibration have been known to cause various intriguing flow phenomena and instabilities depending on the relative direction of temperature gradient and vibration. Here we describe a surprising and interesting phenomenon wherein temperature in the fluid falls below the imposed boundary value when the walls are quenched and the direction of vibration is normal to the temperature gradient. We define these regions in the fluid as sink zones, because they act like sink for heat within the fluid domain. The formation of these zones is first explained using a one-dimensional (1D) analysis with acceleration in constant direction. Subsequently, the effect of various boundary conditions and the relative direction of the temperature gradient to acceleration are analyzed, highlighting the necessary conditions for the formation of sink zones. It is found that the effect of high compressibility and the action of self-weight (due to high acceleration) causes the temperature to change in the bulk besides the usual action of piston effect. This subsequently affects the overall temperature profile thereby leading to the formation of sink zones. Though the examined 1D cases differ from the current two-dimensional (2D) cases, owing to the direction of acceleration being normal as compared to parallel in case of former, the explanations pertaining to 1D cases are judiciously utilized to elucidate the formation of sink zones in 2D supercritical fluids subjected to thermal quench and vibrational acceleration. The appearance of sink zones is found to be dependent on several factors such as proximity to the critical point and acceleration. A surface three-dimensional plot illustrating the effect of these parameters on onset time of sink zones is presented to further substantiate these arguments.

Free vibration and flexural response of functionally graded plates resting on Winkler–Pasternak elastic foundations using nonpolynomial higher-order shear and normal deformation theory

ABSTRACTIn the present work, the flexural and vibration response of a functionally graded plate resting on Pasternak elastic foundation is analyzed using a recently developed nonpolynomial higher-order shear and normal deformation theory by the authors. The novelty of this theory is that it contains only four unknowns and also accommodates the thickness stretching effect. Two kinds of micromechanics models, namely, the Voigt and Mori–Tanaka models, are considered. Material properties of the functionally graded plates are assumed to vary continuously in the thickness direction according to either a simple power law or an exponential law. Finite element formulation is done using C° continuous Lagrangian quadrilateral nine-noded elements with eight degrees of freedom per node. The equations of motion are derived using a variational approach. Convergence and comparison studies are carried out to establish the authenticity and reliability of the solutions. The effect of various boundary conditions, geometric conditions, micromechanics models, and foundation parameters on the flexural and vibration response of the functionally graded plate are investigated.

Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory

• Shear buckling of piezoelectric nanoplate is analyzed based on modified couple stress theory. • Nonlinear equations are found using simplified first order shear deformation theory. • The critical shear load is obtained via closed-form solution with various boundary conditions. • Increasing length scale parameter increases critical shear load. • The effect of external electric voltage on the critical shear load occurring on the piezoelectric nanoplate is insignificant. This paper studies the electro-mechanical shear buckling analysis of piezoelectric nanoplate using modified couple stress theory with various boundary conditions.In order to be taken electric effects into account, an external electric voltage is applied on the piezoelectric nanoplate. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using Hamilton's principle and nonlinear strains of Von-Karman. The modified couple stress theory has been applied to considering small scale effects. An analytical approach was developing to obtain exact results with various boundary conditions. After all, results have been presented by change in some parameters, such as; aspect ratio, effect of various boundary conditions, electric voltage and length scale parameter influences. At the end, results showed that the effect of external electric voltage on the critical shear load occurring on the piezoelectric nanoplate is insignificant.

Light-Induced Bending and Buckling of Large-Deflected Liquid Crystalline Polymer Plates

Cross-linked liquid crystalline polymers (LCPs) are smart materials for large light-activated variation or bend to transfer luminous energy into mechanical energy. We study the light-induced behavior of homeotropic nematic network polymer plates. The perturbation method is applied to find approximate solutions under uniform illumination and compared with finite element simulations. Moreover, situations of nonuniform laser illumination are investigated. Unlike single solution obtained from small displacement assumption, multiple solutions within Föppl–von Kármán nonlinear geometry framework are found in the post-buckling regime and the effect of various boundary conditions is discussed. The nonuniform bending moment generated by the inhomogeneous light-induced strain, membrane force and boundary effects lead to the unconventional nonsymmetric buckling behavior that is rarely observed under traditional mechanical or thermal loading.

Frequency analysis of doubly curved functionally graded carbon nanotube-reinforced composite panels

Vibration characteristics of moderately thick doubly curved functionally graded composite panels reinforced by carbon nanotube are analyzed. Here, special cases of doubly curved shell panels such as spherical, cylindrical and hyperbolic paraboloid panels and five different distributions of carbon nanotubes through the thickness direction are considered. By utilizing the modified rule of mixture, mechanical properties are estimated. The equations of motion are derived via the first-order shear deformation theory, and non-dimensional frequencies are obtained by the use of Galerkin’s method. The suggested model is justified by a good agreement between the results given by present model and available data in the literature. The influences of volume fraction of carbon nanotubes, thickness ratio, aspect ratio, curvature ratio, and shallowness ratio on the frequencies of moderately thick doubly curved nanocomposite shell panels are also examined. Furthermore, the effect of various boundary conditions on the frequency analysis of doubly curved nanocomposite panels is studied, and the corresponding mode shapes are depicted.

Dynamic Stability Analysis of a Circularly Tapered Rotating Beam Subjected to Axial Pulsating Load and Thermal Gradient under Various Boundary Conditions

The dynamic stability of a circularly tapered rotating beam subjected to a pulsating axial external excitation with thermal gradient was studied for all possible combinations of clamped, guided, pinned, fixed, and free boundary conditions. The equations of motion and associated boundary conditions were obtained using the extended Hamilton’s principle. Then these equations of motion and the associated boundary conditions were non-dimensionalised. A set of Hill’s equations were obtained from the non-dimensional equations of motion by the application of the extended Galerkin method. The zones of parametric instability were obtained using Saito-Otomi conditions. The effects of various boundary conditions, thermal gradient, taper, and rotational speed on the regions of parametric instability were investigated and presented through a series of graphs. The results reveal that increasing rotational speed and taper have stabilizing effects, whereas increasing thermal gradient has a destabilizing effect for all boundary conditions of the beam.

Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method

Free vibration of viscoelastic double-bonded polymeric nanocomposite plate reinforced by FG-SWCNTs embedded in viscoelastic foundation based on MSGT is investigated. Different distributions of SWCNTs are considered as: UD, FG-V, FG-X and FG-O. Material properties of viscoelastic nanocomposite plates are defined by extended mixture rule (EMR). The governing equations of motion are extracted using Hamilton’s principle and sinusoidal shear deformation theory. Then, natural frequency of nanocomposite plates is determined by Navier’s and meshless methods. The effects of material length scale parameters, aspect ratio, structural damping and foundation damping coefficients, elastic foundation parameters, magnetic field, Van der Waals (vdW) interaction on non-dimensional natural frequency are investigated. The results illustrate that the elastic foundation, vdW interaction and magnetic field increase the dimensionless natural frequency of the double-bonded nanocomposite plates for CT, MCST and MSGT. The material length scale parameter effects on the non-dimensional natural frequency of the double bonded nanocomposite plates is negligible at h/l⩾5 for CT, and MCST and MSGT. Also, using meshless method, effect of various boundary conditions on dimensionless natural frequency is investigated and the results are compared with the obtained results by other literatures that have a good agreement between them. The obtained results can be employed for MEMS and NEMS.

Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations

We briefly review and investigate the performance of various boundary conditions such as Dirichlet, Neumann, linear, and partial differential equation boundary conditions for the numerical solutions of the Black-Scholes partial differential equation. We use a finite difference method to numerically solve the equation. To show the efficiency of the given boundary condition, several numerical examples are presented. In numerical test, we investigate the effect of the domain sizes and compare the effect of various boundary conditions with pointwise error and root mean square error. Numerical results show that linear boundary condition is accurate and efficient among the other boundary conditions.

Computation of casting solidification feed-paths using gradient vector method with various boundary conditions

In the present work, a computationally efficient numerical approach called gradient vector method (GVM) is proposed to visualise feed-paths and to evaluate the design of feeding systems with various thermal boundary conditions. It involves the computation of liquid–solid interfacial heat flux vector using an analytically derived solution to phase change-heat transport equation. The resultant of flux vectors gives the direction of the highest temperature gradient, which is continuously tracked to generate complete feed-paths. The originating points of the feed-paths indicate hot-spots that manifest as shrinkage defects. Mathematical models are proposed to handle the effect of various boundary conditions like insulation or exothermic sleeves around feeders and chill blocks in mould. The accuracy of GVM in predicting the location of shrinkage porosity defect has been validated by pouring and sectioning benchmark castings. Computation of feed-paths using this method was found to be an order of magnitude faster than level-set method for casting solidification simulation. The implementation of the method in three dimensions and its application to an industrial casting are also presented.

A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method

In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz., cracks and cutouts are represented independent of the mesh within the framework of the extended finite element method and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction and the effective properties are estimated using the Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation theory. The influence of various parameters, viz., the crack length and its location, the cutout radius and its position, the plate aspect ratio and the plate thickness on the critical buckling load is studied. The effect of various boundary conditions is also studied. The numerical results obtained reveal that the critical buckling load decreases with increase in the crack length, the cutout radius and the material gradient index. This is attributed to the degradation in the stiffness either due to the presence of local defects or due to the change in the material composition.

Dynamic analysis of carbon nanotubes under electrostatic actuation using modified couple stress theory

Modified couple stress theory is a size-dependent theorem capturing the micro/nanoscale effects influencing the mechanical behaviors of the micro- and nanostructures. In this paper, it is applied to investigate the nonlinear vibration of carbon nanotubes under step DC voltage. The vibration, natural frequencies and dynamic pull-in characteristics of the carbon nanotubes are studied in detail. Moreover, the effects of various boundary conditions and geometries are scrutinized on the dynamic characteristics. The results reveal that application of this theory leads to the higher values of the natural frequencies and dynamic pull-in voltages.

The Effect of Displacement Field on Bending, Buckling, and Vibration of Cross-Ply Circular Cylindrical Shells

The effect of assumed displacement field is investigated on the bending, buckling, and natural frequencies of cross-ply circular cylindrical shells using first-order shear deformation theory through an analytical solution. Linear strain-displacement relation is assumed. The governing equations are derived from Hamilton's principle. Assuming Levy-type solution, the governing equations are then converted to ordinary differential equations and changed to state-space form introducing ten unknown variables and solved for displacements. Different lamination sequences, including symmetric and asymmetric laminate, are studied and compared. The effect of various boundary conditions (i.e., clamped, simply supported, and free edge), radius-to-thickness, and radius-to-length ratio on the displacement of mid-surface is investigated.

The Effects of Various Boundary Conditions on Thermal Buckling of Functionally Graded Beamwith Piezoelectric Layers Based on Third order Shear Deformation Theory

The Effects of Various Boundary Conditions on Thermal Buckling of Functionally Graded Beamwith Piezoelectric Layers Based on Third order Shear Deformation Theory

Effects of Various Boundary Conditions on the Response of Poisson–Nernst–Planck Impedance Spectroscopy Analysis Models and Comparison with a Continuous-Time Random-Walk Model

Various electrode reaction rate boundary conditions suitable for mean-field Poisson-Nernst-Planck (PNP) mobile charge frequency response continuum models are defined and incorporated in the resulting Chang-Jaffe (CJ) CJPNP model, the ohmic OHPNP one, and a simplified GPNP one in order to generalize from full to partial blocking of mobile charges at the two plane parallel electrodes. Model responses using exact synthetic PNP data involving only mobile negative charges are discussed and compared for a wide range of CJ dimensionless reaction rate values. The CJPNP and OHPNP ones are shown to be fully equivalent, except possibly for the analysis of nanomaterial structures. The dielectric strengths associated with the CJPNP diffuse double layers at the electrodes were found to decrease toward 0 as the reaction rate increased, consistent with fewer blocked charges and more reacting ones. Parameter estimates from GPNP fits of CJPNP data were shown to lead to accurate calculated values of the CJ reaction rate and of some other CJPNP parameters. Best fits of CaCu(3)Ti(4)O(12) (CCTO) single-crystal data, an electronic conductor, at 80 and 140 K, required the anomalous diffusion model, CJPNPA, and led to medium-size rate estimates of about 0.12 and 0.03, respectively, as well as good estimates of the values of other important CJPNPA parameters such as the independently verified concentration of neutral dissociable centers. These continuum-fit results were found to be only somewhat comparable to those obtained from a composite continuous-time random-walk hopping/trapping semiuniversal UN model.

경계조건에 따른 다중벽 탄소나노튜브의 유체유발 불안정성 변화

This paper studies the influence of internal moving fluid and flow-induced structural instability of multi-wall carbon nanotubes conveying fluid. Detailed results are demonstrated for the variation of natural frequencies with flow velocity, and the flow-induced divergence and flutter instability characteristics of multi-wall carbon nanotubes conveying fluid and modelled as a thin-walled beam are investigated. Effects of various boundary conditions, Van der Waals forces, and non-classical transverse shear and rotary inertia are incorporated in this study. The governing equations and three different boundary conditions are derived through Hamilton's principle. Numerical analysis is performed by using extended Galerkin's method which enables us to obtain more exact solutions compared with conventional Galerkin's method. This paper also presents the comparison between the characteristics of single-wall and multi-wall carbon nanotubes considering the effect of van der Waals forces. Variations of critical flow velocity for different boundary conditions of two-wall carbon nanotubes are investigated and pertinent conclusion is outlined.

On the Diffusion of Fluids Through Solids Undergoing Large Deformations

In this paper, we investigate the problem of diffusion of a Newtonian fluid through a non-linearly elastic solid undergoing large deformations, within the framework of mixture theory. Our aim is to delineate the effect of various boundary conditions on the diffusion process. We find that the results are quite insensitive to the boundary conditions in that the predictions agree exceedingly well with the experiments (whether it is the saturation boundary condition used by Rajagopal, Wineman and Gandhi, the traction splitting boundary condition used by Rajagopal and Tao, the natural boundary condition used by Baek and Srinivasa, or the fact that the chemical potential is continuous across the boundary), provided that an appropriate choice is made for the drag.