Position Of Neutral Plane Research Articles

Imperfection sensitivity of the size-dependent postbuckling response of pressurized FGM nanoshells in thermal environments

The purpose of the current study is to address the nonlinear buckling and postbuckling response of nanoscaled cylindrical shells made of functionally graded material (FGM) under hydrostatic pressure aiming to investigate the sensitivity to the initial geometric imperfection in the presence of surface effects and thermal environments. According to a power law distribution, the material properties of the FGM nanoshell are considered change through the shell thickness. Also, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account to eliminate the stretching-bending coupling terms. In order to acquire the size effect qualitatively, the well-known Gurtin-Murdoch elasticity theory is incorporated within the framework of the classical shell theory. Using the variational approach, the non-classical governing equations are displayed and deduced to boundary layer type ones. Afterwards, explicit expressions for the size-dependent radial postbuckling equilibrium paths of imperfect FGM nanoshells are proposed with the aid of a perturbation-based solution methodology. It is displayed that by moving from the ceramic phase to the metal one, the critical buckling pressure decreases, but the postbuckling stiffness increases, because in contrast to the ceramic phase, the surface modulus and residual surface stress associated with the metal phase have the same sign.

Size dependency in axial postbuckling behavior of hybrid FGM exponential shear deformable nanoshells based on the nonlocal elasticity theory

The objective of this study is to examine the nonlocal nonlinear instability of functionally graded cylindrical shells at nanoscale integrated with piezoelectric nanolayers under combination of axial compressive load and lateral electric field. Eringen's nonlocal continuum elasticity is incorporated within the framework of the exponential shear deformation shell theory to consider the influence of transverse shear deformation in a refined form. Additionally, in order to eliminate the stretching-bending coupling terms, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account. With the aid of the boundary layer theory of shell buckling and employing a perturbation-based solution methodology, explicit expressions for the size-dependent equilibrium paths before and after buckling point are proposed for functionally graded hybrid nanoshells with various nonlocal parameters, material property gradient indexes and subjected to different values of lateral electric field. It is indicated that the both width and depth of the snap-through phenomenon related to the axial postbuckling behavior of hybrid FGM nanoshells decrease due to the nonlocality influence.

UNCOUPLED VIBRATIONS IN FUNCTIONALLY GRADED TIMOSHENKO BEAM

Free vibration of FGM Timoshenko beam is investigated on the base of the power law distribution of FGM. Taking into account the actual position of neutral plane enables to obtain general condition for uncoupling of axial and flexural vibrations in FGM beam. This condition defines a class of functionally graded beams for which axial and flexural vibrations are completely uncoupled likely to the homogeneous beams. Natural frequencies and mode shapes of uncoupled flexural vibration of beams from the class are examined in dependence on material parameters and slendernes

Measurement of the neutral plane of an internal fire whirl using the background-oriented Schlieren technique for a vertical shaft model of a high-rise building

Since the height of the neutral plane is related to the direction of the high-temperature smoke and airflow diffusion of fires in high-rise buildings, the identification of the neutral plane is important for both the evacuation of residents and the safety of fire fighters. As yet, there are no effective methods for directly measuring the constantly changing neutral plane position. There are complex internal fire whirl phenomena in the inner space in particular cases. In this study, the background-oriented Schlieren (BOS) technique was used to visualize the neutral plane when a fire whirl occurs in a vertical shaft with a single corner gap. With n-propanol used as the fuel, the scale modeling experiments of fuel trays 5.8cm and 7cm in diameter were tested in a 34cm (W)×35cm (L)×145cm (H) model for open and covered roof types. It is observed in the experimental process that the height of the neutral plane changes dynamically as the fire whirl is formed. The thermocouples were used to measure the temperature variation at different heights of openings to validate the measurement accuracy of the BOS technique. It is found that once a fire whirl occurs in the inner space of a high-rise building, the height of the neutral plane increases instantly. The experimental results demonstrate that the BOS technique can measure the neutral plane position of a large-scale model of a high-rise building fire scene directly, immediately and accurately.

Size-dependent nonlinear bending and postbuckling of functionally graded Mindlin rectangular microplates considering the physical neutral plane position

In this paper, the nonlinear bending and postbuckling characteristics of Mindlin rectangular microplates made of functionally graded (FG) materials are studied based on the modified couple stress theory (MCST). This theory facilitates considering size dependency through introducing material length scale parameters. The FG microplates, whose volume fraction is expressed by a power law function, are considered to be made of a mixture of metals and ceramics. By considering the physical neutral plane position, the stretching–bending coupling is eliminated in both nonlinear governing equations and boundary conditions of FG microplates. With the aid of MCST and the principle of virtual work, the governing equations and corresponding boundary conditions are derived. Then, the obtained governing equations and boundary conditions are discretized through the generalized differential quadrature (GDQ) method. Finally, the resulting nonlinear parameterized equations are solved by the pseudo-arclength continuation technique. The effects of material gradient index, length scale parameter, length-to-thickness ratio, and boundary conditions on the nonlinear bending and postbuckling responses of FG microplates are investigated.

An upper bound solution of axial metal flow in cold radial forging process of rods

Abstract In process design of radial forging, the prediction of axial metal flow, which has an effect on the forging efficiency, is very important. In this paper, based on a kinematically admissible velocity field, an axisymmetric model of radial forging of rods by an upper bound method (UBM) is proposed. Because the deforming process in a stroke is non-steady, it is divided into finite small steps so that the deformation in a step can be assumed as homogeneous steady flow. In addition, front-pull and back-push forces are taken into account. The amounts of metal flowing forward and backward can be predicted reasonably. The UBM model is validated by comparing the predicted forging load with published experimental data, and by comparing the predicted neutral plane position and axial metal flow with that of finite element simulation. Then the influences of friction factor, axial feed per stroke, reduction in cross-section area, inlet angle of hammer, front-pull and back-push forces on the percentage of forward material flow are investigated.

Bending analysis of ultra-thin functionally graded Mindlin plates incorporating surface energy effects

In this paper, an analytical solution for Mindlin plate theory accounting for the position of the neutral plane for continuum incorporating surface effects is investigated to study the bending behavior of ultra-thin simply supported functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Therefore, unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. Moreover, unlike most of previous studies in the literature, the neutral plane position effects are considered for FG plates. A series of continuum governing differential equations which include surface energy and neutral plane position effects are derived. The proposed analytical solution is then used for a comparison between the continuum analysis of simply supported FG ultra-thin plates with and without incorporating surface effects. Also, a parametric study is provided to study the effect of surface parameters and the effect of aspect ratio on the behavior of the simply supported FG plate. The proposed model is verified by previous work.

Finite element analysis of functionally graded nano-scale films

In this paper, a size-dependent finite element model, for Mindlin plate theory accounting for the position of the neutral plane for continuum incorporating surface energy effect, is proposed to study the bending behavior of ultra-thin functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. The classical finite element model is adopted to allow insertion of the surface energy into the total energy of the plate. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Therefore, unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. Moreover, unlike most of previous studies in the literature, the exact neutral plane position is pre-determined and considered for FG plates. A series of continuum governing differential equations which include surface energy and neutral plane position effects are derived. A comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface energy effects is presented.

Post microbuckling mechanics of fibre-reinforced shape-memory polymers undergoing flexure deformation

The buckling mechanics of fibre-reinforced shape-memory polymer composites (SMPCs) under finite flexure deformation is investigated. The analytical expressions of the key parameters during the buckling deformation of the materials were determined, and the local post-buckling mechanics of the unidirectional fibre-reinforced SMPC were further discussed. The cross section of SMPC under flexural deformation can be divided into three areas: the non-buckling stretching area, non-buckling compression area and buckling compression area. These areas were described by three variables: the critical buckling position, the neutral plane position and the fibre buckling half-wavelength. A strain energy expression of the SMPC thermodynamic system is developed. According to the principle of minimum energy, the analytical expressions of key parameters in the flexural deformation process is determined, including the critical buckling curvature, critical buckling position, position of the neutral plane, wavelength of the buckling fibre, amplitude of the buckling fibre and macroscopic structural strain of the composite material. The results showed that fibre buckling occurred in the material when the curvature increasing from infinitesimal to the critical value. If the curvature is greater than the critical curvature, the neutral plane of the material will move towards the outboard tensile area, and the critical buckling position will move towards the neutral plane. Consequently, the half-wavelength of the buckling fibre was relatively stabilised, with the amplitude increasing dramatically. Along with the increasing of the shear modulus, the critical curvature and buckling amplitude increase, while the critical half-wavelength of the fibre buckling decrease and the critical strain of the composite material increase. Finally, we conducted experiments to verify the correction of the key parameters describing SMPC materials under flexural deformation. The values determined by the experiments proved that the theoretical prediction is correct. Additionally, the buckling deformation of the carbon fibre generated a large macroscopic structural strain of the composite material and obtained a resulting large flexural curvature of the structure with minimal material strain of the carbon fibre.

Theory of magnetoelectric effect in multilayer nanocomposites on a substrate: Resonant bending-mode response

Resonant bending-mode magnetoelectric (ME) coefficients of magnetostrictive-piezoelectric multilayer cantilevers are calculated analytically using a model developed for arbitrary multilayers on a substrate. Without quality factor effects the ME coefficient maxima in the four-dimensional parameter space of layer numbers, layer sequences, piezoelectric volume fractions, and substrate thicknesses are found to be essentially constant for nonzero substrate thickness. Global maxima occur for bilayers without substrates. Vanishing magnetoelectric response regions result from voltage cancellation in piezoelectric layers or absence of bending-mode excitation. They are determined by the neutral plane position in the multilayer stack. With Q-factor effects dominated by viscous air damping ME coefficients strongly increase with cantilever thickness primarily due to increasing resonance frequencies. The results yield a layer specific prediction of ME coefficients, resonance frequencies, and Q-factors in arbitrary multilayers and thus distinction of linear-coupling and Q-factor effects from exchange interaction, interface, or nonlinear ME effects.

Effect of low‐temperature processing on dry film photoresist properties for flexible electronics

AbstractThis study presents the mechanical characterization of the dry film photoresist PerMX and its adhesion properties when laminated onto Kapton® E (PI) and Melinex® ST506 (PET). Additionally, the processing temperature, the adhesion strength, and the neutral plane position are investigated and optimized. A relatively low‐temperature (85 °C) process is developed to protect the integrity of the polymers with low glass transition temperature and reduce the thermal mismatch stress. Reduction in processing temperature led to a decrement in the adhesion strength. To counteract this unwanted effect, surface treatments (oxygen plasma) are performed on the polymer surface before lamination. Using the latter techniques, adhesion of PerMX to PET (hard bake: 1 h at 85 °C) is increased from 0.07 to 0.26 N mm−1 (variation of 270%). Finally, the mechanical robustness is investigated and increased by tuning the position of the neutral plane, after 50,000 bending cycles and a radius of curvature of 2.5 mm. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013

Finite Element Analysis of the Deformation of Functionally Graded Plates under Thermomechanical Loads

The first-order shear deformation plate model, accounting for the exact neutral plane position, is exploited to investigate the uncoupled thermomechanical behavior of functionally graded (FG) plates. Functionally graded materials are mainly constructed to operate in high temperature environments. Also, FG plates are used in many applications (such as mechanical, electrical, and magnetic), where an amount of heat may be generated into the FG plate whenever other forms of energy (electrical, magnetic, etc.) are converted into thermal energy. Several simulations are performed to study the behavior of FG plates, subjected to thermomechanical loadings, and focus the attention on the effect of the heat source intensity. Most of the previous studies have considered the midplane neutral one, while the actual position of neutral plane for functionally graded plates is shifted and should be firstly determined. A comparative study is performed to illustrate the effect of considering the neutral plane position. The volume fraction of the two constituent materials of the FG plate is varied smoothly and continuously, as a continuous power function of the material position, along the thickness of the plate.

Bending Stress Distribution in Bi-layer Cement Concrete Pavements

Determination of neutral plane position is the key in the analysis of bi-layer cement concrete slab on Winkler foundation; however, there are no solutions for it when the interface of bi-layer slab is semi-bonded. Based on the Kirchhoff hypotheses, a coefficient c was introduced to characterize the interface condition and the equation of neutral plane was formulated in this paper. The change of position of the neutral plane for the bi-layer semi-bonded slab was investigated. In addition, the ratio of the stress distribution along the depth is derived, which is of great importance in the design of bi-layer cement concrete pavements.

Actuator/sensor modeling for vibration of FGM solid circular plate using Reissner‐Mindlin plate theory

AbstractIn this paper, the vibration of a constant thickness circular plate made of functionally graded material (FGM) is controlled by implementing two piezoelectric layers as a sensor and an actuator. Assuming that the material properties of FGM plate vary only in the thickness direction according to the power law manner, the governing differential equations are derived based on the Reissner‐Mindlin plate theory (RMPT). Moreover, in a parallel work another set of differential equations are also derived using classical plate theory (CPT). Then for two different kinds of plate boundary conditions these coupled differential equations are solved using separation of variable technique and obtained results out of two different theories are compared. Moreover, the effect of exact position of neutral plane, the effects of the power index, feedback gain, aspect ratio of radius‐to‐thickness, thickness of the sensor and actuator layers on the principle natural frequency of the compound plate are studied. Finally, the effects of power index and feedback gain on the higher vibrational modes of the system are investigated.

Thermoelastic stresses in non-uniform geological environments difficult outline

Thermal stresses concern not renewed type of stresses, that is once having liberated, they cannot accumulate more. The estimation of purely thermoelastic contribution to a lithosphere stress state gives the additional information, allowing to predict the danger connected with such natural factors, as seismic and volcanic activity. Some theoretical thermoelastic problems for the geological environment of a difficult outline with non-uniform thermophysical characteristics are considered. The decision is received on the basis of a numerical finite elements method. Influence of the model fixation, the geometrical factor and boundary conditions on distribution of thermal stresses and dislocation is investigated. Computing experiments have shown, that the size of the maximum thermal stresses reaches 500 bar. The maximum values of vertical dislocation are reached by 90 m, and horizontal — 50 m. Neutral plane position are precisely defined.

Centrifuge and numerical modeling of axial load effects on piles in consolidating ground

This paper reports the results of four centrifuge model tests that were undertaken to investigate behavior of floating piles subjected to negative skin friction (NSF) and to study effects of axial load on the load-transfer mechanism along single floating piles and shielded center piles inside a group of sacrificing piles. In addition, three-dimensional numerical analyses of the centrifuge model tests were carried out with elasto-plastic slip considered at the pile–soil interface. Prior to applying load, the measured neutral plane position of the single floating piles was located at approximately the three-quarter depth level of the embedded pile length. The neutral plane elevation shifts lower down the pile shaft as the distance of pile tip above the bearing stratum decreases. Under the application of axial load, the dragload generated by excessive soil settlement decreases and is eventually eliminated. The amount of axial load for complete NSF elimination does not seem to be significantly affected by the presence of sacrificing piles, but it does increase with end-bearing stiffness of the pile. Numerical simulation revealed that the hang-up effect is not altered by the application of axial load.

Study of the effects of die geometry on deformation in the radial forging process

Radial forging is an open forging process used for reducing the diameters of shafts, tubes, stepped shafts and axels, and creating internal profiles for tubes such as rifling of gun barrels. Usually a mandrel is used inside a tubular workpiece to create internal profile and/or size the internal diameter, but the process can also be performed without a mandrel when workpiece geometry does not allow utilizing it or the internal surface quality is not critical. Moreover, in stepped shafts and tubes, often there is a fillet connecting two different sections. If it is possible to produce that fillet during the forging process, the process could be more cost effective. So, in this paper, four different shapes for the die inlet zone including linear, convex, concave and hybrid surfaces are considered and the effects of die shape on the deformation pattern and quality of radially forged products are studied. In this study, slab method analysis is used to obtain the deformation pattern, pressure distribution and the position of neutral plane in both cases; with mandrel and without it.

Normal global motion of the cervical spine:: an electrogoniometric study

Objective: Establishment of a normal database and clinical reference of active global cervical spine motion ranges and patterns using a commercial electrogoniometer. Design: Three-dimensional cervical motion ranges and patterns were analyzed in 250 asymptomatic volunteers. Background: In vivo out-of-plane motion patterns of the cervical spine have not yet been reported in large populations, but could be of clinical interest. Methods: In 250 subjects (aged 14–70 yr), motion range and patterns between the first thoracic vertebra and the head were analyzed for flexion–extension, lateral bending, rotation in neutral sagittal plane position and in full flexion using the CA 6000 Spine Motion Analyzer. Results and Conclusions: Average motion range in the sagittal plane was 122° (SD: 18°). Flexion was slightly more important than extension. Out-of-plane components were negligible. Global bending range averaged 88° (SD: 16°), left and right bending being comparable. Homolateral rotation was associated to lateral bending. Its extent was approximately 40% of the bending range. Global rotation range in neutral sagittal plane position was 144° (SD: 20°), without significant difference between right and left rotations. Associated motion components were small. During rotation in flexed head position, global range (134°, SD: 24°) was comparable to the one in neutral flexion. But heterolateral bending, averaging 60% of the primary motion, was associated to flexed rotation. Significant reduction of all primary (but not conjunct) motions with age were obtained. Sex had no influence on cervical motion range. Relevance Our results agreed with previous observations, validating the methodology used. They thus constitute reference data of cervical out-of-plane motion for clinical applications.

Estimation of Neutral Plane Position in High Rise Buildings

This paper presents a simple method for calculation of the pressure distribution and the neutral plane position in a high rise building. Non-uniform temperature distributions in the stairshaft of the building and discrete door openings are taken into account. The method has been incor porated into a network model for calculating smoke spread in multi-storey buildings. Computational results are compared with experimental data ob tained by other researchers.

Damping Characteristics of Laminated Cantilever under Consideration of Position of Neutral Plane.

This paper deals with damping characteristics of a laminated cantilever. In order to determine the loss factor of a three-layered cantilever with arbitrary thickness, an analytical method of evaluating the position of the neutral plane is presented when it exists in the middle layer. Using both this method presented here and Ross' method applicable to the case wherein the neutral plane exists in the first layer, it was found that the position of the neutral plane can be obtained accurately. In addition, it is shown that its position leads to the determination of the loss factor of the three-layered cantilever. From experiments, it was ascertained that these theoretical values of the loss factor agreed well with the experimental values. Moreover, it was clarified which cantilever has better damping characteristics between three-layered and two-layered cantilevers.