Elastic Bending Theory Research Articles

Shear force distribution mechanism of perfobond leiste connectors in joint between corrugated steel web and concrete top slab

Compared to composite bridges with flat steel webs (FSWs), the corrugation shape and significant shear deformation of the steel web in composite bridges with corrugated steel webs (CSWs) will influence the distribution and magnitude of the shear force of connectors in the joint between the steel web and concrete slab. However, these effects have not been considered in current design specifications, which may lead to unsafe designs. This paper investigates the shear force distribution mechanism of perfobond leiste (PBL) connectors in the joint between the CSW and concrete top slab in composite bridges with CSWs. The theoretical solution for the shear force of the joint per unit length is firstly derived based on the elastic bending theory considering the shear deformation of the CSW. Then, finite element simulations using hybrid models of solid and spring elements are conducted to further investigate the shear force distribution of PBL connectors and influencing parameters. The results show that the shear deformation of the CSW has a negligible effect on the shear force of the joint per unit length. In contrast to composite bridges with FSWs, the CSW induces sinusoidal variations in the shear force of PBL connectors, which leads to an increase in the shear force of partial PBL connectors. The amplification factor for the shear force increases with the wavelength of the CSW and the shear stiffness of the PBL connector, while it decreases with the increasing dimensions of the steel upper flange, perforated ribs, and hole spacing. Finally, a calculation formula and corresponding procedure are proposed for predicting the shear force of PBL connectors in the joint between the CSW and concrete top slab for composite bridges with CSWs.

Design of charge feedback high-frequency drive circuit and amplifier mechanism for piezoelectric actuator

For piezoelectric ceramic actuators working under continuous high-frequency drive signals, there are two issues that have to be considered. The first is the input drive circuit, which must meet the dynamic output power and output accuracy at the same time. The other is the output displacement of the amplifying mechanism. In this paper, a dual closed-loop piezoelectric ceramic high-frequency drive control circuit with overload protection is designed by combining the amplifier circuit with the push-pull output. By establishing displacement-charge model, on the basis of the original displacement feedback control, a series capacitor with leakage compensation method is used to realize the charge feedback control, and the output can be controlled at the same time to ensure the output accuracy, and the dynamic output power is considered. Based on energy conservation and elastic beam bending theory, and considering the influence of beam deformation at high frequency, an eightlever bridge amplifier mechanism is designed. Finally, the performance of the designed circuit and amplifier mechanism is verified by software simulation and experiment.

Prediction of Deflection of Shear-Critical RC Beams Using Compatibility-Aided Truss Model

This study proposes a method for predicting the deflection of shear-critical reinforced concrete (RC) beams. Shear deterioration of shear-critical RC beams occurs before flexural yielding. After shear deterioration occurs in the shear-critical RC beams, the deflection caused by shear is greater than the flexural deflection obtained from the elastic bending theory. To reasonably predict the deflection of shear-critical RC beams, it is necessary to evaluate deflections due to shear as well as flexure. In this study, the deflections produced by flexure and shear were calculated and superposed to evaluate the deflection of shear-critical RC beams. The method recommended by ACI 318-19 was employed to calculate the flexural deflection, and a compatibility-aided truss model able to calculate the shear stress and shear deformation at each load stage was used to consider the shear deflection. A comparison of the experimental and analytical results showed that the proposed analytical method can effectively predict the deflection of shear-critical RC beams.

THE EFFECT OF SUPPORT PLATE ON DRILLING-INDUCED DELAMINATION

Delamination is considered as a major problem in drilling of composite materials, which degrades the mechanical properties of these materials. The thrust force exerted by the drill is considered as the major cause of delamination; and one practical approach to reduce delamination is to use a back-up plate under the specimen. In this paper, the effect of exit support plate on delamination in twist drilling of glass fiber reinforced composites is studied. Firstly, two analytical models based on linear fracture mechanics and elastic bending theory of plates are described to find critical thrust forces at the beginning of crack growth for drilling with and without back-up plate. Secondly, two series of experiments are carried out on glass fiber reinforced composites to determine quantitatively the effect of drilling parameters on the amount of delamination. Experimental findings verify a large reduction in the amount of delaminated area when a back-up plate is placed under the specimen.

Form of circumferential weld-induced imperfections for tapered-wall cylindrical shell structures

Initial geometric imperfections have a great effect on the buckling strength of thin-walled cylindrical shells under axial compression, and the circumferential weld-induced imperfection is usually the most deleterious imperfection form. Two axisymmetric imperfection forms proposed by Rotter and Teng have widely been employed in the buckling analysis of cylindrical shells. However, the applicability of the two forms for tapered-wall cylinders needs further study, since they are derived from the elastic bending theory for long thin-walled cylinders with a constant wall thickness. This paper presents a modified form of circumferential imperfection for tapered-wall cylinders. Finite element analyses are carried out by employing the trapezoidal strain field approach to model the welding process, and the obtained circumferential depression shapes are used to evaluate the availability of the modified imperfection form. It is shown that the modified imperfection form is reasonable for any wall thickness ratio bet...

切向气流对激光加热金属板非熔化穿孔效应的影响

On the basis of elastic bending theory,the bending deflection expression by both quadrate and circinal facula irradiations is deduced for burn-through effect with no-melting of metal heated by a laser caused by tangential airflows.A rupture criterion for burn-through with no-melting is given out by the Mises theory.The study indicates that the material softened by laser heating is the primary mechanism for burn-through effect with no-melting.The maximal deflection of thin plate in the spot area is related to the airflow speed,spot diameter,plate thickness and the elasticity modulus(expression is U2a4/Eh3),the damage temperature is related to the airflow speed,spot diameter and the plate thickness(expression is(Ua/h)2),and the damage threshold under the circinal facula irradiated is higher than that under the quadrate facula.The numerical result indicates that for aluminum alloy shell,the damage threshold of laser energy can decrease much up to 40%-50% under 0.8 Ma tangential airflows,but it can decrease less(about 20%) for a stainless steel shell.The damage threshold decrease under airflows needs more attention.

Numerical Analysis and Optimization of Wedge Box of Diagonal Brace

Force transmission triangular box as the bracing’s bracket is widely applied in the deep foundation, but its performance was not studied in depth. In order to evaluate the working performance of force transmission triangular box as bracing’s bracket, the paper use the finite element software ANSYS to simulate and analyze its mechanical behavior. The bearing capacity, deformation and stress distribution of the components were discussed and compared with the result from elastic bending theory of small deflections of its end-plate deflection. The dangerous sections of member and the inner force distribution in the general work load status were obtained. And the stress concentration was improved. the results can provide reference for the design and construction.

Behavior of Lime Stabilized Gypseous Soil Beams Under static Loads

This work aims to study the stress-strain curves of soil samples subjected to tensile stress. The samples (50*50*300 mm) were prepared from lime stabilized gypseous soil using (3%) lime as stabilization percent. The samples were cured at (25,49 and 600C) for a period of (2,15,30,90 and 180) days. The results obtained from flexural tensile tests were analyzed using three methods of analysis. These methods are, the elastic bending theory, direct, and differential method. The elastic and the direct methods gave, generally similar results of the soil flexural tensile stress while the differential method gave lower values. Also the tensile stress-strain curves obtained by the elastic method were consistent, while the curves from direct and differential methods are in consistent, with the exception of the samples compacted at the dry side of the compaction curve.

Strengthening metallic cylindrical shells against elephant's foot buckling with FRP

Thin metal cylindrical shell structures such as silos and tanks are susceptible to an elastic–plastic instability failure at the base boundary known as elephant's foot buckling, due to its characteristic deformed shape. This form of buckling occurs under high internal pressure accompanied by axial compression in the shell structure. This is a common failure mode for tanks under earthquake loading. Another common situation is in a silo where the silo wall is subjected to both normal pressures from the stored granular solid and vertical compressive forces developed from the friction between the stored solid and the silo wall. This paper presents a novel method of strengthening cylindrical shells against elephant's foot buckling in which a small amount of fibre-reinforced polymer (FRP) composite, used at a critical location, can effectively eliminate the problem and increase the buckling strength. The strengthened shell is analysed using linear elastic bending theory in this preliminary study. Within the scope of this research, the strengthening effect is shown to be sensitive to the thickness, height and location of the FRP sheet. The issue of optimal FRP strengthening to allow the shell to attain pure membrane-state deformation is examined in detail as strengthening with too much and too little FRP are both undesirable. Both pinned-based and fixed-based shells are examined and their responses are compared.

Elastic Bending Theory of Composite Bridge with Corrugated Steel Web Considering Shear Deformation

The classical Euler-Bernoulli girder theory is not applicable due to shear deformation of corrugated steel web, elastic bending theory considering shear deformation is presented to analyze deflection and mechanical property. Differential equation is derived based on displacement field assumption, internal force equilibrium equations, deformation compatibility condition and relation of deformation and internal force, and solutions are obtained according to boundary and load condition. Simply supported I and box girder bridges with corrugated steel web are analyzed with elastic bending theory considering shear deformation, their predicted results are found in good agreement with those by 3D finite element analysis and test. A limit value of depth-span ratio is suggested for considering influence of shear deformation or not, the simplified formula of deflection in middle span is presented to guide deflection design. Corrugated web accounts for more than 80% of total shear force in the whole span under uniform load while one third apart from bearing under concentrated load in mid-span. The elastic bending theory considering shear deformation makes a reference for designing composite bridge with corrugated steel web.

Elastoplastic Analysis of a Miniature Circular Disk Bending Specimen

The miniature disk bending test is used to evaluate the mechanical behavior of irradiated materials and their properties (e.g., yield stress and strain hardening exponent) to determine mainly ductility loss in steel due to irradiation from the load-deflection behavior of the disk specimen. In the miniature disk bending machine the specimen is firmly held between the two horizontal jaws of punch, and an indentor with a spherical ball travels vertically. Analytical solutions for large amplitude plastic deformation become rather unwieldy. Hence, a finite element analysis has been carried out. The finite element model considers contact between the indentor and test specimen, friction between various pairs of surfaces, and elastic plastic behavior. This paper presents the load versus deflection results of a parametric study where the values of various parameters defining the material properties have been varied by ±10% around the base values. Some well-known analytical solutions to this problem have also been considered. It is seen that the deflection obtained by analytical elastic bending theory is significantly lower than that obtained by the elastoplastic finite element solution at relatively small values of load. The finite element solution has been compared with one experimental result and values are in reasonably good agreement. With these results it will be possible to determine the material properties from the experimentally obtained values of load and deflection.

A Simple Remedy for Elephant's Foot Buckling in Cylindrical Silos and Tanks

Metal silos and tanks are susceptible to an elastic-plastic instability failure at the base boundary condition which is known as “elephant's foot buckling”, due to its characteristic shape. This form of buckle occurs under high internal pressure accompanied by axial forces in the shell structure. Current international standards for both the static design and earthquake design include a provision to ensure that this failure mode is prevented. However, the only available remedy is currently to increase the wall thickness of the bottom course or strake. In this paper, an alternative method of strengthening against elephant's foot buckling is explored in which a light ring stiffener is used at a critical location. The strengthened shell is analysed using linear elastic bending theory in this preliminary study. Within the scope of this research, the strengthening effect is shown to be sensitive to the size and location of the ring stiffener. Rings that are too small and rings that are too large both cause the strengths to be lower than that when the optimal ring size is used. This is, therefore, an interesting example of structural behaviour in which the provision of a larger amount of material than the optimum leads to reduced strength.

A new orthogonality relationship for orthotropic thin plate theory and its variational principle

The thought how dual vectors are constructed in a new orthogonality relationship for theory of elasticity is generalized into orthotropic thin plate bending problems by using the analogy theory between plane elasticity problems and plate bending problems. Dual differential equations are directly obtained by using a mixed variables method. A dual differential matrix to be derived possesses a peculiarity of which principal diagonal sub-matrixes are zero matrixes. Two independently and symmetrically orthogonality sub-relatioships are discovered. By using the integral form for elastic bending theory of orthotropic thin plate the orthogonality relationship is demonstrated. By selecting felicitous dual vectors a new orthogonality relationship for theory of elasticity can be generalized into elastic bending theory of orthotropic thin plate. By using the integral form a variational principle which is relative to differential form and a whole function expression are proposed.

Fatigue of glass fiber reinforced injection molded plastics. II: Tensile versus flexural loading

AbstractA previous paper reported fatigue data for several glass fiber reinforced thermoplastic materials by measuring their S‐N, stress versus number of cycles to fail, behavior. It was demonstrated that both fiber orientation and loading mode, tensile versus flexural, strongly influence the resultant S‐N data. The orientation effects are considered real, reflecting the local fiber orientation distributions in the samples, which are determined by geometry, processing and material variables. However, the higher fatigue lives observed in flexural loading are considered an artifact. Specifically for this class of materials, it is concluded that the use of linear elastic beam bending theory equations to calculate bending stresses are inappropriate. It is shown that a plasticity‐based correction factor makes the flexural S‐N data equivalent to the tensile results. In fact this correction applies equally well to monotonic loading, not just fatigue. Although it is concluded that tensile loading is preferred, some cases where flexural loading may be advantageous are indicated. Polym. Compos. 25:569–576, 2004. © 2004 Society of Plastics Engineers.

ANALYSIS OF CORRUGATED STEEL WEB GIRDERS BY AN EFFICIENT BEAM BENDING THEORY

An elastic beam bending theory for analysis of prestressed concrete girders with corrugated steel web is derived by the application of the variational principle. The theory is a shear deformable beam theory which is based on three displacement fields and is similar to the classical Timoshenko beam theory. A two-node linear finite element with full and reduced integration of the theory is provided. It is then used to analyze simply supported and continuous I- and box-girders. Their predicted results are found in good agreement with those by the 3D finite element analysis. A simplified theory which is similar to the proposed theory by Kato et al. (2002) is also discussed and included in appendix.

Experiments and theory in strain gradient elasticity

Conventional strain-based mechanics theory does not account for contributions from strain gradients. Failure to include strain gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scale structures. In this paper, a new set of higher-order metrics is developed to characterize strain gradient behaviors. This set enables the application of the higher-order equilibrium conditions to strain gradient elasticity theory and reduces the number of independent elastic length scale parameters from five to three. On the basis of this new strain gradient theory, a strain gradient elastic bending theory for plane-strain beams is developed. Solutions for cantilever bending with a moment and line force applied at the free end are constructed based on the new higher-order bending theory. In classical bending theory, the normalized bending rigidity is independent of the length and thickness of the beam. In the solutions developed from the higher-order bending theory, the normalized higher-order bending rigidity has a new dependence on the thickness of the beam and on a higher-order bending parameter, b h. To determine the significance of the size dependence, we fabricated micron-sized beams and conducted bending tests using a nanoindenter. We found that the normalized beam rigidity exhibited an inverse squared dependence on the beam's thickness as predicted by the strain gradient elastic bending theory, and that the higher-order bending parameter, b h, is on the micron-scale. Potential errors from the experiments, model and fabrication were estimated and determined to be small relative to the observed increase in beam's bending rigidity. The present results indicate that the elastic strain gradient effect is significant in elastic deformation of small-scale structures.

The shape of circumferential weld-induced imperfections in thin-walled steel silos and tanks

The strength of thin-walled cylindrical shell structures is highly dependent on the nature and magnitude of imperfections. Most importantly, circumferential imperfections have been reported to have an especially detrimental effect on the buckling resistance of these shells under axial load. Due to the manufacturing techniques commonly used during the erection of steel silos and tanks, specific types of imperfections are introduced into these structures, among them circumferential weld-induced imperfections between strakes of steel plates. The shape of such a localised circumferential imperfection has been shown to have a great influence on the degree of strength loss of thin-walled cylindrical shell structures. The results of a survey of imperfections in an existing silo at a location in Port Kembla, Australia in combination with linear elastic shell bending theory was used to develop and calibrate a shape function which accurately describes the geometric features of circumferential weld imperfections. The proposed shape function is the first function to combine shell theory with actual field imperfection measurements. It is a continuous function and incorporates all the necessary features to represent the geometry of a circumferential weld-induced imperfection. It was found that after filtering out the effects of overall imperfections three parameters governed the shape of the surveyed imperfections: the depth, the wavelength and the roundness.

Lateral variations of effective elastic thickness of the subducting Philippine Sea plate along the Nankai trough

We investigated lateral variations of effective elastic thickness of the subducting Philippine Sea plate along the Nankai trough. For this purpose, we applied two-dimensional thin elastic plate bending theory to several profiles almost perpendicular to the trough axis, correcting the effect of thick marine sediments in the Shikoku Basin. The 15 topographic profiles were selected from 61 profiles and were fit to respective theoretical deflection curves by minimization of the L1 norm. Classifying the Shikoku Basin into three regions, namely, the western, the middle, and the eastern regions, we obtained the results that the effective elastic plate thickness tends to decrease gradually from the east of the Ryukyu-Palau ridge to the Kinan seamount chain. This is consistent with heat flow data, seafloor age, formation process of the Shikoku Basin, length of the slab subducted from the Nankai trough, and spatial distribution of subcrustal earthquakes associated with subduction of the Philippine Sea plate.

Equivalent Boundary Integral Equations with indirect unknowns for thin elastic plate bending theory

Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect unknowns are discussed thoroughly and it is shown that all previous results are not EBIE.

Influence of transbilayer area asymmetry on the morphology of large unilamellar vesicles

The morphological consequences of differences in the monolayer surface areas of large unilamellar vesicles (LUVs) have been examined employing cryoelectron microscopy techniques. Surface area was varied by inducing net transbilayer transport of dioleoylphosphatidylglycerol (DOPG) in dioleoylphosphatidylcholine (DOPC):DOPG (9:1, mol:mol) LUVs in response to transmembrane pH gradients. It is shown that when DOPG is transported from the inner to the outer monolayer, initially invaginated LUVs are transformed to long narrow tubular structures, or spherical structures with one or more protrusions. Tubular structures are also seen in response to outward DOPG transport in DOPC:DOPG:Chol (6:1:3, mol:mol:mol) LUV systems, and when lyso-PC is allowed to partition into the exterior monolayer of DOPC:DOPG (9:1, mol:mol) LUVs in the absence of DOPG transport. Conversely, when the inner monolayer area is expanded by the transport of DOPG from the outer monolayer to the inner monolayer of non-invaginated LUVs, a reversion to invaginated structures is observed. The morphological changes are well described by an elastic bending theory of the bilayer. Identification of the difference in relaxed monolayer areas and of the volume-to-area ratio of the LUVs as the shape-determining factors allows a quantitative classification of the observed morphologies. The morphology seen in LUVs supports the possibility that factors leading to differences in monolayer surface areas could play important roles in intracellular membrane transport processes.