Interconnected microstructure and flexural behavior of Ti_(2)C-Ti composites with superior Young’s modulus

To enhance the Young’s modulus(E)and strength of titanium alloys,we designed titanium matrix composites with intercon-nected microstructure based on the Hashin-Shtrikman theory.According to the results,the in-situ reaction yielded an interconnected microstructure composed of Ti_(2)C particles when the Ti_(2)C content reached 50vol%.With widths of 10 and 230 nm,the intraparticle Ti lamellae in the prepared composite exhibited a bimodal size distribution due to precipitation and the unreacted Ti phase within the grown Ti_(2)C particles.The composites with interconnected microstructure attained superior properties,including E of 174.3 GPa and ultimate flexural strength of 1014 GPa.Compared with that of pure Ti,the E of the composite was increased by 55% due to the high Ti_(2)C content and interconnected microstructure.The outstanding strength resulted from the strong interfacial bonding,load-bearing capacity of interconnected Ti_(2)C particles,and bimodal intraparticle Ti lamellae,which minimized the average crack driving force.Interrupted flexural tests revealed preferential crack initiation along the{001}cleavage plane and grain boundary of Ti_(2)C in the region with the highest tensile stress.In addition,the propagation can be efficiently inhibited by interparticle Ti grains,which prevented the brittle fracture of the composites.

Seismic performance evaluation of hybrid coupled shear wall system with shear and flexural fuse-type steel coupling beams

Replaceable flexural and shear fuse-type coupling beams are used in hybrid coupled shear wall(HCSW)systems,enabling concrete buildings to be promptly recovered after severe earthquakes.This study aimed to analytically evaluate the seismic behavior of flexural and shear fuse beams situated in short-,medium-and high-rise RC buildings that have HCSWs.Three building groups hypothetically located in a high seismic hazard zone were studied.A series of 2D nonlinear time history analyses was accomplished in OpenSees,using the ground motion records scaled at the design basis earthquake level.It was found that the effectiveness of fuses in HCSWs depends on various factors such as size and scale of the building,allowable rotation value,inter-story drift ratio,residual drift quantity,energy dissipation value of the fuses,etc.The results show that shear fuses better meet the requirements of rotations and drifts.In contrast,flexural fuses dissipate more energy,but their sectional stiffness should increase to meet other requirements.It was concluded that adoption of proper fuses depends on the overall scale of the building and on how associated factors are considered.

AHermitian C^(2) Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates

This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.

Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.

Surface Processes Driving Intracontinental Basin Subsidence in the Context of India–Eurasia Collision:Evidence from Flexural Subsidence Modeling of the Cenozoic Southern Tarim Basin along the West Kunlun Foreland,NW Tibetan Plateau

The India–Eurasia collision has produced a number of Cenozoic deep intracontinental basins,which bear important information for revealing the far-afield responses to the remote collision.Despite their significance,their subsiding mechanism remains the subject of debate,with end-member models attributing it to either orogenic or sedimentary load.In this study,we conduct flexural subsidence modeling with a two-dimensional finite elastic plate model on the Hotan-Mazatagh section along the southern Tarim Basin,which defines a key region in the foreland of the West Kunlun Orogen,along the NW margin of the Tibetan Plateau.The modeling results indicate that the orogenic load of West Kunlun triggers the southern Tarim Basin to subside by up to less than ~6 km,with its impact weakening towards the basin interiors until ~230 km north from the Karakax fault.The sedimentary load,consisting of Cenozoic strata,forces the basin to subside by ~2 to~7 km.In combination with the retreat of the proto-Paratethys Sea and the paleogeographic reorganization of the Tarim Basin,we propose that surface processes,in particular a shift from an exorheic to an endorheic drainage system associated with the consequent thick sedimentary load,played a decisive role in forming deep intracontinental basins in the context of the India-Eurasia collision.

Factorial Experimental Design to Study the Effects of Layers and Fiber Content on Concrete Flexural Behavior

Experimentation has come a long in helping researchers achieve breakthroughs in their different scientific areas and engineering happens to be one of those areas with the most impact from experimental advancement. The need for valid experimental results free from biases and confounding conclusions has prompted the development of new experimental techniques that takes consideration of all applicable factor and combinations in providing answers on a research topic, and the Factorial Experimental design credited to Sir Ronald Fisher is one technique yielding highly valid results. This paper uses the factorial design of experiments to research the flexural impact of polyvinyl acetate fiber and layered concrete in construction. The experiment considered two levels of fiber contents and two levels of layers, and prepared samples with all combinations of the variable factors. The samples were tested after 7 days from casting for flexural strength and an advance statistical analysis was performed on the flexural responses of the samples using R-program. The results from the analyses revealed the significance of the variables to the flexural strength of the samples, as well as their interactions. The experiment concluded that based on the number of layers and fiber content used for the experiment, casting concrete in layers does have a significant negative effect on the flexural strength of concrete, and the failure pattern of concrete members under flexural load in evidently influenced by the material composition of the concrete, and that it can be evidently influenced by casting the concrete in layers.

Experimental and numerical study on flexural behaviors of steel reinforced engineered cementitious composite beams

To investigate the flexural behaviors of steel reinforced engineered cementitious composite （ECC） beams, the behaviors of the steel reinforced ECC beam and the conventional steel reinforced concrete beam subjected to flexural load are experimentally compared. The experimental results show that the flexural strength and ductility of the steel reinforced ECC beam are 24.8% and 187.67% times larger than those of the steel reinforced concrete beam, and the substitution of concrete with ECC can significantly delay the propagation of cracks. Additionally, a simplified constitutive model of the ECC material is used to simulate the flexural behaviors of beams by the finite element analysis （FEA）. The results show a good agreement between the simulation and test results. The crack width of the steel reinforced ECC beam can be limited to 0.4 mm under the service load conditions. The application of ductile ECC can significantly increase the flexural performance in terms of flexural strength, deformation capacity and ductility of the beams.

Experimental study on ultimate flexural capacity of steel encased concrete composite beams

Based on the experimental study and inelastic theory, the ultimate flexuralcapacity of steel encased concrete composite beams are derived. The difference between steel encasedconcrete composite beams with full shear connection and beams with partial shear connection,together with the relationship between the inelastic neutral axis of steel parts and concrete parts,are considered in the formulae. The calculation results of the eight specimens with full shearconnection and the three specimens with partial shear connection are in good agreement with theexperimental data, which validates the effectiveness and efficiency of the proposed calculationmethods. Furthermore, the nonlinear finite element analysis of the ultimate flexural capacity of thesteel encased concrete composite beams is performed. Nonlinear material properties and nonlinearcontact properties are considered in the finite element analysis. The finite element analyticalresults also correlate well with the experimental data.

Flexural destructive process of unidirectional carbon/carbon composites reinforced with in situ grown carbon nanofibers

Unidirectional carbon/carbon（C/C） composites modified with in situ grown carbon nanofibers（CNFs） were prepared by catalysis chemical vapor deposition. The effect of in situ grown CNFs on the flexural properties of the C/C composites was investigated by detailed analyses of destructive process. The results show that there is a sharp increase in the flexural load-displacement curve in the axial direction of the CNF-C/C composites, followed by a serrated yielding phenomenon similar to the plastic materials. The failure mode of the C/C composites modified with in situ grown CNFs is changed from the pull-out of single fiber to the breaking of fiber bundles. The existence of interfacial layer composed by middle-textured pyrocarbon, CNFs and high-textured pyrocarbon can block the crack propagation and change the propagation direction of the main crack, which leads to the higher flexural strength and modulus of C/C composites.

Ultimate flexural strength of normal section of FRP-confined RC circular columns

Numerical analysis is carried out to study the sectional properties of the fiber-reinforced polymer（FRP）-confined reinforced concrete（RC）circular columns. The axial load ratio, the FRP confinement ratio and the longitudinal reinforcement characteristic value are the three main parameters that can influence the neutral axis depth when concrete compression strain reaches an ultimate value. The formula for computing the central angle θ, corresponding to the compression zone, is established according to the data regression of the numerical analysis results. The numerical analysis results demonstrate that the concrete stress enhancement from transverse confinement and strain hardening of the longitudinal reinforcement can cause a much greater flexural strength than that defined by the design code. Based on the analytical studies and the test results of 36 large scale columns, the formula to calculate the flexural strength when columns fail under seismic loading is proposed, and the calculated results agree well with the test results. Finally, parametric studies are conducted on a typical column with different axial load ratios, longitudinal reinforcement characteristic value and FRP confinement ratios. Analysis of the results shows that the calculated flexural strength can be increased by 50% compared to that of unconfined columns defined by the code.

Flexural behaviors of FRP strengthened corroded RC beams

The flexural behavior of eight FRP （ fiber reinforced polymer） strengthened RC （reinforced concrete） beams with different steel corrosion rates are numerically studied by Ansys finite element software. The influences of the corrosion rate on crack pattern, failure mechanism, ultimate strength, ductility and deformation capacity are also analyzed. Modeling results show that the beams with low corrosion rates fail by the crushing of the concrete in the compression zone. For the beams with medium corrosion rates, the bond slip between the concrete and the longitudinal reinforcement occurs after steel yielding, and the beams finally fail by the debonding of the FRP plates. For the beams with high corrosion rates, the bond slip occurs before steel yielding, and the beams finally fail by the crushing of the concrete in the compression zone. The higher the corrosion rates of the longitudinal reinforcement, the more the carrying capacity of FRP strengthened RC beams reduces. The carrying capacity of RCB-1 （the corrosion rate is 0） is 115 kN, and the carrying capacity of RCB-7 （the corrosion rate is 20% ） is 42 kN. The deformation capacity of FRP strengthened corroded RC beams is higher than that of FRP strengthened uucorroded RC beams. The ultimate deflection of RCB-1 and RCB-7 are 20 mm and 35 nun, respectively, and the ultimate deflection of RCB-5 （the corrosion rate is 10% ） reaches 60 ilUn.

Fracture mechanism of 2D-C/C composites with pure smooth laminar pyrocarbon matrix under flexural loading

Using natural gas as carbon source, 2D needle felt as preform, 2D-C/C composites were prepared by thermal gradient chemical vapor infiltration. Their microstructures were observed under polarized light microscope （PLM） and scanning electron microscope （SEM）, and the flexural behaviors before and after heat-treatment were studied with a universal mechanical testing machine. The fracture mechanism of the composites was discussed in detail. The results show that, carbon matrix exhibits pure smooth laminar （SL） characteristic including numerous wrinkled layered structures and some inter-laminar micro-cracks. With the decreasing density, the strength of the composites decreases and the toughness increases slightly; after 2500 °C heat-treatment, the inter-laminar micro-cracks in matrix increase, the strength decreases, and the toughness obviously increases. The fracture mode of the composites changes from brittle to pseudo-plastic characteristic due to more crack deflections in SL matrix.

Flexural behaviors of steel reinforced ECC/concrete composite beams

An engineered cementitious composite （ECC） is introduced to partially substitute concrete in the tension zone of a reinforced concrete beam to form an ECC/reinforced concrete （RC） composite beam, which can increase the ductility and crack resisting ability of the beam. Based on the assumption of the plane remaining plane and the simplified constitutive models of materials, the stress and strain distributions along the depth of the composite beam in different loading stages are comprehensively investigated to obtain calculation methods of the load-carrying capacities for different stages. Also, a simplified formula for the ultimate load carrying capacity is proposed according to the Chinese code for the design of concrete structures. The relationship between the moment and curvature for the composite beam is also proposed together with a simplified calculation method for ductility of the ECC/RC composite beam. Finally, the calculation method is demonstrated with the test results of a composite beam. Comparison results show that the calculation results have good consistency with the test results, proving that the proposed calculation methods are reliable with a certain theoretical significance and reference value.

SCATTERING OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN MINDLIN'S THICK PLATES WITH A CUTOUT

Using the complex variable method and conformal mapping,scat- tering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout have been studied.The general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique,the dynamic stress problem can be reduced into the solution of a set of infinite algebraic equations.As examples, numerical results for the dynamic stress concentration factor in Mindlin's plates with a circular,elliptic cutout are graphically presented in sequence.

Design of Compliant Straight-line Mechanisms Using Flexural Joints

Straight-line compliant mechanisms are important building blocks to design a linear-motion stage, which is very useful in precision applications. However, only a few configurations of straight-line compliant mechanisms are applicable. To construct more kinds of them, an approach to design large-displacement straight-line flexural mechanisms with rotational flexural joints is proposed, which is based on a viewpoint that the straight-line motion is regarded as a compromise of rigid and compliant parasitic motion of a rotational flexural joint. An analytical design method based on the Taylor series expansion is proposed to quickly obtain an approximate solution. To illustrate and verify the proposed method, two kinds of flexural joints, cross-axis hinge and leaf-type isosceles-trapezoidal flexural（LITF） pivot are used to reconstruct straight-line flexural mechanisms. Their performances are obtained by analytic and FEA method respectively. The comparisons of the results show the accuracy of the approach. Both examples show that the proposed approach can convert a large-deflection flexural joint into approximate straight-line mechanism with a high linearity that is higher than 5 000 within 5 man displacement. This can lead to a new way to design, analyze or optimize straight-line flexure mechanisms.

Rapid repair techniques for severely earthquake-damaged circular bridge piers with flexural failure mode

In this study, three rapid repair techniques are proposed to retrofit circular bridge piers that are severely damaged by the flexural failure mode in major earthquakes. The quasi-static tests on three 1：2.5 scaled circular pier specimens are conducted to evaluate the efficiency of the proposed repair techniques. For the purpose of rapid repair, the repair procedure for all the specimens is conducted within four days, and the behavior of the repaired specimens is evaluated and compared with the original ones. A finite element model is developed to predict the cyclic behavior of the repaired specimens and the numerical results are compared with the test data. It is found that all the repaired specimens exhibit similar or larger lateral strength and deformation capacity than the original ones. The initial lateral stiffness of all the repaired specimens is lower than that of the original ones, while they show a higher lateral stiffness at the later stage of the test. No noticeable difference is observed for the energy dissipation capacity between the original and repaired pier specimens. It is suggested that the repair technique using the early-strength concrete jacket confined by carbon fiber reinforced polymer （CFRP） sheets can be an optimal method for the rapid repair of severely earthquake-damaged circular bridge piers with flexural failure mode.

Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures

The complete flexural vibration band gaps are studied in the thin plates with two-dimensional binary locally resonant structures, i.e. the composite plate consisting of soft rubber cylindrical inclusions periodically placed in a host material. Numerical simulations show that the low-frequency gaps of flexural wave exist in the thin plates. The width of the first gap decreases monotonically as the matrix density increases, The frequency response of the finite periodic thin plates is simulated by the finite element method, which provides attenuations of over 20dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.

Flexural wave band-gaps in phononic metamaterial beam with hybrid shunting circuits

Periodic arrays of hybrid-shunted piezoelectric patches are used to control the band-gaps of phononic metamaterial beams. Passive resistive-inductive （RL） shunting circuits can produce a narrow resonant band-gap （RG）, and active negative capacitive （NC） shunting circuits can broaden the Bragg band-gaps （BGs）. In this article, active NC shunting circuits and passive resonant RL shunting circuits are connected to the same piezoelectric patches in parallel, which are usually called hybrid shunting circuits, to control the location and the extent of the band-gaps. A super-wide coupled band-gap is generated when the coupling between RG and the BG occurs. The attenuation constant of the infinite periodic structure is predicted by the transfer matrix method, which is compared with the vibration transmittance of a finite periodic structure calculated by the finite element method. Numerical results show that the hybrid-shunting circuits can make the band-gaps wider by appropriately selecting the inductances, negative capacitances, and resistances.

Research on Flexural Behavior of Coral Aggregate Reinforced Concrete Beams

Through the flexural behavior test of coral aggregate reinforced concrete beams(CARCB) and ordinary Portland reinforced concrete beams(OPRCB), and based on the parameters of concrete types, concrete strength grades and reinforcement ratios, the crack development, failure mode, midspan deflection and flexural capacity were studied, the relationships of bending moment-midspan deflection, load-longitudinal tensile reinforcement strain, load-maximum crack width were established, and a calculation model for the flexural capacity of CARCB was suggested. The results showed that with the increase in the reinforcement ratio and concrete strength grade, the crack bending moment(Mcr)and ultimate bending moment(Mu) of CARCB gradually increased. The characteristics of CARCB and OPRCB are basically the same. Furthermore, through increasing the concrete strength grade and reinforcement ratio, Mcr/Mu could be increased to delay the cracking of CARCB. As the load increased, crack width(w) would also increase. At the beginning of the loading, w increased slowly. And then it increased rapidly when the load reached to the ultimate load, which then led to beam failure. Meanwhile, with a comprehensive consideration of the effects of steel corrosion on the loss of steel section and the decrease of steel yield strength, a more reasonable calculation model for the flexural capacity of CARCB was proposed.

NONLINEAR FLEXURAL WAVES IN LARGE-DEFLECTION BEAMS

The equation of motion for a large-deflection beam in the Lagrangian description are derived using the coupling of flexural deformation and midplane stretching as a key source of nonlinearity and taking into account the transverse, axial and rotary inertia effects. Assuming a traveling wave solution, the nonlinear partial differential equations are then transformed into ordinary differential equations. Qualitative analysis indicates that the system can have either a homoclinic orbit or a heteroclinic orbit, depending on whether the rotary inertia effect is taken into account. Furthermore, exact periodic solutions of the nonlinear wave equations are obtained by means of the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function m→1 in the degenerate case, either a solitary wave solution or a shock wave solution can be obtained.