Simple Bending Research Articles

Finite element modeling of creep deformation in cellular metals

The creep of reticulated metallic foams is studied through the finite element method using three-dimensional, periodic unit cells with four different architectures characterized by struts which deform primarily by: (i) simple bending, (ii) compression, (iii) a combination of simple bending and compression and (iv) double bending (for Kelvin space-filling tetrakaidecahedra). The creep behavior of each of these models is examined with respect to temperature, stress and foam relative density. Calculated creep rates for both bending and compression models are below those predicted from simplified analytical models and bracket those of the combination model. The simple and double bending models predict nearly identical strain rates despite very different geometries, because in both cases the deflection rates of the fastest deforming struts are similar. Both analytical and numerical predictions are compared to published creep data for metallic foams.

Application of prestressed transparent composite beams in fracture mechanics

This work presents the mixed-mode I/II/III version of the prestressed end-notched flexure system for the general delamination characterization of composite materials. The novel fracture mechanical configuration combines the traditional mode-I double-cantilever beam and the mode-II end-notched flexure specimens with the mode-III modified split-cantilever beam. First, a steel roller with a given diameter - which should not exceed the critical crack opening - is inserted to the delamination front, this fixes the mode-I part of the total energy release rate. Second, the prestressed specimen is put into the special rig of the MSCB specimen, and with the help of a prestressing screw the mode-III part of the total energy release rate is also fixed. Third, the prestressed specimen is put into a simple three-point bending setup and the mode-II part of the total energy release rate is increased up to fracture initiation. Using this method, i.e. varying the crack opening displacement by the steel roller and the crack te aring displacement by the MSCB rig the fracture surface in the GI-GII-GIII space can be obtained. To demonstrate the applicability and limitations of the novel system experiments on glass-fiber reinforced polyester specimens were performed including separated mode-I, mode-II, mode-III, mixed-mode I/II, II/III, I/III and I/II/III fracture tests. To reduce the measured data a previously validated improved beam theory scheme is applied. Finally, the surface of the fracture criterion is constructed by the generalization of the traditional criterion by Williams.

Insight into 3-node triangular shell finite elements: the effects of element isotropy and mesh patterns

In this paper, we study the convergence characteristics of some 3-node triangular shell finite elements. We review the formulations of three different isotropic 3-node elements and one non-isotropic 3-node element. We analyze a clamped plate problem and a hyperboloid shell problem using various mesh topologies and present the convergence curves using the s-norm. Considering simple bending tests, we also study the transverse shear strain fields of the shell finite elements. The results and insight given are valuable for the proper use and the further development of triangular shell finite elements.

Assessment of an edge type settlement of above ground liquid storage tanks using a simple beam model

Analysis of deformation and bending moment distributions along sections of the bottom plate of a large unanchored cylindrical liquid storage tank with appreciable out-of-plane localized differential edge settlement is considered. The analysis uses approximate simple slender beam bending theory to model localized edge settlements of the plate and takes into account the effects of foundation compliance, initial settlement shape, shell and hydrostatic loadings and the shell-bottom plate junction stiffness. The obtained model is solved, in the elastic range, using a combined analytical–numerical procedure for the deflection and bending moment distributions along the beam. The obtained approximate solutions were displayed graphically for selected values of system parameters: edge settlement amplitude, plate thickness, foundation stiffness, and hydrostatic load. The maximum allowable edge displacement amplitudes based on the plate yielding stress predicted by the present study are compared for the selected values of system parameters with those recommended in the API standard 653.

Conducting IPN actuators: From polymer chemistry to actuator with linear actuation

Among electroactive actuators, those based on electronic conducting polymers (ECPs) possess several advantages (low actuation voltages, large deformations, etc.) but also some drawbacks (bending movements only, delamination, etc.). In order to overcome the delamination process observed in working three-layered actuators, we have developed a new concept of actuator consisting in an interpenetrating polymer network (IPN) matrix in which 3,4-ethylenedioxythiophene (EDOT) is chemically polymerized. The typical IPN matrix results from the association of the two following cross-linked polymers: the first one, polyethylene oxide (PEO), will ensure the ionic conductivity of the system after salt incorporation while the second one, polybutadiene (PB), will allow to adjust the required mechanical properties. The chemical polymerization of EDOT within the IPN leads to the formation of a PEDOT gradient, its concentration decreasing from the outside faces towards the centre of the IPN. So, such a one-piece actuator is equivalent to a three-layered actuator. Applying a low potential (2–5 V) at a frequency from 0.1 to 15 Hz, up to 10 6 bending deformations in open air have been observed after incorporation of a room temperature ionic liquid. However, linear deformations are more interesting for a number of applications than simple bending motions. The description of the design of an open air working actuator with linear actuation is presented.

Identification of elasto-plastic characteristics by means of air-bending test

A new identification method of material elasto-plastic characteristics by means of simple testing is proposed. The outcome of the procedure is the true-stress versus true-strain curve. The result is proposed in analytical form, according to Swift's law. The method requires acquisition of actual force-penetration values, carried out during a standard air-bending test. One of the main advantage of this method is that it allows an immediate identification of the material behaviour just in-process, that is to say that material characteristics can be accounted differently for each sheet subjected to bending; this is a fundamental preliminary step to achieve a bending adaptive control of sheets. Input requirements for identification include the geometry of tools and sheet, and the friction coefficient between sheet and die which needs to be estimated previously. In the proposed method, at a first stage the bending moment–curvature curve for the sheet is obtained by the numerical computation of force-penetration data through a multi-joint model of sheet during air-bending. Then, a simplified bending model, characterized by linear strain distribution across the thickness and plane-stress assumption, is employed to calculate the stress–strain curve.

T-stress Solutions for Cracks Emanating from a Circular Hole in a Finite Plate

The boundary element method is employed to obtain T-stress solutions for cracks emanating from a circular hole in finite rectangular plates. Numerical values of the T-stress are obtained using the M-contour integral approach. A range of crack lengths are analyzed for two hole sizes, and the cases of a single crack and double-cracks emanating from the hole in the plate under both uniform remote tension and simple bending are considered. For completeness, stress intensity factor solutions are also presented. These results will be useful for failure assessments using two-parameter linear elastic fracture mechanics.

Influence of the Weld on the Mechanical Behaviour of Tailor Welded Blanks

In new car production, an innovative method to produce strong and light panels consists in applying Tailor Welded Blanks (TWBs) in the body-in-white base structure. Since the fusion welding processes can induce significant changes in the material properties of the base materials, an important question is whether the weld bead has a significant influence on the overall behaviour of the welded blanks. In this work, some preliminary conclusions on this subject were achieved based on results of the numerical simulation of simple mechanical tests: tensile, shear and simple bending. The numerical simulations were performed with a fully implicit finite element program (DD3IMP). The results obtained show that for a slight mismatch of properties between the weld and the base materials, no important influence of the weld in the TWBs behaviour is noticed. However, a significant strength reduction can be observed for strong undermatch conditions (lower mechanical properties in the weld) even when the weld bead is very narrow.

Prestressed fracture specimen for delamination testing of composites

The prestressed end-notched flexure fracture specimen is developed in the present work, which combines the traditional double-cantilever beam and the end-notched flexure specimens in a very simple way. The most important features of the new beam-like specimen are that it is able to provide any combination of the modes I and II strain energy release rates and it may be performed by using a simple three-point bending fixture. The mode-I part of the strain energy release rate is fixed by inserting a steel roller, which causes a fixed crack opening displacement. The mode-II part of the energy release rate is provided by the external load. A simple closed-form solution using beam theory is developed for the energy release rates of the new configuration. The applicability and the limitations of the novel configuration are demonstrated using unidirectional glass/polyester composite specimens. If only propagation onset is involved then the prestressed end-notched flexure specimen can be used to obtain the fracture criterion of transparent composite materials in a very simple way.

Bending of long, rectangular-section bonded rubber blocks

Readily-calculable explicit closed-form representations are determined for the bending stiffness of, and stresses within, generally loaded bonded rubber blocks of long, rectangular cross-section. They satisfy exactly the stated governing equations and conditions based upon the classical theory of elasticity. From these, more detailed investigations are given for the especially interesting loading cases corresponding to simple bending, cantilever loading and apparent shear. It is observed that the deformed profiles of the side surfaces are not in general parabolic as has been usually assumed previously. In simple bending an improved approximate elementary expression is deduced for the couple needed to create a specified rotation of the loaded end of the block. Similarly, in apparent shear a more realistic simple estimate is derived from the exact expression for the ratio of the true to the apparent shear modulus.

Structural Tests of Precast, Prestressed Concrete Deck Panels for California Freeway Bridges

Full-scale structural tests of five precast, prestressed concrete bridge deck panels have been carried out in simple bending to failure at the San Diego State University Structural Engineering Laboratory in San Diego, Calif. The purpose of the tests was to demonstrate to Caltrans that the precast concrete panels act compositely in flexure with a cast-in-place topping slab so that they can be used for California bridges. To ensure that the full deck width was active in resisting the applied loads, steel I-beams the width of the deck were used under the load and at the reaction points. Neoprene bearing pads were incorporated at the supports to allow free rotations at the deck ends. Each bridge deck consisted of a precast, prestressed concrete deck panel with a cast-in-place topping slab, with no reinforcing bars crossing the interface between slabs. Of particular interest was the verification that no horizontal shear slip occurred between the two slabs and that the deck acted as a fully composite member to failure. One test featured the precast concrete slab by itself, three of the tests investigated the deck behavior in positive bending with different roughening levels applied to the top of the precast concrete slab, and the fifth test was performed in negative bending (upside down). Nonlinear prediction analyses were conducted for each of the tests, including the formation and spreading of flexural cracking along the deck and plastic hinging at the critical section in the center of the span. Test results, supported by detailed structural analyses, demonstrated that there was no horizontal shear slip between the precast concrete panels and cast-in-place slabs, allowing them to respond in flexure as a single composite slab.

Effects of steel fiber addition on mechanical properties of concrete and RC beams

C20 and C30 classes of concrete are produced each with addition of Dramix RC-80/0.60-BN type of steel fibers (SFs) at dosages of 0, 30, 60 kg/m 3, and their compressive strengths, split tensile strength, moduli of elasticity and toughnesses are measured. Nine reinforced concrete (RC) beams of 300 × 300 × 2000 mm outer dimensions, designed as tension failure and all having the same steel reinforcement, having SFs at dosages of 0, 30, 60 kg/m 3 with C20 class concrete, and nine other RC beams of the same peculiarities with C30 class concrete again designed as tension failure and all having the same reinforcement are produced and tested under simple bending. The load versus mid-span deflection relationships of all these RC and steel-fiber-added RC (SFARC) beams under simple bending are recorded. First, the mechanical properties of C20 and C30 classes of concrete with no SFs and with SFs at dosages of 30 and 60 kg/m 3 are determined in a comparative way. The flexural behaviours and toughnesses of RC and SFARC beams for C20 and C30 classes of concrete are also determined in a comparative way. The experimentally determined (mid-section load)–(SFs dosage) and (toughness)–(SFs dosage) relationships are given to reveal the quantitative effects of concrete class and SFs dosage on these crucial properties.

Analysis of bending properties of worsted wool yarns and fabrics based on quasi-three-point bending

The bending behavior of worsted wool yarns and fabrics plays a crucial role in handling and performance of end-use textiles. Hence, the fabric/yarn bending properties were studied based on a quasi-three-point bending model by means of the theoretical modeling and the corresponding measuring method. By means of the formula and the measured curves, the curve of bending rigidity and the curvature of a fabric or a yarn can be calculated so as to characterize the bending behavior more precisely than in the previous work. All the experiments on the fabric/yarn bending rigidity have been conducted for both the worsted wool fabrics and the corresponding yarns procured from the fabrics, with the same apparatus bending evaluation system of fabric and yarn, which was developed independently. The measured results of bending rigidity and curvature curve show good correlation with the bending moment and the curvature relationship of the theoretical modeling, and the comparisons of bending rigidity among KES-FB2 (Kawabata Evaluation System for Fabrics-2 pure bending tester), FAST-2 (Fabric Assurance by Simple Testing-2 bending meter), and the independently developed apparatus show that the three systems exhibist reasonably high correlations. It is confirmed that the new apparatus and the theoretical model are both viable and precious. Meanwhile, the theoretical relationship between the yarns and the fabrics has also been discussed, and the theoretical analysis of the bending behavior between the yarns and the fabrics is helpful in selecting a better theoretical model of the fabric-to-yarn bending rigidity ratio.

Degradation of critical current by the mixed strain of bending and tension in Bi-2223/Ag HTS tape

Influences of the mixed strain mode of bending tension on Ic degradation at the bent region of a commercially available Bi-2223 tape without external reinforcement were investigated and discussed. The Ic degradation behaviors were examined at 77K in each and in the mixed strain mode. A newly devised sample holder, which provides a mixed strain mode, ε(t+b), of bending tension to the HTS tape by applying tension to bent tapes, was used. Some variations in the Ic degradation existed in the Bi-2223 tape resulting from non-uniform deformation in the tension mode. In the mixed strain mode, the Ic degradation was expressed as a function of the total strain derived by the superposition principle. The irreversible strain, εirr.(b+t), for the onset of Ic degradation at the mixed strain mode region of the tape was larger as compared with the simple bending case. For strains larger than the εirr.(b+t), the Ic at the bent region of the tape degraded gradually as compared with the simple tension case. As the initially imparted bending strain to the tape increased, the εirr.(b+t) of the tape increased. It was found that the friction between the tape and the mandrel at the mixed strain mode region of the tape contributed to improve the apparent strain tolerance of Bi-2223 tapes at the bent region.

Polarization-selective waveguide bends in a photonic crystal structure with layered square symmetry

We demonstrate single-mode horizontal and vertical waveguides in a recently proposed photonic crystal having layered square symmetry. The vertical waveguide supports two degenerate polarizations, and thus light can be selectively steered into horizontal waveguides oriented at 90° based on its polarization. We calculate the transmission of 90° bends, both from horizontal waveguide to horizontal waveguide and from horizontal waveguide to vertical waveguide. In the case of the horizontal-horizontal bend, we show a transmission of 83% for a simple (“zero” radius of curvature) bend, and a peak transmission of 100% for a bend which has been optimized by moving one rod from the inner corner to the outer corner of the bend. For the vertical to horizontal bend, we find a transmission of 95% for the allowed polarization, but with a much smaller bandwidth than in the case of the optimized horizontal bend.

Propagation of ultrasonic waves in materials under bending forces

Ultrasound longitudinal and linearly polarised shear waves propagating through a piece submitted to bending stresses rely on some physical properties such as the volume density, the elastic constants and the strain resulting from the applied forces. The present paper deals with the acoustoelasticity theory in stressed and elastically deformed media under simple bending forces. For a piece made of carbon steel (C 35) with known macroscopic properties, acoustoelastic measurements have been achieved in three zones under bending stresses (compressed, central and extended fibres). The waveforms provided by ultrasound transducers correspond to the average value of the applied stress on their surface. These responses have been simulated numerically by dividing of the transducer in slices. Simulated and measured ultrasonic waveforms in transmission configuration allow the verification of the delay effect induced by bending stresses and the amplitude modification resulting from the effect of averaging over the transducer according to its finite dimension. This method constitutes an investigating tool for the evaluation of the acoustic properties of homogeneous materials loaded elastically by variable or heterogeneous stresses.

Geodynamics of continental plate collision during late tertiary foreland basin evolution in the Timor Sea: constraints from foreland sequences, elastic flexure and normal faulting

Tectonic subsidence of the Australian lithosphere during the Late Tertiary propagates from the southwest to the northeast in the Timor Sea, as a consequence of the oblique collision between the Eurasian and Australian plates. We reconstruct the asynchronous nature of deflection of the Australian plate created during the plate convergence by best-matching the geometry of de-compacted foreland strata against the predictions of simple bending elastic beam models. We infer a maximum subsidence of 3500 m and a maximum width for the basin of ∼470 km. The effective elastic thickness of the Australian lithosphere (∼80 to 100 km) does not change significantly during basin evolution. The low curvature imposed on the plate (∼5.1×10 −8 m −1) during bending is too small to weaken the plate. Yet, abundant but small-slip, normal faulting related to bending implies some degree of inelastic yielding. The polarity of fault propagation supports the oblique nature of the collision. Flexural models indicate that at least 570 km of Australian plate (mostly areas of stretched continental crust) was flexed, primarily by the tectonic loading of the Timor Island and that the total amount of subducted plate was at least 100 km during basin evolution.

A smart bending sensor with a novel temperature- and strain-insensitive long-period grating

A simple bending sensor is performed with a novel insensitive long-period fiber grating (LPG). The characteristic of the insensitive LPG has been experimentally presented, which has the pitch and the notch wavelength of 440 μm and 1516.2 nm at 20 °C. We have investigated temperature and strain insensitivities. The temperature coefficient is about 0.003 nm/°C from 10 to 50 °C, and the strain coefficient is only about 15 nm/ε, which are about 1/30 and 1/100, compared with the corresponding coefficients of the conventional devices with typical values of 0.083 nm/°C and 1521 nm/ε, respectively. It is fabricated as a bending sensor without any treatment to eliminate the temperature and strain effects, and the bending sensitivity is the same order as the ordinary one. At the same time, the temperature- and strain-insensitive LPG will have wide prospect for other smart fiber sensors and communication devices.

Degradation behavior of critical current in Bi-2223 tapes in bending–tension strain mode

Influences of mixed bending–tension strain on the I c degradation of Bi-2223 superconducting tapes were investigated. For the experiment, a test fixture that applies mixed bending–tension strains to HTS tapes has been devised. When the strain induced in the Bi-2223 tape in the mixed strain mode was expressed by a total strain, the irreversible strain, ε irr.(t+b), for the onset of the I c degradation at the bent region of the Bi-2223 tape was larger as compared with the simple bending case. The I c at the bent region of the tape after the ε irr.(t+b) degraded quite rapidly as compared with the simple bending case. As the bending strain, which was imparted initially to the tape increased, namely, as the mandrel diameter adopted decreased, the induced apparent irreversible strain of Bi-2223 tapes due to the mixed bending–tension strain increased, but the increment (marginal strain) decreased gradually.

The transition from thin plates to moderately thick plates by using finite element analysis and the shear locking problem

Two simple plate bending elements, based on Mindlin theory for analysis of both moderately thick and thin plates, are presented in this paper. These elements have either four nodes or eight nodes with 12 and 24 DOF, respectively. To illustrate the accuracy of these finite elements named as TURE12 and TURE24, several numerical examples of displacements and stresses for both thin and moderately thick plate bending problems are presented and discussed with a range of finite element meshes and thickness-to-plate length ratios. In addition, the bending and shearing behaviours of a Mindlin plate are analyzed with respect to shear locking. In order to test the shear locking, the results obtained from the Mindlin plate analysis using 4- or 8-noded elements with full, reduced, and selective reduced integration are compared with the exact classical thin plate solution.