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2021 Vol. 42, No. 6
Published: 2021-12-28
623
A new radial basis function differential quadrature method with fictitious points and its application in thin plate bending
In this paper, the radial basis function differential quadrature method with fictitious points (FRBF-DQ) is proposed and applied to simulate thin plate bending problems. The FRBF-DQ method is a new meshless method based on the traditional radial basis function differential quadrature method. While the traditional radial basis function differential quadrature method (RBF-DQ) method places the centers exclusively inside the solution domain, the proposed method expands the region for the centers allowing them to place both inside and outside the computational domain. The FRBF-DQ method applies radial basis functions and weight coefficients to solve differential equations approximately. Meanwhile, the solution accuracy has been significantly improved without the increasing of calculation cost and storage. The thin plate bending problems are controlled by the fourth order partial differential equation based on the Kirchhoff and the Winkler hypothesis. The examples reveal that the FRBF-DQ method works even for arbitrary distributed nodes with better computational convergence and higher computational accuracy than the traditional RBF-DQ method. The proposed method can be considered as a good alternative method for engineering problems.
2021 Vol. 42 (6): 623-632 [
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633
Optimization of band-gap characteristics of hierarchical periodic beam
In order to improve the vibration reduction performance of hierarchical periodic beam, the vibration band-gap characteristics are optimized. The spectral element method (SEM) is used to calculate the frequency response curves of the periodic beam, the dispersion relation curves of the structure is calculated by the transfer matrix method and the two methods are combined to study the vibration band-gap characteristics of the structure. The band-gap ratio function is constructed as the optimization objective function, and the sizes of the unit-cell are used as the optimization parameters to optimize the band-gap characteristics. After optimization, the band-gap characteristics in the considered frequency ranges are greatly improved. Compared with the finite element method (FEM) and vibration experiment, the correctness of the calculation results of the SEM is verified. The research content provides a useful reference for improving the vibration band-gap characteristics of periodic structures and the application of vibration reduction.
2021 Vol. 42 (6): 633-641 [
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642
Study on thermal deformation and astuteness of conductive concrete sensors
Abstract Sensors are widely used in the field of concrete structure health detection. Compared with traditional sensors, cement-based sensors have better compatibility with concrete. However, Addition of conductive dope will change its characteristics. Therefore, it is necessary to study the sensitivity of cement-based sensors in concrete. In this paper, cement-based sensors with different sensitivity are designed. The thermal deformation characteristics and the law of astuteness of the sensor are tested. The feasibility of the sensor being embedded in concrete for structural deformation detection is verified. It is found by experiment that the conductive concrete, which contains carbon nanotubes, possesses thermal expansion - thermal contraction characteristics. Therefore, there is a thermal expansion - thermal contraction transition temperature. When the environment temperature is less than such a transition temperature, the material will undergo expansion with the temperature. However, if the environment temperature is greater than the transition temperature, the material shrinks with the temperature. The experiment proves the transition temperature linearly decreases with content of carbon nanotube. The experiment also indicates that the piezoresistive effect of carbon nanotube could be affected by the concrete dry shrink stress if sensors are embedded in concrete samples. The nucleation and growth of micro-damage lead to an increase in the spacing of conductive fillers, and this could cause an increase in the resistivity of the sensor. Therefore, there is a competition mechanism, namely, compressive load leads to decrease of resistivity of sensors, while damage evolution causes the increase of the resistivity. The piezoresistive effect of sensors has non-linear characteristics due to such a competition mechanism. Based on the experimental results and the tunnel effect theory of electronic leap, the piezoresistive model of cement-based sensor is established. It is believed that the experimental results and theoretical model obtained in this paper have guiding significance for the design of cement-based sensors.
2021 Vol. 42 (6): 642-655 [
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656
Study on failure mechanism of hierarchical corrugated structure with a second order core under local failure defects
Based on the elastic beam theory, the failure mechanism of hierarchical corrugated structure with a second order core under local failure defects was studied. Firstly, through the force analysis of the original structural system of the hierarchical corrugated structure with a second order core and the structural system under local failure defects, six failure mechanisms of the structure are obtained, and the corresponding nominal force expressions of each failure mechanism are given.?Then the failure mechanism diagram was drawn according to the dominant relationship between the failure mechanism. The influence of parameter l1/l、θ and α on the failure mechanism diagram was discussed. at the same time, taking the corresponding nominal force of each failure mechanism as the constraint condition and minimizing the amount of structural materials (relative density) as the optimization objective, the structure lightweight optimization formula is given according to the optimization design of specific failure sequences.?Finally, some numerical simulations and experiments are given to verify the correctness of the failure prediction of the corrugated hierarchical structure with a second order core after local failure and the feasibility of the design of the hierarchical failure sequence. It is found that the change of different parameters will lead to different failure modes of the structure, and the occurrence of the failure mode on the secondary transfer path member of the hierarchical corrugated structure can not necessarily be used as the failure criterion of the structure. only when the structural failure mode appears on the main transfer path member, the failure mode can be used as the failure criterion of the structure, and the hierarchical corrugated structure can be used as the failure criterion of the structure according to the loss caused by the occurrence of each failure mode. It can be obtained that the relatively benign failure transfer path sequence of the structure is as follows: the first secondary transfer path component failure, and then the main transfer path component failure. The results of this paper can accurately grasp the change law of hierarchical corrugated structure system and the structural failure mechanism under local failure defects, and provide theoretical value for engineering application.
2021 Vol. 42 (6): 656-670 [
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671
PHASE FIELD SIMULATION ON THE GRAIN ORIENTATION DEPENDENT SUPER-ELASTICITY OF NANOCRYSTALLINE NITI SHAPE MEMORY ALLOYS
In the super-elastic deformation process of nano-polycrystalline NiTi shape memory alloys (SMAs), different grain orientations can lead to a complex stress field in the polycrystalline system, which may affect the martensitic transformation and the super-elasticity capability of such alloys. Therefore, in this work, based on the Ginzburg-Landau’s theory, a two-dimensional phase field model was proposed to investigate the grain-orientation dependent super-elasticity of nano-polycrystalline NiTi SMAs. The super-elastic deformation processes of four nano-polycrystalline NiTi SMA systems with different distributions of grain orientations were simulated by utilizing the proposed phase field model. From the simulated microstructure evolution and stress-strain responses of the polycrystalline systems, the microscopic mechanism of the dependence of super-elasticity on the grain orientation was discussed and revealed. It is illustrated that the super-elasticity of nano-polycrystalline NiTi SMAs strongly depends on the grain orientation: Within the range of parameters considered, the wider the distribution range of grain orientation is (i.e., no obvious texture), the lower the super-elastic capability is; the narrower the distribution range of grain orientation is (i.e., with obvious texture), the higher the super-elastic capability is. Such a phenomenon can be explained as follows: the mismatched deformation between adjacent grains occurred during the martensitic transformation varies if the grain orientations are different, that is, within the range of parameters considered, the larger the orientation difference between adjacent grains, the more serious the mismatched deformation at the grain boundary is; further, the local internal stress caused by such a mismatched deformation can hinder the expansion of martensite transformation, and then the super-elastic capability of nano-polycrystalline NiTi SMAs decreases. The microscopic mechanism of the grain-orientation-dependent super-elasticity of nano-polycrystalline NiTi SMAs revealed in this work can provide a valuable reference for designing the NiTi SMA devices with different super-elastic capabilities by adjusting the texture to a prescribed degree in the polycrystalline systems in terms of some specific methods such as electroplating, rolling, annealing, cold working, etc.
2021 Vol. 42 (6): 671-681 [
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682
Theoretical model and experimental analysis of normal dynamic contact stiffness and damping of solid-liquid mechanical joint
The solid-liquid contact state widely exists in the contact kinematic pairs of the key parts of the machine tool core unit. To acquisition of normal contact stiffness and damping parameters of solid-liquid interface is a key theoretical and technical problem in the research and development stage of high-end CNC machine tools, and it is still not fundamentally solved. The interface is the contact between two rough surfaces at the mesoscopic level, while it is the contact between asperities and at the micro level. Asperities of rough surfaces may produce elastic/elastic-plastic/plastic deformation under the medium/heavy loads. In order to reveal the influence of static and dynamic external load on the contact stiffness and damping of solid-liquid interface, the elastic/elasto-plastic/plastic deformation of contact asperity is studied based on the GW model, the KKE model and the AF model, respectively. And then, the contact stiffness and damping models of solid-liquid interface considering elastic/elasto-plastic/plastic deformation of contact asperity are established by combining with the Reynolds equation of hydrodynamic lubrication. Finally, it is verified by experiments. It is found that: the normal dynamic contact stiffness of solid-liquid mechanical joints decreases quickly and then increases with the increase of preload. The dynamic contact stiffness is smaller than the static contact stiffness when the contact load is over a certain threshold value. The normal dynamic contact stiffness increases with the increase of the amplitude of normal relative displacement. The normal dynamic contact stiffness increases linearly with the increase of excitation frequency. The normal contact damping increases nonlinearly with the increase of normal relative displacement amplitude and the contact load, but it’s almost unchanged with the increase of excitation frequency. There is great theoretical significance for the analysis, design, optimization and static and dynamic performance control of mechanical system to accurately obtain the normal contact stiffness and damping of solid-liquid mechanical joint and the key influencing factors.
2021 Vol. 42 (6): 682-696 [
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169
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697
NEURAL NETWORK METHOD FOR THIN PLATE BENDING PROBLEM
Recently, deep learning has made good progress in various disciplines. In order to develop the application of deep learning technology in solid mechanics, a neural network method with fully connected layers is proposed to solve the Kirchhoff thin plate bending problems which is governed by the fourth-order partial differential equation (PDE). Firstly, the training points from domain and boundary are randomly generated and feed into the forward propagation system of neural network to obtain the prediction solution. Then the errors are calculated by the loss function proposed in this paper. The parameters inside neural network are then optimized by the back propagation system. Finally, the neural network is trained continuously to make the errors converge, and the deflection solution of thin plate bending is then obtained. Taking triangle, ellipse and rectangular thin plates with different boundary and load conditions as examples, the partial differential equation is solved by the method proposed, and the results are compared with the theoretical solution or finite element method solution. In the end, the factors affecting the convergence of the neural network method are studied. It is found that the method is capable of solving the fourth order partial differential equations of thin plate bending problems. The convergence of this method is affected by the boundary conditions, optimization algorithms, numbers of hidden layers and neurons, and the chosen of learning rate. Compared to finite element method, the neural network method faces the problem of slow convergence speed. However, it is not based on the variational principle. It can obtain high accuracy without the calculation of stiffness matrix. The solution domain is discretized by the randomly generated points. The neural network method is flexible and can also be treated as meshless method. It can provide new ideas in the research of large deformation and nonlinear problems in the future.
2021 Vol. 42 (6): 697-706 [
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707
Research on On-line Monitoring Method of Sintered Nd-Fe-B Fatigue Damage in Geomagnetic Field
Sintered Nd-Fe-B which is a typical hard magnetic material, crises characterized by unexpectedness, uncertainty, and urgency during fatigue cracking. Therefore, it is difficult to monitor its fatigue damage propagation process online. In order to realize the online monitoring the whole process of fatigue damage expansion for sintered Nd-Fe-b during its long-time service, the fatigue state evolution equation of sintered Nd-Fe-B under the geomagnetic field environment is constructed by utilizing coupling effects of stress and magnetic. The magnetic induction value is used as the state parameter to describe the fatigue damage. The magnetic induction intensity of the weak magnetic which is collected by high precision magnetic sensor is used to monitor the fatigue damage prop-agation process online. The fatigue test results show that: it can accurately predict the point of fracture in time during fatigue damage propagation process for sintered Nd-Fe-B by the trends of the magnetic induction intensity value and the residual value of the polynomial fitting curve. Meanwhile, the variation of magnetic induction signal curve reflects the whole process of Nd-Fe-B fatigue damage propagation under stress without distortion.
2021 Vol. 42 (6): 707-717 [
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718
INITIAL YIELD LIMITS OF PARTICLE-REINFORCED COMPOSITES
A yield criterion of the particle-reinforced composites is developed based on the asymptotic homogenization method. According to the yield criterion, the initial yield stresses are predicted in analytical forms. Because the elastic modulus of the particle reinforcement is much higher than that of the elastic-plastic matrix, the difference of the elastic modulus results in an assembly stiffness in the reinforcement and the matrix. The assembly stiffness can be obtained by solving a local problem. It can be seen from the expressions of the yield stress that the increase of yield stress of the composites is determined by the ratio of the average assembly stiffness and shear modulus of the reinforcement and matrix. Two numerical examples are given. A rhombic dodecahedron cell is used to solve the local problem. The advantages of using rhombic dodecahedron as a cell are that the volume ratio of reinforcement can be as high as 74%.
2021 Vol. 42 (6): 718-724 [
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725
A theoretical study on the ductile-brittle transition of hexagonal boron nitride
In this paper, by establishing a stick-spiral model of chirality-dependent hexagonal boron nitride (h-BN) which based on the Tersoff potential function between hexagonal boron nitride atoms, the nonlinear mechanical behavior of chirality-dependent h-BN under large deformation have been investigated. The findings indicate that the fracture modes of h-BN range from ductile fracture to brittle fracture when the chiral angle changes from armchair (AC, chiral angle is 0o) to zigzag (ZZ, chiral angle is 30o). That the change of bond angles plays a more important role in the stretching process than that of bond lengths is the main reason of the occurrence of ductile fracture, through the analysis of the change of bond lengths and bond angles in the stretching process. By analysing the distribution of maximum stress and fracture stress of h-BN with chiral angle, the chiral angle of brittle-ductile transition is around 15°. The change of bond length dominates the fracture mode of graphene in the stretching process, while the change of both bond length and bond angle dominate the fracture mode of h-BN, by comparison the h-BN and graphene under the same conditions. Finally, checking against the molecular dynamics simulations shows that the theoretical results are reasonable. This study provides theoretical support for understanding the excellent mechanical properties of h-BN and its application in the field of micro-nano devices.
2021 Vol. 42 (6): 725-735 [
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736
Research on the Numerical Design Method of Asphalt Concrete Gradation Curve and Its Influence on Effective Elastic Modulus
The prediction and assessment of the effective property of asphalt concrete is a key issue in its application in road engineering and dam seepage prevention. This paper uses meso-random modeling technology and finite element method to study the effect of gradation curve on the effective elastic modulus of asphalt concrete. First of all, based on the improved Monte Carlo method, the efficient generation of an asphalt concrete meso-random model that obeys the experimental sieve grading curve or the given function grading curve is realized. Then, the established model was used to analyze the influence of aggregate content, elastic modulus and sample size on the effective elastic modulus of asphalt concrete, and compared with the experimental results to verify the reliability of the built model. Therefore, the degree of unevenness of the gradation curve in the AC-13 gradation range, that is, the influence of the composition ratio of coarse and fine aggregates on the effective elastic modulus of asphalt concrete, is predicted. The calculation results show that the concavity and convexity of the gradation curve has a big difference in the effect of its effective elastic modulus; the depression of the gradation curve (increasing the proportion of coarse aggregate) results in the rapid increase of the effective elastic modulus, and the convexity of the gradation curve (increasing the proportion of fine aggregate) also incurs the small rise of the effective elastic modulus. In addition, the proposed random modeling method can realize the customized design of the gradation curve, that is, the composition ratio of coarse and fine aggregates.
2021 Vol. 42 (6): 736-745 [
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128
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