Structural Crack Identification Based on the Variational Mode Decomposition北大核心CSCD

In order to enrich the bridge damage detection method and further improve the accuracy of bridge damage identification, a detection method for simply supported beams with cracks under dynamic loads was proposed not based on the complete finite element model. Under the premise of not blocking traffic, the method only needs to analyze and deal with the acceleration responses of the simply supported beam span, which reduces the mounting, dismounting and maintenance of sensors in practical engineering. At the same time, based on the model, an analytical formula of the acceleration at the midspan of the simply supported cracked beam was derived. Based on the theoretical derivation, the instantaneous energy and the mean energy difference were constructed through the variational mode decomposition and the Hilbert transform, and these 2 crack identification indexes were used to effectively identify small cracks with a crack depth ratio of only 5%. Then the influences of different wheel loads, environmental noises and damage degrees on detection results were studied. The results show that: ① the instantaneous frequency has a better recognition effect for crack positions; ② the mean energy difference is sensitive to crack depth ratio δ and the wheel load magnitude; ③ this method has strong noise robustness. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Interlaminar Crack Propagation Analysis of ENF Specimens Based on the Cohesive Zone Model北大核心CSCD

Based on the classical laminated plate theory and the cohesive zone model, a theoretical model for general delamination cracked laminates was established for crack propagation of pure mode Ⅱ ENF specimens. Compared with the conventional beam theory, the proposed model fully considered the softening process of the cohesive zone and introduced the nonlinear behavior of ENF specimens before failure. The predicted failure load is smaller than that under the beam theory and closer to the experimental data in literatures. Compared with the beam theory with only fracture toughness considered, the proposed model can simultaneously analyze the influences of the interface strength, the fracture toughness and the initial interface stiffness on the load-displacement curves in ENF tests. The results show that, the interface strength mainly affects the mechanical behavior of specimens before failure, but has no influence on crack propagation. The fracture toughness is the main parameter affecting crack propagation, and the initial interface stiffness only affects the linear elastic loading stage. The cohesive zone length increases with the fracture toughness and decreases with the interface strength. The effect of the interface strength on the cohesive zone length is more obvious than that of the fracture toughness. When the adhesive zone tip reaches the half length of the specimen, the adhesive zone length will decrease to a certain extent. Copyright ©2022 Applied Mathematics and Mechanics. All rights reserved.     

Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip北大核心CSCD

The solution of an infinite plane containing a macro crack and a cluster of micro cracks under uniaxial tensile load was presented based on Muskhelishvili’s complex function method and the stepwise recursive method. The stress field and stress intensity factor K were obtained. Combined with the damage mechanics, damage parameter D of the macro-crack tip and the micro-crack tip under uniaxial tension was redefined, and the influence of different damage zone forms on the damage of the crack tip was analyzed. The results show that, both the chain-distribution and the reverse-chain-distribution micro cracks have an amplifying effect on the macro crack growth, and the damage parameter increases with the decrease of the inclination angle of the micro crack and the reduction of the distance between the macro crack and the micro cracks. For a relatively small inclination angle of the micro crack, the damage parameters of the macro crack and the micro crack heightens, and the damage parameter of the macro crack increases with the micro-crack length. For evenly distributed micro cracks in the continuous damage zone, the micro cracks have an amplifying effect on the macro-crack growth, and the damage parameter of the macro crack increases with the micro-crack number. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Recent progresses in studies on wave-current loads on foundation structure with piles and slab?

The foundation structure with piles and slab is widely used in o?shore wind farm construction in shallow water. Experimental studies on the hydrodynamic loads acting on the piles and slab under irregular waves and currents are summarized with discussion on the e?ects of pile grouping on the wave forces and wave impact loads on the slab locating near the free surface. By applying the theoretical solution of the wave di?racted by the slab and using the Morison equation to evaluate the wave force on the piles, the e?ects of the slab on the wave forces acting on the piles are analyzed. Based on the Reynolds-averaged Navier-Stokes (RANS) equations and the volume of ?uid (VOF) method, a numerical wave basin is developed to simulate the wave-structure interaction. The computed maximum wave force on the foundation structure with piles and slab agrees well with the measured data. The violent deformation, breaking, and run-up of the wave around the structure are presented and discussed. Further work on the turbulent ?ow structures and large deformation of the free surface due to interaction of the waves and foundation structures of o?shore wind farms needs more e?cient approaches for evaluating hydrodynamic loads under the e?ects of nonlinear waves and currents.     

Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method北大核心CSCD

Based on the homotopy analysis method, the nonlinear vibration of porous functionally graded material (FGM) conveying pipes under generalized boundary conditions was studied. Based on the power-law distribution of the FGM and the Voigt model, the physical properties of the porous pipe material were described. Under the Euler-Bernoulli beam theory and the von Kármán nonlinear theory, and by means of Hamilton’s variational principle, the dynamic control equations and generalized boundary conditions for porous FGM conveying pipes were established. The homotopy analysis method was used to solve the nonlinear vibration characteristics of the porous FGM conveying pipe under generalized boundary conditions. The numerical results show that, the translation spring has little effect on the critical velocity of instability, while the rotation spring increases the critical velocity of instability, making the system more stable; in the nonlinear system, the viscoelastic coefficient does not change the critical velocity; the pipe length, the power-law exponent and the porosity all influence the nonlinear free vibration of the porous FGM conveying pipe. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

A Spatial Geometric Nonlinearity Spline Beam Element With Nodal Parameters Containing Strains北大核心CSCD

Many slender rods in engineering can be modeled as Euler-Bernoulli beams. For the analysis of their dynamic behaviors, it is necessary to establish the dynamic models for the flexible multi-body systems. Geometric nonlinear elements with absolute nodal coordinates help solve a large number of dynamic problems of flexible beams, but they still face such problems as shear locking, nodal stress discontinuity and low computation efficiency. Based on the theory of large deformation beams’ virtual power equations, the functional formulas between displacements and rotation angles at the nodes were established, which can satisfy the deformation coupling relationships. The generalized strains to describe geometric nonlinear effects in this case were derived. Some parameters of boundary nodes were replaced by axial strains and sectional curvatures to obtain a more accurate and concise constraint method for applying external forces. To improve the numerical efficiency and stability of the system’s motion equations, a model-smoothing method was used to filter high frequencies out of the model. The numerical examples verify the rationality and effectiveness of the proposed element. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Mesoscopic Numerical Study on Flow Boiling Heat Transfer Performance in Channels With Multiple Rectangular Heaters北大核心CSCD

The flow boiling phenomenon in a channel with multiple rectangular heaters under a constant wall temperature was numerically studied with the lattice Boltzmann method. The effects of spacings between heaters, heater lengths and heater surface wettabilities on the bubble morphology, the bubble area and the heat flux on the heater surface, were studied. The results show that, the bubble growth rate increases with the spacing between heaters. The larger the bubble area is, the earlier the nucleated bubbles will leave the heater surface. The corresponding boiling heat transfer performance increases by 12% with the spacing between heaters growing from 250 lattices to 1 000 lattices. On the other hand, the longer the heater length is, the earlier the bubble will nucleate and leave the heater surface, and the better the boiling heat transfer performance will be. The boiling heat transfer performance increases by 13% with the heater length rising from 16 lattices to 22 lattices. In addition, the bubble nucleates later on the hydrophilic surface than on the hydrophobic surface. Compared with the hydrophilic surface, the hydrophobic surface retains residual bubbles after the leaving of bubbles from the heater. The average heat flux and the bubble area of the hydrophilic surface are less than those of the hydrophobic surface. With the contact angle changing from 77° to 120°, the heat transfer performance increases by 26%. Finally, the orthogonal test results indicate that, the wettability of the heat exchanger surface has the greatest influence on the flow boiling heat transfer performance, while the heater length has the least influence. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Application of bamboo laminates in large-scale wind turbine blade design?

From the viewpoint of material and structure in the design of bamboo blades of large-scale wind turbine, a series of mechanical property tests of bamboo laminates as the major enhancement materials for blades are presented. The basic mechanical characteristics needed in the design of bamboo blades are brie?y introduced. Based on these data, the aerodynamic-structural integrated design of a 1.5 MW wind turbine bamboo blade relying on a conventional platform of upwind, variable speed, variable pitch, and doubly-fed generator is carried out. The process of the structural layer design of bamboo blades is documented in detail. The structural strength and fatigue life of the designed wind turbine blades are certified. The technical issues raised from the design are discussed. Key problems and direction of the future study are also summarized.     

ON GENERALIZED BUFFON NEEDLE PROBLEM FOR LATTICES

Two new concepts, the generalized support function and restricted chord function, both referring to a convex set, were introduced in [1]. General formulae to yield the kinematic measure of a segment of fixed length in a convex set were established based on these concepts. In this article , using the partial intersection method, we consider the generalized Buffon problem for three kinds of lattices. We determine the probability of intersection of a body test needle of length l, l < a.     

Multi-Scale Prediction of Thermal and Mechanical Properties of C/SiC Braided Composites北大核心CSCD

C/ SiC composites have been widely used in aerospace, national defense, and chemical industries due to their excellent mechanical and thermal properties. Accurate knowledge about the mechanical/ thermal properties of C/ SiC composites is very important for their efficient application in related fields. Based on the representative volume element (RVE) and periodic boundary conditions, a micro/ meso single-cell model for C/ SiC composites was established in view of the non-uniform and multi-scale characteristics of fiber bundles, such as the volume fraction, the interweaving mode, and the weaving dimension. The finite element software ABAQUS was used to predict the micro-scale thermal and mechanical properties of the fiber bundle, and the fiber bundle properties were introduced into the mesoscopic model to analyze and obtain the macroscopic thermal and mechanical properties of the composite. Based on this multi-scale correlation analysis method, the thermal conductivity and thermal expansion coefficient of fiber bundles and C/ SiC composites were further studied at the operating temperatures ranging from 27~1 227 ℃. The study has certain guiding significance for the application of C/ SiC composites in engineering. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Bond-slip behavior of CFRP plate-concrete interface

The paper deals with evaluation of the bond performance between a CFRP plate and concrete with respect to various compressive strengths of concrete and bond lengths of the CFRP plate as parameters. To consider stress conditions in the tensile zone of reinforced concrete (RC) structures, double-lap axial tension tests were conducted for eight specimens with CFRP plates bonded to concrete prisms. In addition, a simple linear bond-slip model for the CFRP plate/concrete joints, developed from the bond tests, was used. To verify the model proposed, a total of seven RC beams were strengthened with CFRP plates and tested in flexure employing various bond lengths, strengthening methods, and numbers of CFRP plates. A nonlinear finite-element analysis, with the bond–slip model incorporated in the DIANA program, was performed for the strengthened RC beams. Also, the results of flexural test and analytical predictions are found to be in close agreement in terms of yield and ultimate loads and ductility.     

Bond of FRP Reinforcement in Concrete - a Challenge

The bond of ordinary steel reinforcement in concrete depends on many factors, such as the pullout resistance, the geometry of a concrete member, the placement of a bar in the member cross section, the cover splitting, the confinement caused by concrete and the surrounding reinforcement, the order of bond-crack appearance, and the bond-stress distribution along the bond length. The bond of FRP reinforcement depends on even a greater number of factors. Moreover, the types of FRP bars are numerous. Their surface is weaker than that of steel bars and may fracture by bond forces. The surface of FRP bars is softer and does not create as high local stress concentrations in bond contact points to concrete as the harder steel bars do. This fact often delays the appearance of cover splitting cracks along the bars. However, the load necessary for developing the crack pattern of ultimate splitting failure in concrete is then very dependent on whether the bar surface is glossy or rough. The FRP reinforcement can also be used for external shear and/or flexural strengthening of existing members. For this application, FRP bars are placed in grooves cut on the surface of the member to be strengthened and are fixed there with a cement mortar or epoxy paste. In such an application, the performance of bond between the FRP rod and the mortar or resin and then between the mortar or resin and concrete is critical for the effectiveness of the technique. The presence of two interfaces increases the number of parameters needed to characterize the global joint behavior and introduces new possible failure modes. The fundament for the bond resistance estimation should be an accepted bond philosophy linked to appropriate models. A system of bond tests should provide necessary coefficients for the models.     

Análise da confiabilidade de estruturas de concreto armado com uma metodologia para inclusão de efeitos estocásticos de propriedades dos materiais

In this paper, special emphasis is given to the inclusion of uncertainties in the evaluation of structural behaviour aiming at a better representation of the system characteristics and the quantification of the importance of these uncertainties in the project. It deals with the structural reliability analysis problem accounting the effect of spatial variability of material properties. To this end it is proposed a finite element model to represent the behaviour of reinforced concrete for short and long-term loads, which includes the main features observed in this material. It was developed a model for the generation of multidimensional non-Gaussian stochastic fields for the material properties that is independent of the finite element mesh. First, an example of a two-dimensional non-Gaussian stochastic field generation in a square steel plate is presented. Latter, the reliability analysis is performed to a limit state function based on prescribed values of mid-span displacements on a simply-supported reinforced beam. Finally, the influence of long-term effects on the reliability of a reinforced concrete beam is studied considering the effect of steel reinforcement corrosion.     

A homotopy analysis solution to large deformation of beams under static arbitrary distributed load

In this article, homotopy analysis method (HAM) is employed to investigate non-linear large deformation of Euler–Bernoulli beams subjected to an arbitrary distributed load. Constitutive equations of the problem are obtained. It is assumed that the length of the beam remains constant after applying external loads. Different auxiliary parameters and functions of the HAM and the extra auxiliary parameter, which is applied to initial guess of the solution, are employed to procure better convergence rate of the solution. The results of the solution are obtained for two different examples including constant cross sectional beam subjected to constant distributed load and periodic distributed load. Special base functions, orthogonal polynomials e.g. Chebyshev expansion, are employed as a tool to improve the convergence of the solution. The general solution, presented in this paper, can be used to attain the solution of the beam under arbitrary distributed load and flexural stiffness. Ultimately, it is shown that small deformation theory overestimates different quantities such as bending moment, shear force, etc. for large deflection of the beams in comparison with large deformation theory. Finally, it is concluded that solution of small deformation theory is far from reality for large deflection of straight Euler–Bernoulli beams.     

Anchorage strength models for end-debonding predictions in RC beams strengthened with FRP composites

The increase in the flexural capacity of RC beams obtained by externally bonding FRP composites to their tension side is often limited by the premature and brittle debonding of the external reinforcement. An in-depth understanding of this complex failure mechanism, however, has not yet been achieved. With specific regard to end-debonding failure modes, extensive experimental observations reported in the literature highlight the important distinction, often neglected in strength models proposed by researchers, between the peel-off and rip-off end-debonding types of failure. The peel-off failure is generally characterized by a failure plane located within the first few millimetres of the concrete cover, whilst the rip-off failure penetrates deeper into the concrete cover and propagates along the tensile steel reinforcement. A new rip-off strength model is described in this paper. The model proposed is based on the Chen and Teng peel-off model and relies upon additional theoretical considerations. The influence of the amount of the internal tensile steel reinforcement and the effective anchorage length of FRP are considered and discussed. The validity of the new model is analyzed further through comparisons with test results, findings of a numerical investigation, and a parametric study. The new rip-off strength model is assessed against a database comprising results from 62 beams tested by various researchers and is shown to yield less conservative results. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 373–388, May–June, 2008.     

Experimetal study on the FRP-concrete bond behavior under repeated loadings

In this study, the effects of repeated loads on the FRP-concrete bond strength were investigated experimentally by direct pull out tests according to CSA S806-02. A conventional reinforcing steel bar and two types of glass-fiber-reinforced plastic (GFRP) bars were embedded in concrete and tested under four different loading patterns. The bond strength–slip curves of the bars were obtained and analyzed. The results showed that the maximum bond strengths under the repeated loads differed from those obtained under monotonic ones. In addition, noticeable differences in degradation of the bond strength with respect to the magnitude of slip were observed between the different bar types tested. On the basis of an image analysis of failure surfaces, they were attributed to the different bond failure mechanisms associated with the steel and GFRP bars.     

Moment redistribution in continuous reinforced concrete beams strengthened with carbon-fiber-reinforced polymer laminates

The results of tests on continuous steel-fiber-reinforced concrete (RC) beams, with and without an external strengthening, are presented. The internal flexural steel reinforcement was designed so that to allow steel yielding before the collapse of the beams. To prevent the shear failure, steel stirrups were used. The tests also included two nonstrengthened control beams; the other specimens were strengthened with different configurations of externally bonded carbon-fiber-reinforced polymer (CFRP) laminates. In order to prevent the premature failure from delamination of the CFRP strengthening, a wrapping was also applied. The experimental results obtained show that it is possible to achieve a sufficient degree of moment redistribution if the strengthening configuration is chosen properly, confirming the results provided by two simple numerical models. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 667–686, September–October, 2007.     

计算主梁绝对最大挠度的数学模型与0.618法

纵横梁桥面系统中主梁的跨度较长,纵梁上直接承受的车队荷载数量多且数值大,主梁设计中绝对最大挠度的确定是关键内容.研究了一组平行车队荷载直接沿着纵梁移动时,主梁承受结点活载下绝对最大挠度数学模型的建立;并给出了相应的计算方法,以计算机为工具,适用于任意有限多个平行移动荷载作用工况,对于主梁的设计计算与安全评估,有一定的实用价值.     

Free vibration analysis of cracked composite beams subjected to coupled bending–torsion loads based on a first order shear deformation theory

In this paper, free vibration analysis of cracked composite beam subjected to coupled bending–torsion loading is presented. The composite beam is assumed to have an open edge crack of length a. A first order shear deformation theory is applied to count for the effect of shear deformations on natural frequencies as well as the effect of coupling in torsion and bending modes of vibration. Governing equations and boundary conditions are derived using Hamilton principle. Local flexibility matrix is used to obtain the additional boundary conditions of the beam in cracked area. After obtaining the governing equations and boundary conditions, generalized differential quadrature (GDQ) method is applied to solve the obtained eigenvalue problem. Finally, some numerical results of beams with various boundary conditions and different fiber orientations are given to show the efficiency of the method. In addition, to study the effect of shear deformations, numerical results of the current model are compared with previously given results in which shear deformations were neglected.