Bending Components Research Articles

Mechanical and thermal buckling analysis of functionally graded plates resting on elastic foundations: An assessment of a simple refined nth-order shear deformation theory

In present study, a refined nth-order shear deformation theory is proposed, formulated and validated for a variety of numerical examples of functionally graded (FG) plates resting on elastic foundation for the mechanical and thermal buckling responses. The present refined nth-order shear deformation theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a parabolic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Governing equations are derived from the principle of minimum total potential energy. A Navier type closed form solution methodology is also proposed for simply supported FG plates resting on elastic foundation which provides accurate solution. The accuracy of the present theory is verified by comparing the obtained results with those predicted by classical plate theory (CPT), first-order shear deformation theory (FSDT), higher-order shear deformation theory (HSDT) and refined plate theory (RPT). Moreover, results show that the present theory can achieve the same accuracy of the existing higher-order shear deformation theories which have more number of unknowns.

Analysis of the annual variations in the dynamic behavior of a ballasted railway bridge using Hilbert transform

In this paper the variations in dynamic properties (eigenfrequency and damping) due to seasonal effects of a single span, ballasted railway bridge are studied. It is demonstrated that both the eigenfrequency and characteristic damping vary importantly with environmental conditions and amplitude of vibration. For this, acceleration signals corresponding to roughly a year of monitoring are analyzed with the Hilbert transform and the instantaneous frequency and equivalent viscous damping ratio are calculated during the free vibrations. Over 1000 trains passages were analyzed, with temperatures ranging from -30 to +30°C and amplitudes of vibration varying from 0.5m/s2 to 0. The location of the accelerometers allowed for separation of the signals into their bending and torsional components. It was found that during the cold season, with months of temperatures below 0°C, the dynamic properties varied the most. Not only did the frequencies (for small vibrations) differ more than 9% even for a given temperature, but the non-linearity present in the structure did also change in a matter of hours. These findings are important in the context of Structural Health Monitoring. Any system that aims at warning early in the onset of damage by analyzing changes in the dynamic characteristic of a structure needs to first fully understand and account for the natural variability of these parameters, often much larger than what could be expected from reasonable levels of damage.

Free Vibration Analysis of Laminated Composite Plates Resting on Elastic Foundations by Using a Refined Hyperbolic Shear Deformation Theory

The free vibration of laminated composite plates on elastic foundations is examined by using a refined hyperbolic shear deformation theory. This theory is based on the assumption that the transverse displacements consist of bending and shear components where the bending components do not contribute to shear forces, and likewise, the shear components do not contribute to bending moments. The most interesting feature of this theory is that it allows for parabolic distributions of transverse shear stresses across the plate thickness and satisfies the conditions of zero shear stresses at the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns in the present theory is four, as against five in other shear deformation theories. In the analysis, the foundation is modeled as a two-parameter Pasternak-type foundation, or as a Winkler-type one if the second foundation parameter is zero. The equation of motion for simply supported thick laminated rectangular plates resting on an elastic foundation is obtained through the use of Hamilton’s principle. The numerical results found in the present analysis for free the vibration of cross-ply laminated plates on elastic foundations are presented and compared with those available in the literature. The theory proposed is not only accurate, but also efficient in predicting the natural frequencies of laminated composite plates.

Research on Analysis Method of Fatigue Strength for New Type Crushing Ripper Based on the Composite Load Spectrum

In view of the problem that new type crushing ripper installation of tamping equipment in circulation under the action of different load working multiple cases may occur structural fatigue damage, analysis of its force characteristic, establishment ripper rack compression bending component model, according to the working condition of the most unfavorable load combinations, using the allowable stress method to calculate structural fatigue strength; the combined effect of road load spectrum and vibrating load is also taken into consideration, then statics analysis and fatigue analysis of new type crushing ripper are calculated with the finite element analysis software Ansys Workbench. The results show that theoretical calculations are in accordance with the finite element analysis results, it evidences that the fatigue strength analysis method of crushing ripper is feasible and correct. It provides a reference for the anti-fatigue optimization design of new type crushing ripper, to guarantee its meet the operational requirements under of bad conditions.

Tensile‐bending coupling in the limitting 1D beam equations resulting from the frictional contact

AbstractThe asymptotic dimension reduction for beam contact problems without friction leads to decoupled ODE systems in the longitudinal variable, see [4]. This decoupling is due to the fact that friction is not taken into account. In this work we extend [2] by an alternative scaling of the tensile force in the 3D formulation that permits us to reduce the dimension of a contact problem with friction in tensile direction, too. The tension and the bending component in the direction of the contact normal are coupled due to the friction. The coupling of the displacement components is illustrated by a numerical example. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Thermoelastic damping in torsion microresonators with coupling effect between torsion and bending

Predicting thermoelastic damping (TED) is crucial in the design of high Q MEMS resonators. In the past, there have been few works on analytical modeling of thermoelastic damping in torsion microresonators. This could be related to the assumption of pure torsional mode for the supporting beams in the torsion devices. The pure torsional modes of rectangular supporting beams involve no local volume change, and therefore, they do not suffer any thermoelastic loss. However, the coupled motion of torsion and bending usually exists in the torsion microresonator when it is not excited by pure torque. The bending component of the coupled motion causes flexural vibrations of supporting beams which may result in significant thermoelastic damping for the microresonator. This paper presents an analytical model for thermoelastic damping in torsion microresonators with the coupling effect between torsion and bending. The theory derives a dynamic model for torsion microresonators considering the coupling effect, and approximates the thermoelastic damping by assuming the energy loss to occur only in supporting beams of flexural vibrations. The thermoelastic damping obtained by the present model is compared to the measured internal friction of single paddle oscillators. It is found that thermoelastic damping contributes significantly to internal friction for the case of the higher modes at room temperature. The present model is validated by comparing its results with the finite-element method (FEM) solutions. The effects of structural dimensions and other parameters on thermoelastic damping are investigated for the representative case of torsion microresonators.

A new first shear deformation beam theory based on neutral surface position for functionally graded beams

In this paper, a new first-order shear deformation beam theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded beams. The proposed theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The neutral surface position for a functionally graded beam which its material properties vary in the thickness direction is determined. Based on the present new first-order shear deformation beam theory and the neutral surface concept together with Hamilton\'s principle, the motion equations are derived. To examine accuracy of the present formulation, several comparison studies are investigated. Furthermore, the effects of different parameters of the beam on the bending and free vibration responses of functionally graded beam are discussed.

Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory

Nonlinear behavior of functionally graded material (FGM) plates under thermal loads is investigated here using an efficient sinusoidal shear deformation theory. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the sinusoidal distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed efficient sinusoidal shear deformation theory contains only four unknowns. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the sinusoidal shear deformation theory based on exact neutral surface position is employed here. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The non-linear strain–displacement relations are also taken into consideration. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.

Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams

In this paper, unified nonlocal shear deformation theory is proposed to study bending, buckling and free vibration of nanobeams. This theory is based on the assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. In addition, this present model is capable of capturing both small scale effect and transverse shear deformation effects of nanobeams, and does not require shear correction factors. The equations of motion are derived from Hamilton's principle. Analytical solutions for the deflection, buckling load, and natural frequency are presented for a simply supported nanobeam, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory and Reddy beam theories.

Variation of Young’s modulus of high-strength TA18 tubes and its effects on forming quality of tubes by numerical control bending

Young’s modulus is one of the most important material parameters that influence the plastic-forming quality of bent components, especially spring-back. Young’s modulus actually changes with plastic strain, and its accurate characterisation is necessary to improve simulation accuracy for the tube bending and obtain stable, high-accuracy bent parts by practical bending. Using cyclic loading–unloading tensile tests, the variation of Young’s modulus of high-strength TA18 titanium alloy tubes (TA18-HS tubes) with respect to plastic strain has been obtained. Next, the effects of the variation of Young’s modulus on the spring-back, cross-section flattening, and wall thinning of TA18-HS tubes by numerical control bending are described. The results show the following. (1) With an increase in plastic strain, the value of Young’s modulus reduces rapidly at first, then reduces more slowly, and finally settles to a stable value. This behaviour can be expressed as an exponential function. (2) The variation of Young’s modulus has no effect on the trends of spring-back angles or spring-back radius with the bending angle, however it makes the values increase. (3) The cross-section flattening before spring-back is larger with considering the variation of Young’s modulus than without considering the variation, and the cross-section flattening after spring-back is less with considering the variation of Young’s modulus than without considering the variation. Thus, the recovery of cross-section flattening with considering the variation of Young’s modulus is larger than that without considering the variation. (4) The variation of Young’s modulus has a limited effect on the wall thinning of tubes.

Ion-beam-induced bending of freestanding amorphous nanowires: The importance of the substrate material and charging

Ion-beam irradiation offers great flexibility and controllability in the construction of freestanding nanostructures with multiple advanced functionalities. Here, we present and discuss the bending of free-standing nanowires, against, towards, and ultimately parallel to a flux of directional ion irradiation. Bending components both along and perpendicular to the incident ion beam were observed, and the bending behavior was found to depend both on the ion beam scanning strategy and on the conductivity of the supporting substrate. This behavior is explained by an ion-irradiation-related electrostatic interaction. Our findings suggest the prospect of exploiting this technique to engineer 3D nanostructures for advanced applications.

Elastic large deflection analysis of plates subjected to uniaxial thrust using meshfree Mindlin-Reissner formulation

A meshfree approach for plate buckling/post-buckling problems in the case of uniaxial thrust is presented. A geometrical nonlinear formulation is employed using reproducing kernel approximation and stabilized conforming nodal integration. The bending components are represented by Mindlin---Reissner plate theory. The formulation has a locking-free property in imposing the Kirchhoff mode reproducing condition. In addition, in-plane deformation components are approximated by reproducing kernels. The deformation components are coupled to solve the general plate bending problem with geometrical non-linearity. In buckling/post-buckling analysis of plates, the in-plane displacement of the edges in their perpendicular directions is assumed to be uniform by considering the continuity of plating, and periodic boundary conditions are considered in assuming the periodicity of structures. In such boundary condition enforcements, some node displacements/rotations should be synchronized with others. However, the enforcements introduce difficulties in the meshfree approach because the reproducing kernel function does not have the so-called Kronecker delta property. In this paper, the multiple point constraint technique is introduced to treat such boundary conditions as well as the essential boundary conditions. Numerical studies are performed to examine the accuracy of the multiple point constraint enforcements. As numerical examples, buckling/post-buckling analyses of a rectangular plate and stiffened plate structure are presented to validate the proposed approach.

Large deformation analysis for functionally graded carbon nanotube-reinforced composite plates using an efficient and simple refined theory

In this paper, the nonlinear cylindrical bending behavior of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) is studied using an efficient and simple refined theory. This theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The fundamental equations for functionally graded nanocomposite plates are obtained using the Von-Karman theory for large deflections and the solution is obtained by minimization of the total potential energy. The numerical illustrations concern the nonlinear bending response of FG-CNTRC plates under different sets of thermal environmental conditions, from which results for uniformly distributed CNTRC plates are obtained as comparators.

Condensation of circular DNA

A simple model of a circularly closed double-stranded DNA in a poor solvent is considered as an example of a semi-flexible polymer with self-attraction. To find the ground states, the conformational energy is computed as a sum of the bending and torsional elastic components and the effective self-attraction energy. The model includes a relative orientation or sequence dependence of the effective attraction forces between different pieces of the polymer chain. Two series of conformations are analysed: a multicovered circle (a toroid) and a multifold two-headed racquet. The results are presented as a diagram of state. It is suggested that the stability of particular conformations may be controlled by proper adjustment of the primary structure. Application of the model to other semi-flexible polymers is considered.

A generalized beam theory with shear deformation

A new formulation of the Generalized Beam Theory (GBT) that coherently accounts for shear deformation is presented in this paper. In particular, a modified formulation of the kinematics early proposed by Silvestre and Camotim for shear deformable GBT is devised. The new formulation, which preserves the general format of the original GBT for flexural modes, introduces the shear deformation along the wall thickness direction besides that along the wall midline, so guaranteeing a coherent matching between bending and shear strain components of the beam. According to the new kinematics, a reviewed form of the cross-section analysis procedure is devised, based on a unique modal decomposition for both flexural and shear modes. Much attention is posed on the mechanical interpretation of the deformation parameters in the modal space. It is shown that, in the modal space, it is possible to clearly distinguish bending deflections from deflections due to shearing strains, and to recover classical beam degrees of freedom and standard beam theories as special cases. The effectiveness of the proposed approach is illustrated on two typical benchmark problems.

The PZT system (PbTi Zr1−O3, 0≤x≤1.0): The dependences of electrophysical properties of solid solutions on the electric field strength and component concentration (Part 5)

Abstract The physical properties of PZT (PbTi x Zr 1− x O 3 , 0.0≤ x ≤1.0) ceramics were studied in broad ranges of constant and alternating electric field strengths (0 kV/cm≤ E ≤30 kV/cm). Dielectric, piezoelectric and elastic parameters of the solid solutions at room temperature were investigated. The results can be helpful to develop of PZT based materials for use in various high-voltage devices and bend components such as varactors, phase shifters, etc.

Thermal Buckling Behavior of Nanobeams Using an Efficient Higher-Order Nonlocal Beam Theory

AbstractThis paper presents an efficient higher-order nonlocal beam theory for the thermal buckling of nanobeams. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stress vanishes on the nanobeam surfaces. Therefore, there is no need to use a shear correction factor. The present model is capable of capturing both the small-scale effect and transverse shear deformation effects of nanobeams, and it has strong similarities with the nonlocal Euler–Bernoulli beam theory in aspects such as equations of motion, boundary conditions, and stress resultant expressions. Using the nonlinear strain–displacement relations, the equilibrium and stability equations of nanobeams are derived. The theoretical development presented herein may serve as a reference for nonlocal theories as ...

Distributed neural signals on parabolic cylindrical shells

Parabolic cylindrical shells are commonly used as key components in communication antennas, space telescopes, solar collectors, etc. This study focuses on distributed modal neural sensing signals on a flexible simply-supported parabolic cylindrical shell panel. The parabolic cylindrical shell is fully laminated with a piezoelectric layer on its outer surface and the piezoelectric layer is segmented into infinitesimal elements (neurons) to investigate the microscopic distributed neural sensing signals. Since the dominant vibration component of the shell is usually the transverse oscillation, a new transverse mode shape function is defined. Two shell cases, i.e., the ratio of the meridian height to the half span distance of a parabola at 1:4 (shallow) and 1:1 (deep), are studied to reveal the curvature effect to the neural sensing signals. Studies suggest that the membrane signal component dominates for lower natural modes and the bending signal component dominates for higher natural modes. The meridional membrane and bending signal components are mostly concentrated on the high-curvature areas, while the longitudinal bending component is mostly concentrated on the relatively flat areas. The concentration behavior becomes more prominent as the parabolic cylindrical shell deepens, primarily resulting from the enhanced membrane effect due to the increased curvature.

Research Status of Local Stability in the Web of Castellated Components

Castellated components have many advantages such as high bearing capacity, better bending stiffness, reasonable cross-section form and significant economic benefit. Castellated components are weakened by the reason of web openings, so it is more prone to appear local stability problem. Therefore, the researches of local stability in castellated components play a very important role in the application of the castellated components. In this issue, scholars at home and abroad do a lot of researches, including theoretical research, numerical simulation analysis and experimental research. But the research of castellated bending components are still in groping stage .That has seriously hampered the application and promotion of castellated components in China. So it is necessary to study the local stability of castellated components.

Fatigue life of cast Inconel 713LC with/without protective diffusion coating under bending, torsion and their combination

Fatigue behaviour of cylindrical specimens made of cast Inconel 713LC nickel-based superalloy with/without diffusion aluminide and Cr-modified aluminide protective coatings was studied under bending, torsion and combined bending–torsion loading regimes. Experiments were conducted at room temperature by using sinusoidal loading of a frequency f≈30Hz. It was found that the presence of either coating system enhances the high cycle fatigue strength for all tested loading regimes. In the low cycle fatigue region, the fatigue strength was slightly improved for torsional loading, while it was almost the same or modestly lower for loading regimes with non-zero bending component. This behaviour seems to be linked to different nucleation efficiency of secondary-phase particles within the diffusion zone. Acquired experimental data were also used to evaluate predictive capabilities of stress-based multiaxial fatigue failure criteria proposed by Gough, Matake and Crossland that were selected as representatives of main multiaxial fatigue failure prediction classes. Results revealed that, for a given material and loading conditions, the Matake criterion based on a critical plane approach provides the best fatigue life data estimations most of which are within a factor of two bandwidth.