Bending Part Research Articles

A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations

In this work, a novel simple first-order shear deformation plate theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded plates and supported by either Winkler or Pasternak elastic foundations. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The governing equations are derived by employing the Hamilton\'s principle and the physical neutral surface concept. 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. Numerical results of present theory are compared with results of the traditional first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.

Theoretical rovibrational spectroscopy beyond fc-CCSD(T): the cation CNC+

An accurate near-equilibrium potential energy surface (PES) for CNC+ is constructed based on a high-level composite ab initio method. By combining explicitly correlated all-electron CCSD(T)-F12b with scalar relativistic effects and higher order correlation up to coupled cluster theory with singles, doubles, triples and quadruples (CCSDTQ) we achieve convergence in the wavenumbers of the fundamentals to ca. 1 cm−1. Rovibrational energies are calculated in a variational approach and vibrational term energies and rotational constants are in excellent agreement with available experimental data. Accurate values for centrifugal distortion constants of CNC+ in different vibrational states are predicted. Especially the centrifugal distortion constants in the vibrational ground state of D0 = 0.563 · 10−6 cm−1 and H0 = 0.188 · 10−10 cm−1 should be superior to experimentally derived values. Reassignments of some experimentally observed transitions are suggested based on a comparison of experimental and calculated term differences. The bending part of the PES appears to be almost quartic and the band origin of the bending vibration is predicted at 94.2 cm−1. Absolute line intensities are calculated for various transitions in CNC+. For the bending vibration, an intensity is predicted that is three orders of magnitude smaller than for the antisymmetric stretching vibration.

Thermal buckling of functionally graded plates using a n-order four variable refined theory

This paper presents a simple n-order four variable refined theory for buckling analysis of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and eliminates the shear stresses at the top and bottom surfaces. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present n-order refined theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.

Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories

In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.

An experimental study on the springback in bending of w-shaped micro sheet-metal parts

In sheet-metal bending, defects relating to the component-forms such as springback are common. This is due to the elastic deflection that occurs in the material after the bending process takes place. The objective of the research is to study on the springback behaviour in micro sheet-metal parts. This paper reports an investigation concerning the influence of the material rolling direction on springback in the case of w-shaped bending parts. Micro bending parts using 316 L annealed stainless steel strips having thickness of 50 μm, 75 μm and 100 μm respectively were formed. The tensile and bending behaviours of the parts were observed through the experiment by considering the effect of rolling direction and size-effect related errors. The results revealed that various parameters influence the springback, such as thickness of the sheet, force applied, material rolling-direction and holding time during the sheet-deformation. The scale of the springback was also observed to be random among the parts made with a same sheet material.

Variation simulation of stress during assembly of composite parts

Weight reduction requirements in aerospace and automotive industry lead to an increased use of composite materials. However, composite parts cannot be bent like sheet metal parts. Hence, only low forces can be applied to close gaps between parts, caused by geometrical variation in parts and assembly fixtures. Shimming is therefore used to compensate for bad fitting, with increase cost as a consequence. This paper investigates how variation in assembly fixtures and parts give rise to variation in gaps and thereby also to variation in stress. Monte Carlo simulations are used to find the distribution of stress, which supports shimming strategies.

受弯件上粘贴型光纤布拉格光栅的应变传递规律

受弯件上粘贴型光纤布拉格光栅的应变传递规律

Collapsing Strength Analysis of Bending Part Casing in Horizontal Wells under Three-Point Bending

According to the mechanical characteristics of bending part casing in horizontal well, established the three-point bending casing mechanical model. By analyzing the stress distribution of casing under three-point bending, considering the effects of shear, extrusion, and bending, using the fourth strength theory and Lame formula, collapsing strength formula of bending part casing in horizontal wells under the three-point bending are derived. Effect of built-up rate on the casing collapsing strength was investigated and evaluated using analytical approach as well as FEM. The results show that built-up rate has a significant impact on casing collapsing strength, and collapsing strength of casing decreases significantly as the increasing of the built-up rate. When built-up rate is large, collapsing strength of thick-walled, large diameter casing decreases faster as the increasing of built-up rate; the casing with bigger wall thickness has bigger collapsing strength under the same borehole curvature and steel grade.

形状記憶合金ワイヤーを用いた低侵襲医療用一方向能動屈曲機構とワイヤーの電気抵抗変化を用いたフィードバック制御

The bending mechanism of a conventional endoscope operates by drawing wires from outside the human body. The shaft structure of endoscopes is relatively complex to avoid buckling caused by wire traction. In this study, one directional bending mechanisms using shape memory alloy (SMA) wires have been developed for minimally invasive medicine. A large bending angle was accomplished by positioning a working point of driven SMA wires near a center point of the mechanism and by surrounding the SMA wires and an inner tube by helical thin metal wire. External diameter and length of the bending part of the mechanism are 4.1 mm and 35 mm respectively. The curvature radius of the fabricated device is 20 mm while maintaining the surface temperature of the device under 41°C in environmental temperature (38°C). Servo control has been considered to be suitable for the application of active bending mechanisms as micro robots. Feedback control by changing in the electrical resistance of the SMA wire was utilized for precise and safty actuation.

Compact dual-wideband bandpass filter with good selectivity using side-coupled λ/4 shorted SIR

A compact dual-wideband bandpass filter featuring two controllable center frequencies and passbands using a single side-coupled shorted λ/4 stepped-impedance resonator (SIR) is presented. The resonant frequencies of the two passbands can be adjusted by tuning the impedance ratio and length of the SIR. The bandwidth of the two passbands is determined by the coupling strength between the meandering feedlines and the resonator. The generation mechanism of filter’s transmission zeroes was investigated by equivalent models of the filter and the bending parts of the open-end meandering feedlines. Owing to the cross-coupling between the two open-end meandering feedlines and the phase shifted characteristic of the open-end meandering feedlines, several transmission zeroes can be generated to improve the selectivity. To verify the design concept, one dual-wideband bandpass filter has been designed, fabricated, and measured. The simulated and measured results are presented with good agreement.

Optical Properties of a Y-Splitter Based on Hybrid Multilayer Plasmonic Waveguide

A Y-splitter based on hybrid multilayer plasmonic waveguide structure composed of silver–silica–silicon–silica–silver is introduced. Properties, such as the transmission rate and split ratio, are numerically investigated by changing the thickness of dielectric layers, bending radii of the bending parts, as well as input working wavelength. Results indicate that the proposed structure can have high transmission rates of >47% at the two output branches with split ratio close to 1:1. When the symmetry of the structure is broken by adjusting the bending radii of the bending parts, one may control the transmission rate of the two different output branches and then control the split ratio for a given working wavelength to a certain degree. Comparison reveals that the proposed Y-splitter is superior to the T-splitter within the wavelength range of 1000–1600 nm. These properties are helpful in the design and application of photonic devices and integration.

A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations

This paper deals with the thermo-mechanical deformation behaviour of shear deformable functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The presented theory is variationally consistent, does not require shear correction factor and gives rise to transverse shear stress variation such that the transverse shear stresses vary in hyperbolic manner across the thickness satisfying shear stress-free surface conditions. A power-law distribution for the mechanical characteristics is adopted to model the continuous variation of properties from those of one component to those of the other. The sandwich plate faces are made of isotropic, two-constituent (ceramic–metal) material distribution through the thickness. The core layer is still homogeneous and made of an isotropic metal material. Several kinds of non-symmetric sandwich plates are presented. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical results of the present simple shear deformation theory are presented to show the effect of material distribution and foundation parameters on the deflections and stresses. A wide variety of results is presented for the static response of sandwich plates under thermo-mechanical loads.

A New Approach for Quantitative Evaluation of Bending Components

During the bending of tubes, specific geometric deviations from the desired shape geometry occur. These deformations comprise cross-sectional deformation, wall-thinning of the outer arc and wall-thickening of the inner arc. During the bending of parts with small bend factors, geometric deviations on the inner arc in form of waves and wrinkles may arise as other typical quality criteria. A quantitative evaluation of those deviations has yet to be defined. Currently, only an instruction for measuring the height of the wrinkles at the inner arc according to DIN EN 13480-4 is known. In this standard, only the two highest wrinkles and the valley in between are included. The characteristics of the wrinkle, especially the flank angle and the rise of deformation are disregarded, although they are responsible for the failure of the bent part. Tool damages can also occur. A development of an evaluation factor to assess deformations in the bow area for bent parts is presented in this paper. In addition, it will be possible to quantify geometric deviations in the bow area. By using the newly developed evaluation factor for geometrical deformations in the bow area, the determination of the quality of the bent part should become more reproducible.

3D modeling of earthquake cycles of the Xianshuihe fault, southwestern China

We perform 3D modeling of earthquake generation of the Xianshuihe fault, southwestern China, which is a highly active strike-slip fault with a length of about 350km, in order to understand earthquake cycles and segmentations for a long-term forecasting and earthquake nucleation process for a short-term forecasting. Historical earthquake data over the last 300years indicates repeated periods of seismic activity, and migration of large earthquake along the fault during active seismic periods. To develop the 3D model of earthquake cycles along the Xianshuihe fault, we use a rate- and state-dependent friction law. After analyzing the result, we find that the earthquakes occur in the reoccurrence intervals of 400–500years. Simulation result of slip velocity distribution along the fault at the depth of 10km during 2694years along the Xianshuihe fault indicates that since the third earthquake cycle, the fault has been divided into 3 parts. Some earthquake ruptures terminate at the bending part of the fault line, which may means the shape of the fault line controls how earthquake ruptures. The change of slip velocity and displacement at 10km depth is more tremendous than the change of the shallow and deep part of the fault and the largest slip velocity occurs at the depth of 10km which is the exact depth of the seismic zone where fast rupture occurs.

A n-order four variable refined theory for bending and free vibration of functionally graded plates

This paper presents a simple n-order four variable refined theory for the bending and vibration analyses of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.

A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass

The novelty of this paper is the use of trigonometric four variable plate theory for free vibration analysis of laminated rectangular plate supporting a localized patch mass. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The Hamilton's Principle, using trigonometric shear deformation theory, is applied to simply support rectangular plates. Numerical examples are presented to show the effects of geometrical parameters such as aspect ratio of the plate, size and location of the patch mass on natural frequencies of laminated composite plates. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of laminated rectangular plate supporting a localized patch mass.

INFLUENCE OF TECHNOLOGICAL PARAMETERS ON THE SPRINGBACK ANGLE OF HIGH-STRENGTH STEELS

The most common problem in area of sheet metal forming technology is a problem of achieving accurate and repeatable shapes of drawn and bent parts. This phenomenon is caused by the elastic springback. Springback can be defined as an elastically-driven change of shape of the deformed part upon removal of external loads. Several technological parameters influence amount of springback, between these belong friction coefficient, blankholder force, different geometry of tools, etc. In this paper is presented this topic, and also numerical simulation of this process. For an experimental process were used two high-strength steels. Steel with TRIP effect and dual phase steel DP 600. Numerical simulation was performed in the static implicit code Autoform. Results were compared and discussed.

Experimental Study on Three-Dimensional Flexible Stretch Bending Formability for Complex Cross-Sectional Profiles of TWB

Taking the upper strip of automobile doorframe which is complex profiles roll bending part of high-strength steel welded blanks as the research object, and then to Investigate its three-dimensional flexible stretch-bending formability under force control mode; the law of tensile force and clamp rotation angles’ influences on forming precision of the product is obtained. The results show that the springback of the line contour precision is largely affected by the comprehensive impact of tensile force and the clamp rotation angles, the values mentioned above reached minimum when the tensile force is 1.1 times the material yield strength, the springback will increase when greater or less than this value. Because of the surface torsion springback, internal and external surface contour accuracy mainly affected by the stage rotation angle when the profile bending curvature is large enough, and the effect is not obvious when the bending curvature is small.

Design Rules, Experimental Evaluation, and Fracture Models for High-Strength and Stainless-Steel Hourglass Shape Energy Dissipation Devices

Steel yielding hysteretic devices provide a reliable way to increase the energy dissipation capacity of structures under seismic loading. Steel cylindrical pins with hourglass shape bending parts (called web hourglass shape pins—WHPs) have been recently used as the energy dissipation system of posttensioned connections for self-centering steel moment-resisting frames. This work evaluates the cyclic behavior of WHPs made of high-strength steel and two grades of stainless steel, i.e., austenitic grade 304 and duplex. Design rules for WHPs are established using principles of mechanics. Twenty-six tests using different cyclic loading protocols and different WHP geometries were conducted. The tests showed that the WHPs have stable hysteretic behavior and high fracture capacity. WHPs made of duplex stainless steel have the most favorable and predictable performance for seismic applications. Two micromechanics-based fracture models, i.e., the void growth model and the stress-modified critical strain model, were calibrated and their parameters are provided for high-strength steel and the two types of stainless steel. The ability of the cyclic void growth model to predict fracture in WHPs under cyclic loading is also evaluated.

Numerical simulation and experimental investigation to improve the dimensional accuracy in electric hot incremental forming of Ti–6Al–4V titanium sheet

Electric hot incremental forming is feasible and easy to control to form hard-to-form sheet metals, but the limited accuracy is a major deficiency. In order to find methods to improve precision, single-point electric hot incremental of Ti–6Al–4V titanium sheet was numerically simulated using MSC.Marc, and experimental investigations were also carried out in this paper. Through numerical analysis, distributing laws of temperature, thermal strain, stress, and equivalent strain were revealed, and impacts of cold contract and thermal strain on forming were also revealed. Analysis showed that electric hot incremental forming is a complex pyroplastic deformation, and there is a large internal stress in single-point electric hot incremental forming. The incremental sheet forming region can be divided into three parts: bending deformation at the beginning, shear forming at middle, and reverse bending at last; it is important to enhance the accuracy of the bending part and the reverse bending part, and adequate support must be provided in the beginning to reduce the bending part. In order to form a workpiece with small angle, two-point incremental forming was adopted at first because the gravity of clamp can reduce the reverse bending, then single-point electric hot incremental forming was adopted to enhance the accuracy and reduce internal stress of workpiece.